4. Pyn rents a heavy-duty sewing machine to sew sails. He pays \( \$ 12 \) the first day and \( \$ 8 \) a day afterwards. A similar heavy-duty sewing machine costs \( \$ 348 \). How many days of rent would make it worth his while to buy one? A 17.4 B -29 C - 42 D_ 43

3. \( \sqrt[7]{\frac{x^{4}}{\sqrt{x}}}= \)

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: \( f(x)=\left(x-x_{1}\right)\left(x-x_{2}\right)^{2}\left(x-x_{3}\right)^{3} \) \( x_{1}=\square \) \( x_{2}=\square \) \( x_{3}=\square \)

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 polynomial long division to divide \( \frac{\left(3 x^{3}-x^{2}-2 x+6\right)}{\left(x^{2}+1\right)} \). Express your answer in the form \( \frac{f(x)}{d(x)}=q(x)+\frac{r(x)}{d(x)} \).

Simplify completely: \[ \frac{\frac{1}{m}+\frac{8}{3}}{\frac{1}{m}+\frac{7}{10}} \] Enter the numerator and denominator separately in the boxes below. If the denominator is 1 , enter the number 1. Do not leave either box blank. Make sure that the coefficient on \( x \) is positive. Answer: