ATH 6TH PERIOD Opics -4: Cumulative/Benchmark Assessment Evan uses \( \frac{1}{2} \) quart of yellow paint and adds \( 5 \frac{1}{2} \) jars of red paint. They end up with the same volume of paint. Part A Which equation represents the situation? \( 2 x+3 \frac{1}{4} x=\frac{1}{2} x+5 \frac{1}{2} x \) \( 2+3 \frac{1}{4} x=\frac{1}{2}+5 \frac{1}{2} x \) \( 2 x+3 \frac{1}{4} y=\frac{1}{2} a+5 \frac{1}{2} b \) \( 2+5 \frac{1}{2} x=\frac{1}{2}+3 \frac{1}{4} x \)

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 \( \square>\square \)

a) \( 7 x+(3 x-5)=6 x-9 \)

Solve the equation. If necessary, round to the nearest thousandth. \( 7^{x+3}=6^{x} \) A. \( \{37.87\} \) B. \( \{-39.33\} \) C. \( \{-37.87\} \) D. \( \{-36.41\} \)

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. \[ C(x)=\left\{\begin{array}{cc}10 & \text { if } 0 \leq x \leq 75 \\ 10+0.10(x-75) & \text { if } 75<x \leq 125 \\ 10+0.10(50)+0.40(x-125) & \text { if } x>125\end{array}\right. \]