Pratap Puri rowed 18 miles down a river in 2 hours, but the return trip took him \( 4 \frac{1}{2} \) hours. Find the rate Pratap can row in still water and find the rate of the current. Let \( x= \) rate Pratap can row in still water and \( y= \) rate of the current. What is the rate that Pratap rows in still water? Pratap can row at a rate of (Type an integer or a decimal.)

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 \( \boldsymbol{x}= \)

Solve for \( x \) : (a) \( 10^{x} \cdot 9^{x}=1000 \) (b) \( 10^{x} \cdot 9^{2 x}=1000 \)

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 \( \frac{f(x)}{d(x)}=q(x)+\frac{r(x)}{d(x)} \).

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 \( (x, y) \).

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