Write the system of equations as an augmented matrix \( \left\{\begin{aligned} a-2 r+5 n & =150 \\ r-3 n & =250 \\ a+3 r-9 n & =200\end{aligned}\right. \)

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:

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

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

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