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# Coordinate Algebra Final Exam Study Guide Answer Key

## Questions From Chapters 7 To 9

Algebra 1 Final Exam Giant Review

In problems 13, perform the indicated operations and simplify.

For questions 46, simplify each expression.

For questions 7 and 8, solve by any convenient method.

In problems 9 and 10, find the solution set of each system by any convenient method.

• The length of a rectangle is 5 cm longer than twice the width. If the area of the rectangle is 75 cm2, find its length and width.
• Find three consecutive odd integers such that the product of the first and the second is 25 less than 8 times the third.
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## Questions From Chapters 1 To 3

• \begin \\ \\ \\ \\ \\ \\ â\sqrt \\ \\ -6-\sqrt \\ \\ -6-\sqrt \\ \\ -6-2=-8 \end
• \begin \\ \\ \\ \\ 6x& +& 24& =& 35& -& 5x& -& 8& +& 12x \\ 6x& +& 24& =& 27& +& 7x& & & & \\ -7x& -& 24& & -24& -& 7x& & & & \\ \hline & & -x& =& 3& & & & & & \\ & & \therefore x& =& -3& & & & & & \\ \end
• \phantom\left \\\begin 2& -& 1& =& x& +& 2 \\ 2x& +& 8& -& 2& =& x& +& 2 \\ -x& -& 8& +& 2& & -x& -& 8+2 \\ \hline & & & & x& =& -4& & \end
• x=-2
• \begin \\ \\ \\ \\ \\ \\ d^2& =& \Delta x^2+\Delta y^2 \\ & =& ^2+^2 \\ & =& 6^2+8^2 \\ & =& 36+64 \\ & =& 100 \\ \\ \therefore d& =& \sqrt=10 \end
• 2x-3y=6
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## Coordinate Algebra Final Exam Study Guide Answer Key

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## Questions From Chapters 4 To 6

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• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ & 2x& +& 5y& =& -18 \\ +& -2x& +& y& =& 6 \\ \hline & & & \dfrac& =& \dfrac \\ \\ & & & y& =& -2 \\ \\ & \therefore y& -& 6& =& 2x \\ & -2& -& 6& =& 2x \\ & & & 2x& =& -8 \\ & & & x& =& -4 \endAnswer:
• \begin \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ & \\ & \\ \\ & -16x& -& 14y& =& -102 \\ +& 35x& +& 14y& =& \phantom140 \\ \hline & & & \dfrac& =& \dfrac \\ \\ & & & x& =& 2 \\ \\ \end & \hspace \begin \\ \\ \\ \\ \\ \therefore 5x& +& 2y& =& 20 \\ 5& +& 2y& =& 20 \\ 10& +& 2y& =& 20 \\ -10& & & & -10 \\ \hline & & 2y& =& 10 \\ & & y& =& 5 \end \endAnswer:
• \begin \\ \\ \\ \\ \\ \\ \begin \\ \\ \\ \\ & -2x& -& 2y& -& 12z& =& -10 \\ +& 2x& & & -& 3z& =& \phantom4 \\ \hline & & & \\ & & & \\ \\ & & & -6y& -& 45z& =& -18 \\ & & +& 6y& +& 8z& =& \phantom18 \\ \hline & & & & & -37z& =& 0 \\ & & & & & z& =& 0 \\ \\ \end & \hspace \begin 2x& -& \cancel0& =& 4 \\ & & x& =& \dfrac\text2 \\ \\ 3y& +& \cancel0& =& 9 \\ & & y& =& \dfrac\text3 \end \endAnswer
• \begin \\ \\ 24+\1\}+3x \\ 24-3x-1+3x \\ 23 \end
• 2ab^3\Rightarrow 2a^3b^3-32ab^3
• \begin \\ \\ \\ \\ \\ \\ ^ \\ \\ ^ \\ \\ x^y^7 \\ \\ \dfrac \end
• \begin \\ \\ 3x^2+3x+8x+8 \\ 3x+8 \\ \end
• ^3-y^3\Rightarrow
• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ & \\ & \\ \\ & -370A& -& 370B& =& -18500 \\ +& 395A& +& 370B& =& \phantom19125 \\ \hline & & & 25A& =& 625 \\ \\ & & & A& =& \dfrac\text25 \\ \\ & A& +& B& =& 50 \\ & 25& +& B& =& 50 \\ & & & B& =& 25 \\ \end
• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ & \\ & 10d& +& 25q& =& 235 \\ \\ & -10d& -& 10q& =& -160 \\ +& 10d& +& 25q& =& \phantom235 \\ \hline & & & \dfrac& =& \dfrac \\ \\ & & & q& =& 5 \\ & & & \therefore d& =& 16-5=11 \\ \end
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## Questions From Chapters 7 To 10

• \dfrac3s^2}}1}\cdot \dfrac1\cancel}1\cancel}\cdot \dfrac}2\cancel}\Rightarrow \dfrac
• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \text= \\ \\ \dfrac \\ \\ \dfrac \\ \\ \dfrac \\ \\ \dfrac \end
• \begin \dfrac-9\right)y^3}\right)y^3}\Rightarrow \dfrac\Rightarrow \dfrac\Rightarrow \dfrac}} \\ \\ \Rightarrow y \end
• \begin \\ \\ \\ \\ 3\cdot 5\sqrt-2\sqrt-\sqrt \\ \\ 15\sqrt-2\cdot 6\sqrt-4x\sqrt \\ \\ 15\sqrt-12\sqrt-4x\sqrt \end
• \dfrac}}}}\Rightarrow \dfrac}\cdot \dfrac}}\Rightarrow \dfrac}
• \left^}\Rightarrow \dfrac}}}d^}}\Rightarrow \dfrac}\Rightarrow \dfrac
• \begin \\ =0 \\ x=5,-1 \end
• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ & & & ^2& =& ^2 \\ \\ & x^2& -& 6x& +& 9& =& \phantomx^2 \\ -& x^2& & & & & & -x^2 \\ \hline & & & -6x& +& 9& =& 0 \\ \\ & & & & & \dfrac& =& \dfrac \\ \\ & & & & & x& =& \dfrac \end
• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ A& =& \dfracbh \\ \\ 20& =& \dfrach \\ \\ 40& =& h^2+6h \\ \\ 0& =& h^2+6h-40 \\ 0& =& h^2+10h-4h-40 \\ 0& =& h-4 \\ 0& =& \\ \\ h& =& 4, \cancel \\ b& =& 4+6=10 \end
• \phantomx, x+2, x+4 \\\begin & & & & x& =& \phantom8& +& 6 \\ x^2& +& 2x& & & & & =& \phantom8& +& 6x& +& 24 \\ & -& 6x& -& 8& -& 24& & -8& -& 6x& -& 24 \\ \hline & & x^2& -& 4x& -& 32& =& 0& & & & \\ \\ x^2& +& 4x& -& 8x& -& 32& =& 0& & & & \\ x& -& 8& =& 0& & & & \\ & & & =& 0& & & & \\ & & & & & & x& =& -4,8& & & & \end\phantom