\begin{tabular}{|l|l|}\hline \multicolumn{2}{|l|}{ For each equation, decide how many solutions it has and explain how you know. } \\ \hline a. \( (x-4)^{2}=25 \) & b. \( \sqrt{x-4}=5 \) \\ \hline c. \( x^{3}-7=-20 \) & d. \( 6 \cdot \sqrt[3]{x}=0 \) \\ \hline\end{tabular}

Simplify. \[ \frac{3 x^{2}-6 x}{4 x^{2}-8 x} \]

Simplify. \[ \frac{10 y^{2}-25 y}{5 y^{2}-15 y} \]

10. Matador Wireless offers a data plan that charges \( \$ 10.00 \) a month for access, with no additional charge if usage is at or below 75 MB . If a customer exceeds 75 MB of data they are also charged 10 cents for each MB above 75 . If a customer exceeds 125 MB of data, they are charged 40 cents for each MB above 125 . a. What is the monthly cost to store 125 MB of data? b. Write a formula for the piecewise function of the cost function for storing \( x \mathrm{MB} \) of data a month. Fill in the boxes for the piecewise definition for the cost \( C(x) \) of storing \( x \) MB of data a month. \[ C(x)=\left\{\begin{array}{cc}10 & \text { if } 0 \leq x \leq 75 \\ 10+0.10(x-75) & \text { if } 75<x \leq 125 \\ 10+0.10(50)+0.40(x-125) & \text { if } x>125\end{array}\right. \]

10. Matador Wireless offers a data plan that charges \( \$ 10.00 \) a month for access, with no additional charge if usage is at or below 75 MB . If a customer exceeds 75 MB of data they are also charged 10 cents for each MB above 75 . If a customer exceeds 125 MB of data, they are charged 40 cents for each MB above 125 . a. What is the monthly cost to store 125 MB of data? b. Write a formula for the piecewise function of the cost function for storing \( x \mathrm{MB} \) of data a month. Fill in the boxes for the piecewise definition for the cost \( C(x) \) of storing \( x \) MB of data a month. \[ C(x)=\left\{\begin{array}{cc}10 & \text { if } 0 \leq x \leq 75 \\ 10+0.10(x-75) & \text { if } 75<x \leq 125 \\ 10+0.10(50)+0.40(x-125) & \text { if } x>125\end{array}\right. \]

Find the range of the quadratic function, \[ y=-3 x^{2}-12 x-15 \] Write your answer as an inequality using \( x \) or \( y \) as appropriate, Or, you may instead click on "Empty set" or "All reals" as the answer, प<ロ \( \square>\square \)