Twice last month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her \( \$ 207.50 \). On her second business trip she drove 200 miles in 3 days, and paid \( \$ 135.00 \) for the rental. Find the daily fee, and find the mileage charge. Daily fee is \( \$ \square \), and the mileage charge is \( \$ \square \).

16. คอกสัตว์แห่งหนึ่ง ถ้านำวัวออกไปแล้ว 15 ตัว จะเหลือควายเป็น 2 เท่าของวัว หลังจากนั้นถ้านำควาย ออกไปอีก 45 ตัว วัวที่เหลือจะเป็นจำนวน 5 เท่าของควาย อยากทราบว่าเดิมในคอกสัตว์แห่งนี้มีวัวกี่ ตัว 1. 30 ตัว 2. 36 ตัว 3. 40 ตัว

Use common bases to solve the logarithmic equation \( \log _{3}\left(x^{2}-20\right)=\log _{3}(2 x+4) \). If necessary, round your answers to the nearest hundredth. One solution at \( x= \) Extraneous solution at \( \boldsymbol{x}= \)

Use logarithms to solve the exponential equation \( 7^{x}=128 \). If necessary, round your answer to the nearest hundredth. \( x= \)

Suppose \( f \) is a polynomial function whose graph has the following properties: 1. the graph bounces off of the \( x \)-axis at \( x=1 \) 2. the graph passes straight through the x - axis at \( x=2 \) 3. the graph swivels through the x-axis at \( x=3 \) Complete the expression of the function below: \( f(x)=\left(x-x_{1}\right)\left(x-x_{2}\right)^{2}\left(x-x_{3}\right)^{3} \) \( x_{1}=\square \) \( x_{2}=\square \) \( x_{3}=\square \)

Consider the polynomial function \( f(x)=(2 x-1)(x-2)(x+1)^{2} \) Use the function expression above to fill in the blanks: Degree of \( f \) is x-intercepts at y-inould be entered as an ordered pair \( \begin{array}{l}(x, y) .)\end{array} \) answer should be entered as an ordered pair \( (x, y) \).