91Ó°ÊÓ

A board of length \(\left(3 x^{4}+6 x^{2}-18\right)\) meters is to be cut into three pieces of the same length. Find the length of each piece.

Perform the indicated operation. If possible, simplify your answer. $$ \left(\frac{2 x}{3}\right)^{2} \div\left(\frac{x}{3}\right)^{2} $$

Complete the following table for the inverse variation \(y=\frac{k}{x}\) over each given value of \(k .\) Plot the points on a rectangular coordinate system. $$ \begin{array}{|c|c|c|c|c|c|} \hline x & {\frac{1}{4}} & {\frac{1}{2}} & {1} & {2} & {4} \\ \hline y =\frac{k}{x} & {} & {} & {} & {} & {} \\ \hline \end{array} $$ $$ k=5 $$

Perform each indicated operation. See Section 1.3 $$ \frac{4}{10}-\frac{7}{10} $$

Perform the indicated operation. If possible, simplify your answer. $$ \left(\frac{2 x}{3}\right)^{2} \cdot\left(\frac{3}{x}\right)^{2} $$

The perimeter of a regular hexagon is given to be \(\left(12 x^{5}-48 x^{3}+3\right)\) miles. Find the length of each side.

If the area of the rectangle is \(\left(15 x^{2}-29 x-14\right)\) square inches, and its length is \((5 x+2)\) inches, find its width.

Perform each indicated operation. See Section 1.3 $$ \frac{5}{28}-\frac{2}{21} $$

Perform the indicated operation. If possible, simplify your answer. $$ \left(\frac{x}{x+1}-\frac{x}{x-1}\right) \div \frac{x}{2 x+2} $$

If the area of a parallelogram is \(\left(2 x^{2}-17 x+35\right)\) square centimeters and its base is \((2 x-7)\) centimeters, find its height.