/ algebra 1 Fie functia f(x)=ax2+bx+c , unde a=#a, b=#b şi c=#c. 

Dacă ecuaţia f(x)=0 are soluţii reale să se scrie valoarea  expresiei 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»E«/mi»«mo»=«/mo»«mfrac»«mrow»«msup»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mn»2«/mn»«/msup»«mo»+«/mo»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»+«/mo»«mn»2«/mn»«/mrow»«mrow»«msup»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mn»2«/mn»«/msup»«mo»+«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»+«/mo»«mn»2«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 delta=#d]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>m</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>m</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>&nbsp;</mo><mo>&gt;</mo><mn>0</mn><mo>)</mo></mrow><mrow><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>t</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi><mspace linebreak="newline"/></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> algebra 1 Fie funcţiile«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»f«/mi»«mo»,«/mo»«mi mathvariant=¨normal¨»g«/mi»«mo»:«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#8594;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»f«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»m«/mi»«/mrow»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»n«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨normal¨»g«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«mo»#«/mo»«mi mathvariant=¨normal¨»n«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»m«/mi»«/mrow»«msqrt»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«msup»«mi mathvariant=¨normal¨»n«/mi»«mn»2«/mn»«/msup»«/msqrt»«/mfrac»«/math»

Asociaţi răspunsul corect cerinţelor de mai jos.

]]> 1.0000000 0.3333333 0 true Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> (f o f)(x)

]]> #compusa1 (g o g)(x)

]]> #compusa2 (f o g)(x)

]]> #compusa3 (g o f)(x)

]]> #compusa4 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>b</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>m</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>n</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>m</mi></mrow><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>n</mi><mn>2</mn></msup></mrow></msqrt></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>compusa1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>compusa2</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>compusa3</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>compusa4</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> analiza 1 Se consideră funcţia «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»b«/mi»«mo»)«/mo»«/mrow»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfrac»«/math».

Să se aleagă varianta corectă pentru derivata lui f.

]]> 1.0000000 0.3333333 0 true true abc Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> #d

]]> #d1

]]> #d2

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>m</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></mrow><mrow><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><msup><mo>)</mo><mn>2</mn></msup></mrow></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> analiza 1 Fie funcţiile :

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»f«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«msqrt»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»n«/mi»«/msqrt»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»p«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨normal¨»g«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»m«/mi»«mo»)«/mo»«/mrow»«msqrt»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»n«/mi»«/msqrt»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨normal¨»h«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»p«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»n«/mi»«mo»§#160;«/mo»«/mrow»«msqrt»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»r«/mi»«/msqrt»«/mfrac»«/math»

Să se selecteze răspunsul corespunzător:

Derivata lui f: {#1}

Derivata lui g: {#2}

Derivata lui h: {#3}

]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>b</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>b</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msup><mi>m</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi></mrow></msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>p</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>m</mi></mrow><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi></mrow></msqrt></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>p</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n</mi></mrow><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>r</mi></mrow></msqrt></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D2</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D3</mi><mo>=</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> analiza 1 Graficul funcţiei  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»f«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«/math» admite asimptota oblică de forma y=#y.

]]> 1.0000000 1.0000000 0 Adevărat Fals <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>m</mi><mo>≠</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>m</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>m</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>±∞</cn></mrow></munder><mfrac><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>x</mi></mfrac></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>±∞</cn></mrow></munder><mfenced><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>-</mo><mi>b</mi><mo>*</mo><mi>x</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> analiza 1 Derivata funcţiei «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»f«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»m«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»n«/mi»«mo»)«/mo»«/mrow»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»m«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»n«/mi»«mo»)«/mo»«/mrow»«/mfrac»«/math» este: 

 

]]> 1.0000000 0.3333333 0 0 Derivata lui f=#Derivata]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>b</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><msup><mi>m</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mi>n</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>Derivata</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>a</mi><mo>&#160;</mo><mi>l</mi><mi>u</mi><mi mathvariant="normal">i</mi><mo>&#160;</mo><mi>f</mi><mo>=</mo><mo>#</mo><mi>D</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>v</mi><mi>a</mi><mi>t</mi><mi>a</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer><correctAnswer id="3"></correctAnswer><correctAnswer id="4"></correctAnswer><correctAnswer id="5"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_rational_function_form"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> analiza 1 Fie funcţiile «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»f«/mi»«mo»,«/mo»«mi mathvariant=¨normal¨»g«/mi»«mo»:«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#8594;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math»:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»f«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»m«/mi»«/mrow»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»n«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨normal¨»g«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mrow»«mo»#«/mo»«mi mathvariant=¨normal¨»m«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»n«/mi»«/mrow»«msqrt»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»n«/mi»«/msqrt»«/mfrac»«/math»

Asociaţi răspunsul corect cerinţelor de mai jos.

]]> 1.0000000 0.3333333 0 true Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> Derivata lui f

]]> #derivata1 Derivata lui g

]]> #derivata2 O primitiva lui f

]]> #primitiva1 O primitiva lui g

]]> #primitiva2 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>b</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>m</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n</mi></mrow><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi></mrow></msqrt></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>derivata1</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>derivata2</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>&apos;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>primitiva1</mi><mo>=</mo><mo>∫</mo><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>primitiva2</mi><mo>=</mo><mo>∫</mo><mrow><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> bisectoare 1 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C. 

Determinati unghiurile triunghiului.

]]> 1.0000000 1.0000000 0 true Unghiul A (exprimat în grade):

]]> #unghiulA Unghiul B (exprimat în grade):

]]> #unghiulB Unghiul C (exprimat în grade):

]]> #unghiulC <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800">library</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>&nbsp;</mo><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>triangle</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>unghiulA</mi><mo>=</mo><mi>angle</mi><mo>(</mo><mi>T</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>unghiulB</mi><mo>=</mo><mi>angle</mi><mo>(</mo><mi>T</mi><mo>,</mo><mn>2</mn><mo>)</mo><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>unghiulC</mi><mo>=</mo><mi>angle</mi><mo>(</mo><mi>T</mi><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> bisectoare 2 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C. 

Determinati cosinusurile unghiurilor triunghiului.

]]> 1.0000000 1.0000000 0 true cos A:

]]> #cos1 cos B:

]]> #cos2 cos C:

]]> #cos3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800">library</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>&nbsp;</mo><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>triangle</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos1</mi><mo>=</mo><mi>cos</mi><mo>(</mo><mi>angle</mi><mo>(</mo><mi>T</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos2</mi><mo>=</mo><mi>cos</mi><mo>(</mo><mi>angle</mi><mo>(</mo><mi>T</mi><mo>,</mo><mn>2</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos3</mi><mo>=</mo><mi>cos</mi><mo>(</mo><mi>angle</mi><mo>(</mo><mi>T</mi><mo>,</mo><mn>3</mn><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> bisectoare 3 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C şi notăm cu I intersecţia bisectoarelor triunghiului (centrul cercului înscris în triunghi).

Să se scrie ecuaţia bisectoarei AI {#1}, ecuaţia bisectoarei BI {#2} şi ecuaţia bisectoarei CI{#3}

]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800">library</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>triangle</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mi>incenter</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>I</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>I</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>I</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> bisectoare 4 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C. Notăm cu A1 piciorul bisectoarei din A, cu B1 piciorul bisectoarei din B şi cu C1 piciorul bisectoarei din C. Precizaţi coordonatele punctelor A1, B1 şi C1.

]]> 1.0000000 1.0000000 0 true Coordonatele lui A1:

]]> #A1 Coordonatele lui B1:

]]> #B1 Coordonatele lui C1:

]]> #C1 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>&nbsp;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>bisector</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>bisector</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>bisector</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi><mo>=</mo><mi>intersect</mi><mo>(</mo><mi>d1</mi><mo>,</mo><mi>l1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi><mo>=</mo><mi>intersect</mi><mo>(</mo><mi>d2</mi><mo>,</mo><mi>l2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C1</mi><mo>=</mo><mi>intersect</mi><mo>(</mo><mi>d3</mi><mo>,</mo><mi>l3</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> bisectoare 5 Fie triunghiul RST cu vârfurile R#R, S#S şi T#T. Notăm cu I intersecţia bisectoarelor, centrul cercului înscris în triunghi. Precizaţi care sunt coordonatele lui I.

]]> 1.0000000 1.0000000 0 true true abc #I

]]> Răspuns corect!

]]> #N

]]> Răspuns greşit!

]]> #P

]]> Răspuns greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>&nbsp;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mi>incenter</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>T</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> determinant 1 Fie matricele A=#A, B=#B şi C=#C. 

Să se selecteze răspunsul corespunzător cerinţei:

det (A): {#1}

det (B): {#2}

det (C): {#3}

]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mfenced close="|" open="|"><mi>A</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mfenced close="|" open="|"><mi>B</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mfenced close="|" open="|"><mi>C</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> Distante Asociaţi perechilor de puncte de mai jos distanţele corespunzătoare.

]]> 1.0000000 1.0000000 0 true Fie A#A și B#B. Distanța dintre A și B este:

]]> #d1 Fie C#C și D#D. Distanța dintre C și D este: 

]]> #d2 Fie M#M și N#N. Distanța dintre M și N este:

]]> #d3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Distante 1 Fie punctele A#A, B#B şi C#C.

Asociaţi distanţele AB, BC şi AC cu valorile afisate.

]]> 1.0000000 1.0000000 0 true Foarte bine!

]]> Mai încercaţi!

]]> Distanţa AB este:

]]> #d1 Distanţa BC este:

]]> #d2 Distanţa AC este:

]]> #d3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>distance</mi><mo>&nbsp;</mo><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Distanţe 2 Fie triunghiul ABC cu vârfurile A#A, B#B și C#C. Se notează cu M mijlocul lui BC, cu N mijlocul lui AC și cu P mijlocul lui AB. Alegeți varianta corectă pentru perimetrul triunghiului MNP.

]]> 1.0000000 1.0000000 0 true true abc Perimetrul este #per

]]> Răspuns corect!

]]> Perimetrul este #p1

]]> Răspuns greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>triangle</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>,</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>per</mi><mo>=</mo><mi>perimeter</mi><mo>(</mo><mi>T2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>per</mi><mo>/</mo><mn>3</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> distante 3 Fie punctele A#A, B#B și C#C. Se notează cu M mijlocul segmentului BC. 

Alegeți varianta corectă pentru distanța AM.

]]> 1.0000000 1.0000000 0 true true abc AM=#d

]]> Răspuns corect!

]]> AM=#d1

]]> Răspuns greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> Distante 4 Fie punctele A#A, B#B, C#C, M#M, N#N, P#P, R#R, S#S şi T#T

Asociaţi triunghiurilor ABC, MNP şi  şi RST perimetrele corespunzătoare.

]]> 1.0000000 1.0000000 0 true Foarte bine!

]]> Mai încercaţi!

]]> Perimetrul triunghiului ABC este:

]]> #p1 Perimetrul triunghiului MNP este:

]]> #p2 Perimetrul triunghiului RST este:

]]> #p3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>triangle</mi><mo>&nbsp;</mo><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>triangle</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>,</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T3</mi><mo>=</mo><mi>triangle</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>T</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>perimeter</mi><mo>(</mo><mi>T1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>perimeter</mi><mo>(</mo><mi>T2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>perimeter</mi><mo>(</mo><mi>T3</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> distante 5 Fie punctele A#A, B#B și C#C. Se notează cu M mijlocul segmentului BC şi cu N mijlocul lui AM.  

Alegeți varianta corectă pentru distanța AN.

]]> 1.0000000 1.0000000 0 true true abc AN=#d

]]> Răspuns corect!

]]> AN=#d1

]]> Răspuns greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>*</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> distante 6 Fie punctele A#A, B#B, C#C şi D#D. Atunci distanţele AB şi CD sunt egale.

]]> 1.0000000 1.0000000 0 Adevărat Fals <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mn>3</mn><mo>*</mo><mi>x1</mi><mo>,</mo><mn>3</mn><mo>*</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>x1</mi><mo>,</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>*</mo><mi>x1</mi><mo>,</mo><mo>&nbsp;</mo><mo>-</mo><mn>4</mn><mo>*</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> distante 7 Punctele A#A, B#B și C#C sunt coliniare.

]]> 1.0000000 1.0000000 0 Adevărat Raspuns corect!

]]> Fals Răspuns greșit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800">library</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mn>2</mn><mo>*</mo><mi>x1</mi><mo>,</mo><mn>2</mn><mo>*</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mn>4</mn><mo>*</mo><mi>x1</mi><mo>,</mo><mn>4</mn><mo>*</mo><mi>x2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> drepte 20 Pentru punctele A#A şi B#B scrieţi coordonatele mijlocului segementului AB {#1}, distanţa AB {#2} şi ecuaţia dreptei AB {#3}.

]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>*</mo><mi>distance</mi><mo>&nbsp;</mo><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>distance</mi><mo>&nbsp;</mo><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> drepte 21 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C şi notăm cu M mijlocul lui BC, cu N mijlocul lui AC şi cu P mijlocul lui AB.

Scrieţi coordonatele centrului de greutate G {#1}, ecuaţia medianei  AM {#2} , ecuaţia linie mijlocii NP {#3} şi ecuaţia dreptei PG {#4}

]]> 4.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>barycenter</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>P</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>P</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> drepte 22 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C şi notăm cu M mijlocul lui BC, cu N mijlocul lui AC şi cu P mijlocul lui AB.

Scrieţi ecuaţia liniei mijlocii  MN {#1}, ecuaţia dreptei BC {#2} şi ecuaţia dreptei AG {#3}, unde G este centrul de greutate al triunghiului.

]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>barycenter</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> drepte 23 Fie punctele A#A, B#B, C#C şi D#D.

Să se precizeze coordonatele mijlocelor segmentelor de mai jos:

mijlocul lui AB {#1}

mijlocul lui AC {#2}

mijlocul lui AD  {#3}

mijlocul lui BC {#4}

mijlocul lui CD  {#5}

]]> 5.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ecuatii drepte 1 Fie punctele R#R şi S#S. Ecuaţia dreptei RS este #l.

]]> 1.0000000 1.0000000 0 Adevărat Corect!

]]> Fals Răspuns greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ecuatii drepte 2 Fie punctele D#D, K#K, T#T şi fie M mijlocul lui DK. Ecuaţia dreptei MT este #l.

]]> 1.0000000 1.0000000 0 Adevărat Corect!

]]> Fals Răspuns greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>D</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ecuatii drepte 5 Fie punctele A#A, B#B, M#M şi N#N. Dacă C mijlocul lui AB şi P mijlocul lui MN. Precizaţi care este ecuaţia dreptei CP.

]]> 1.0000000 1.0000000 0 true true abc #l1

]]> Răspuns corect!

]]> #l2

]]> Greşit!

]]> #l3

]]> Greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> ecuatii drepte 6 Fie punctele A#A, B#B, M#M şi N#N. Dacă C mijlocul lui AM şi P mijlocul lui BN. Precizaţi care este ecuaţi dreptei CP.

]]> 1.0000000 1.0000000 0 true true abc #l1

]]> Răspuns corect!

]]> #l2

]]> Greşit!

]]> #l3

]]> Greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ecuatii drepte3 Se consideră punctele A#A, K#B şi R#C.

Asociaţi dreptelor de mai jos ecuaţiile corespunzătoare. 

]]> 1.0000000 1.0000000 0 true Ecuaţia dreptei AK

]]> #l1 Ecuaţia dreptei KR

]]> #l2 Ecuaţia dreptei AR

]]> #l3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>A</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> ecuatii drepte4 Se consideră punctele A#A, B#B, C#C şi D#D.

Asociaţi dreptelor de mai jos ecuaţiile corespunzătoare. 

]]> 1.0000000 1.0000000 0 true Ecauţia dreptei AB

]]> #l1 Ecuaţia dreptei AC

]]> #l2 Ecuaţia dreptei AD

]]> #l3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> functia de gradul 2 Fie funcţia «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»f«/mi»«mo»:«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#8594;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»f«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»a«/mi»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»b«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»#«/mo»«mi mathvariant=¨normal¨»c«/mi»«/math»

Vârful graficului funcţiei f(x) notat cu V are coordonatele V(#xv, #yv).

]]> 1.0000000 1.0000000 0 Adevărat Corect!

]]> Fals Răspuns greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>m</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>p</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>delta</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xv</mi><mo>=</mo><mo>-</mo><mfrac><mi>b</mi><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yv</mi><mo>=</mo><mo>-</mo><mfrac><mi>delta</mi><mrow><mn>4</mn><mo>*</mo><mi>a</mi></mrow></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> functia de gradul 2 Fie funcţia: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»f«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»a«/mi»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»b«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»#«/mo»«mi mathvariant=¨normal¨»c«/mi»«/math»

Să se aleagă răspunsul corect pentru soluţia inecuaţiei f(x)≥0.

]]> 1.0000000 0.3333333 0 true true abc Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> #s1

]]> #s2

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>m</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>m</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>solve_inequation</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>⩾</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>solve_inequation</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>⩽</mo><mn>0</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> functia de gradul 2 Fie

S1: {#1}

S2: {#2}

S3: {#3}

]]> 3.0000000 0.3333333 0 <question><correctAnswers><correctAnswer></correctAnswer></correctAnswers></question> functia de gradul 2 Fie funcţia:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»f«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»a«/mi»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»b«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»c«/mi»«/math»

Asociaţi cerinţelor de mai jos răspunsul corect:

]]> 1.0000000 0.3333333 0 true Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> Discriminantul delta este:

]]> #delta Rădăcina x1 a ecuaţiei f(x)=0 este:

]]> #x1 Rădăcina x2 a ecuaţiei f(x)=0 este:

]]> #x2 Soluţia inecuaţiei f(x)≥0 este:

]]> #I1 Soluţia inecuaţiei f(x)≤0 este:

]]> #I2 Suma x13+x23 este:

]]> #S1 Suma «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«msup»«mn»1«/mn»«mn»3«/mn»«/msup»«mo»+«/mo»«mi»x«/mi»«msup»«mn»2«/mn»«mn»3«/mn»«/msup»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mi»x«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mi»x«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»este:

]]> #S2 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>m</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>m</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>delta</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><msub><mi>S</mi><mn>2</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I1</mi><mo>=</mo><mi>solve_inequation</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>⩾</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I2</mi><mo>=</mo><mi>solve_inequation</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>⩽</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Suma</mi><mo>=</mo><mo>-</mo><mfrac><mi>b</mi><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Produsul</mi><mo>=</mo><mfrac><mi>c</mi><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><msup><mi>Suma</mi><mn>3</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>Suma</mi><mo>*</mo><mi>Produsul</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S2</mi><mo>=</mo><msup><mi>Suma</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>Suma</mi><mo>*</mo><mi>Produsul</mi><mo>+</mo><mfrac><mi>Suma</mi><mi>Produsul</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> inaltimi 1 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C. Notăm cu D piciorul înălţimii din A, cu E al înălţimii din B şi cu F pe cel al înălţimii din C.

Să se asocieze ecuaţiile corespunzătoare înălţimilor AD, BE şi CF.

]]> 1.0000000 1.0000000 0 true Ecuaţia dreptei AD este

]]> #d1 Ecuaţia dreptei BE este

]]> #d2 Ecuaţia dreptei CF este

]]> #d3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>&nbsp;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>orthocenter</mi><mo>&nbsp;</mo><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>H</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>H</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>H</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> inaltimi 2 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C. Notăm cu H ortocentrul triunghiului. 

Asociaţi distanţelor AH, BH şi CH valorile corespunzătoare.

]]> 1.0000000 1.0000000 0 true Distanţa CH este

]]> #d3 Distanţa AH este

]]> #d1 Distanţa BH este

]]> #d2 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>&nbsp;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>orthocenter</mi><mo>&nbsp;</mo><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>barycenter</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>H</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>H</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>H</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> inaltimi 3 Fie triunghiul RST cu vârfurile R#R, S#S şi T#T. Notăm cu H ortocentrul triunghiului. Precizaţi care sunt coordonatele lui H.

]]> 1.0000000 1.0000000 0 true true abc #H

]]> Răspuns corect!

]]> #N

]]> Răspuns greşit!

]]> #P

]]> Răspuns greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>&nbsp;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>orthocenter</mi><mo>&nbsp;</mo><mo>(</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>T</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> inaltimi 4 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C. Notăm cu D piciorul înălţimii din A, cu E piciorul înălţimii din B şi cu F piciorul înălţimii din C. Precizaţi coordonatele punctelor D, E şi F.

]]> 1.0000000 1.0000000 0 true Coordonatele lui D

]]> #D Coordonatele lui E:

]]> #E Coordonatele lui F:

]]> #F <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>&nbsp;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>height_foot</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mi>height_foot</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>height_foot</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> inaltimi 5 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C şi notăm cu H ortocentrul triunghiului.

Să se scrie ecuaţia înălţimii AH {#1}, ecuaţia înălţimii BH {#2} şi ecuaţia înălţimii CH{#3}

]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800">library</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>orthocenter</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>H</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>H</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>H</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> matrice 1 Fie matricele A=#A şi B=#B.

Să se aleagă matricea răspuns corespunzătoare cerinţei:

A+B: {#1}

A·B: {#2}

2A+3B: {#3}.

]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>A</mi><mo>+</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>A</mi><mo>*</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mn>2</mn><mi>A</mi><mo>+</mo><mn>3</mn><mi>B</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> matrice 2 Fie matricele A=#A, B=#B şi C=#C. 

Să se selecteze matricea răspuns corespunzătoare:

A+B+C: {#1}

A·C: {#2}

2B-3C: {#3}

C2: {#4}

]]> 4.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>+</mo><mi>C</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>A</mi><mo>*</mo><mi>C</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mn>2</mn><mi>B</mi><mo>-</mo><mn>3</mn><mi>C</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><msup><mi>C</mi><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> matrice 3 Fie matricele A=#A, B=#B şi C=#C.

Să se asocieze matricelor M=#d·A+(#f)·B, N=#f·A·B+#d·C şi P=A#e matricele corespunzătoare.

]]> 1.0000000 0.3333333 0 true Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> M:

]]> #S1 N:

]]> #S2 P:

]]> #S3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>m</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>n</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>p</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mi>d</mi><mo>*</mo><mi>A</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S2</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>A</mi><mo>*</mo><mi>B</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>C</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S3</mi><mo>=</mo><msup><mi>A</mi><mi>e</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> mediatoare 1 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C. 

Determinati mijloacele laturilor triunghiului notate cu M pe BC, N pe AC şi P pe AB.

]]> 1.0000000 1.0000000 0 true Mijlocul M al lui BC:

]]> #M Mijlocul N al lui AC:

]]> #N Mijlocul P al lui AB:

]]> #P <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800">library</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> mediatoare 2 Fie triunghiul ABC cu vârfurile A#R, B#S şi C#T. Notăm cu O intersecţia mediatoarelor triunghiului, centrul cercului circumscris triunghiului. Precizaţi care sunt coordonatele lui O.

]]> 1.0000000 1.0000000 0 true true abc #O

]]> Răspuns corect!

]]> #N

]]> Răspuns greşit!

]]> #P

]]> Răspuns greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>&nbsp;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mo>=</mo><mi>circumcenter</mi><mo>&nbsp;</mo><mo>(</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>T</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> mediatoare 3 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C şi notăm cu O intersecţia mediatoarelor triunghiului (centrul cercului circumscris triunghilui).

Să se scrie ecuaţia mediatoarei OM {#1}, ecuaţia mediatoarei ON: {#2} şi ecuaţia mediatoarei OP{#3}, M este mijlocul lui BC, N al lui AC şi P al lui AB.

]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800">library</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>triangle</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mo>=</mo><mi>circumcenter</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>O</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>N</mi><mo>,</mo><mi>O</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>P</mi><mo>,</mo><mi>O</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> mediatoare 4 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C şi notăm cu O centrul cercului circumscris triunghiului.

Să se scrie ecuaţia dreptei AO {#1}, ecuaţia dreptei BO {#2} şi ecuaţia dreptei CO{#3}

]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800">library</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mo>=</mo><mi>circumcenter</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>O</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>O</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>O</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> mediatoare 5 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C. Se notează cu r1 raza cercului înscris în triunghi, R raza cercului circumscris triunghiului, cu I centrul cercului înscris în triunghi şi cu O centrul cercului circumscris triunghiului.

Asociaţi variantele corecte pentru r1, R, I, şi O.

]]> 1.0000000 1.0000000 0 true Raza r1:

]]> #r1 Raza R:

]]> #R Punctul I:

]]> #I Punctul O:

]]> #O <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mi>incenter</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mo>=</mo><mi>circumcenter</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>O</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>triangle</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>area</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow><mrow><mi>l1</mi><mo>+</mo><mi>l2</mi><mo>+</mo><mi>l3</mi></mrow></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> mijloace Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C.

Asociaţi punctelor de mai jos coordonatele corespunzătoare.

]]> 1.0000000 1.0000000 0 true M este mijlocul lui BC

]]> #M N este mijlocul lui AC

]]> #N P este mijlocul lui AB

]]> #P <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> mijloace 5 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C şi fie AM mediana din A. 

Alegeţi ecuaţia corespunzătoare dreptei AM.

]]> 1.0000000 1.0000000 0 true true abc #l

]]> Răspuns corect!

]]> #l1

]]> Mai încearcă!

]]> #l2

]]> Mai încearcă!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>10</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>7</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>7</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>10</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>7</mn><mn>5</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> mijloace 7 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C.

Distanţa AG, unde G este centrul de greutate al triunghiului ABC este #d.

]]> 1.0000000 1.0000000 0 Adevărat Fals <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>barycenter</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> mijloace 8 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C. Fie G centrul de greutate al triunghiului ABC.

Ecuaţia dreptei AG este #l.

]]> 1.0000000 1.0000000 0 Adevărat Ai calculat corect!

]]> Fals Mai încearcă!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800">library</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>barycenter</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> mijloace2 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C. Fie M mijlocul lui BC, N mijlocul lui AC şi P mijlocul lui AB.

Asociaţi segmentelor de mai jos lungimile corespunzătoare

]]> 1.0000000 1.0000000 0 true Segmentul AM are lungimea

]]> #d1 Segmentul BN are lungimea

]]> #d2 Segmentul CP are lungimea

]]> #d3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> mijloace3 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C. Fie M mijlocul lui BC, N mijlocul lui AC şi P mijlocul lui AB.

Asociaţi liniilor mijlocii ale triunghiului ABC lungimile corespunzătoare.

]]> 1.0000000 1.0000000 0 true Lungimea linie mijlocii MN 

]]> #d1 Lungimea linie mijlocii NP

]]> #d2 Lungimea linie mijlocii PM

]]> #d3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>N</mi><mo>,</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>distance</mi><mo>(</mo><mi>P</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> mijloace4 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C şi fie M mijlocul lui BC, N mijlocul lui AC şi P mijlocul lui AB.

Asociaţi ecuaţiile corespunzătoare dreptelor precizate.

]]> 1.0000000 1.0000000 0 true Ecuaţia medianei AM

]]> #l1 Ecuaţia medianei BN

]]> #l2 Ecuaţia medianei CP

]]> #l3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> mijloace6 Fie triunghiul ABC cu vârfurile A#A, B#B şi C#C şi fie M mijlocul lui BC, N mijlocul lui AC şi P mijlocul lui AB.

Asociaţi ecuaţiile corespunzătoare dreptelor precizate.

]]> 1.0000000 1.0000000 0 true Ecuaţia liniei mijlocii NP

]]> #l1 Ecuaţia liniei mijlocii MP

]]> #l2 Ecuaţia liniei mijlocii MN

]]> #l3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>point</mi><mo>(</mo><mi>x1</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>y1</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>midpoint</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>N</mi><mo>,</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>P</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3</mi><mo>=</mo><mi>line</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> rang1 Fie matricele A=#A, B=#B şi C=#C. 

Să se selecteze răspunsul corespunzător cerinţei:

rang (A): {#1}

rang (B): {#2}

rang (C): {#3}

]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>rank</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>rank</mi><mo>(</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>rank</mi><mo>(</mo><mi>C</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> raspuns scurt Fie triunghiul ABC cu unghiul B având 90o. Să se scrie relaţia pentru teorema lui Pitagora în acest triunghi. 

]]> 1.0000000 1.0000000 0 0 AC2=AB2+BC2]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>C</mi><mn>2</mn></msup><mo>=</mo><mi>A</mi><msup><mi>B</mi><mn>2</mn></msup><mo>+</mo><mi>B</mi><msup><mi>C</mi><mn>2</mn></msup></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> transpuse 1 Fie matricele A=#A, B=#B şi C=#C. 

Să se selecteze matricea răspuns corespunzătoare:

AT+BT+C: {#1}

A·CT: {#2}

(B-C+I3)T: {#3}

(B2)T : {#4}

]]> 4.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><msup><mi>A</mi><mo>T</mo></msup><mo>+</mo><msup><mi>B</mi><mo>T</mo></msup><mo>+</mo><mi>C</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>A</mi><mo>*</mo><msup><mi>C</mi><mo>T</mo></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><msup><mfenced><mrow><mi>B</mi><mo>-</mo><mi>C</mi><mo>+</mo><msub><ident definitionURL="http://www.wiris.com/XML/csymbol"/><mn>3</mn></msub></mrow></mfenced><mo>T</mo></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><msup><mfenced><msup><mi>B</mi><mn>2</mn></msup></mfenced><mo>T</mo></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question>