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Home Question Bank Math Algebra Archive 2025 January 13

Algebra Questions from Jan 13,2025

Browse the Algebra Q&A Archive for Jan 13,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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10. Open-Ended Sketch a graph of a quadratic function that has \( x \)-intercepts at 0 and 4 . For the following function, \( h(x)=x^{2}+3 x-28 \) : (a) Find the values of \( x \) for which \( h(x)=0 \). (b) Find \( h(0) \). Express numbers using integers or simplified fractions. Part: \( \mathbf{0} / \mathbf{2} \) Part 1 of 2 \( h(x)=0 \) when \( x=\square \) Separate multiple answers using a comma, if necessary. ar,... Because of the coaster's features, there is both a minimum and maximum for the height range. The minimum height to ride is 25 inches less than the maximum height to ride the coaster. Twice the maximum height is 154 inches. - What will the number line for the height range look like for the sign? Justify your reasoning. For the following function, \( g(x)=x^{2}+7 x \) : (a) Find the values of \( x \) for which \( g(x)=0 \). (b) Find \( g(0) \). Express numbers using integers or simplified fractions. Part: \( \mathbf{0} / \mathbf{2} \) Part 1 of 2 Separate multiple answers with a comma, if necessary. \( g(x)=0 \) when \( x=\square \) Rearrange the formula below to make \( y \) the subject. PART (A) \( \quad \) PART (B) \[ 2 x=\frac{1}{2} y+3 \] \( \frac { 154 mi } { 5.5 gal } = \frac { 900 mi } { x } \) Solve the equation. Separate multiple answers with a comma, if necessary. \[ 3 w^{3}-5 w^{2}-12 w+20=0 \] The solution set is \( \square \). 6. Find an expression for \( T_{n} \) of the sequence \( 8,5,2, \ldots \) For what value of \( n \) is \( T_{n}=-34 \) ? Solve the equation. Separate multiple answers with a comma, if necessary. \[ 2 x^{3}+8 x^{2}-24 x=0 \] The solution set is \( \square \). \begin{tabular}{l} Solve the equation. \\ \( \qquad z(12 z+7)=12 \) \\ The solution set is \\ \hline\( \square\}, \frac{\square}{\square} \)\end{tabular}
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