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Home Question Bank Math Algebra Archive 2025 January 21

Algebra Questions from Jan 21,2025

Browse the Algebra Q&A Archive for Jan 21,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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C) Write a system of linear equations that has the solution (4, 3). 56. What are the solutions to the polynomial: \( p(x)=(x-5)(3 x+5)\left(x^{2}-7 x+15\right) \) B) Check whether \( (6,9) \) is a solution of the systems of linear equations. \begin{tabular}{ll} 5) \( s+7 t=69 \) & 6) \( \begin{array}{l}-2 p+5 q=34 \\ -7 q=-61-8 p \\ 6 t+4 s=73\end{array} \) \\ \hline\end{tabular} \begin{tabular}{l} Check whether \( (6,9) \) is a solution of the systems of linear equations. \\ \( \begin{array}{l}s+7 t=69 \\ \begin{array}{l}-2 p+5 q=34 \\ 6 t+4 s=78\end{array} \\ -7 q=-61-8 p\end{array} \) \\ \hline\end{tabular} 20. Solve using substitution. \( \begin{array}{r}-8 x+7 y=-4 \\ \\ x+y=-7\end{array} \) Consider the line \( -x-8 y=8 \). Find the equation of the line that is parallel to this line and passes through the point \( (3,-3) \). Find the equation of the line that is perpendicular to this line and passes through the point \( (3,-3) \). Equation of parallel line: Equation of perpendicular line: \( y=8 x-27 \) Benny the carhop has 2 times as many dimes as quarters. If Benny has \( \$ 41.85 \) worth of dimes and quarters combined, how many quarters does 10. Reducir la siguiente fracción algebraica. \( \left[\frac{a^{2}+b^{2}}{2 a b}+1\right]\left[\frac{a-b}{a+b}+\frac{a+b}{a-b}\right]\left[\frac{a b(a-b)}{a^{2}+b^{2}}\right] \) Solve this equation by using the quadratic formula \( x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} \), and select the choice that contains all of the solutions. \[ 2 x^{2}+5 x-5=0 \] Write a system of linear equations that has the solution \( (4,3) \).
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