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Home Question Bank Math Algebra Archive 2025 January 12

Algebra Questions from Jan 12,2025

Browse the Algebra Q&A Archive for Jan 12,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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actor completely: \( 2 y^{2}-3 y-9 \) 34. Mr. Joseph shares 500 marbles for his two sons Mike and Paul. He decides to give Mike 50 more than Paul. How many marbles does each boy receive? Answer. \( \qquad \) (1) Answer. \( \qquad \) (1) The equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \) Write down the equation of the new function that is formed when \( f \) is translormed as follows: 3.1 \( \begin{array}{ll}\text { Shifi two units to the left } & \text { Shift } 3 \text { units up } \\ 3.2 & \text { Shift } 1 \text { unit right and } 2 \text { units down } \\ 3.4 & \text { The equation of the new hyperbola has new asymptotes at } x=-4 \text { and } y=-1 \\ \text { asymptote }\end{array} \) Simplify the expression \( \frac{3 x^{3}-4 x^{2}-4 x}{4 x^{2}-13 x+10} \) and give your answer in the form of \( \frac{f(x)}{n(x)} \) Factor the polynomial by grouping: \( 6a^{2}b + 9ab^{2} - 4a - 6b \) The line \( y=a x-3 \) and the hyperbola \( y=\frac{5}{2 x+3} \) intersect at \( x=1 \) and \( x=b \). (a) Determine the \( y \)-coordinate of the point of intersection if \( x=1 \). (b) Determine the value of \( a \). (c) Determine the value of \( b \). \( x=b \). (a) Determine the \( y \)-coordinate of the point of intersection if \( x=1 \). (b) \( \quad \) Determine the value of \( a \). (c) Determine the value of \( b \). If \( x=\sqrt{5}+2, x y=1 \) , find \( : y \), then prove that \( x \) and y are two conjugate numbers. Ezercice 25 1. Détermine le nombre \( a \) tel que : \( x^{2}+4 x=(x+a)^{2}-4 \). 2. Utilise ce résultat pour factoriser Kexpression : \( x^{2}+4 x-5 \). Simplify the expression \( \frac{5 x^{3}-6 x^{2}-8 x}{4 x^{2}-10 x+4} \) and give your answer in the fo
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