Algebra Questions from Dec 13,2024

Browse the Algebra Q&A Archive for Dec 13,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Factor. Then find all zeros. \( \begin{array}{l}\text { 46) } f(x)=x^{3}-2 x^{2}-8 x \\ \text { A) }\{0,-2 \text { mult. } 2\} \\ \text { B) }\{0,-2,4\} \\ \text { C) }\{0,-2,-5\} \\ \text { D) }\{0 \text { mult. } 2,4\}\end{array} \) Find an equation for the line that passes through the points \( (3,-4) \) and \( (-3,5) \). \( \square=\square \frac{\square}{\square} \) Writing the equation of a line through two given points Find an equation for the line that passes through the points \( (6,-2) \) and \( (-6,1) \). Simplify. 6. \( \frac{a^{2} b^{2} c}{12 a^{2} c^{2}} \) Solve. Separate your answers with a comma, and please write fractions in reduced form, no decimals. \( 8|4 x-9|=16 \) Find a degree 3 polynomial with real coefficients having zeros 3 and \( 4 i \) and a lead coefficient of 1 . Write \( P \) in expanded form. \( P(x)=\square \) 3. Wonne made one batch of butter coobies and four batches of sugar cookies. Below is the amount of sugar one batch of each cookie type needs. - Butter cookies need \( \frac{3}{4} \) cup of sugar - Sugar cookies need 3 cups of sugar a. Write an expression to show how many cups of sugar she needs. Solve the following system of equations. \[ \begin{array}{l}3 x-8 y=-5 \\ 2 x-7 y=-10\end{array} \] A town has a population of 1600 people at time \( t=0 \). In each of the following cases, write a formula for the population \( P \), of the town as a function of year \( t \). (a) The population increases by 60 people per year. \( P=\square \) people (b) The population increases by 5 percent a year. \( P=\square \) people Solve the following system of equations. \[ \begin{array}{l}7 x+3 y=-18 \\ -9 x+2 y=-12\end{array} \]
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