91Ó°ÊÓ

Multiply or divide, as indicated. Simplify, if possible. $$\frac{\sqrt[4]{x^{3}}}{\sqrt[3]{x^{4}}}$$

Solve. $$\left(x^{2}-5 x-1\right)^{2}-18\left(x^{2}-5 x-1\right)+65=0$$

Let \(f(x)=\frac{x^{2}}{x-2}+1\) and \(g(x)=\frac{4 x-2}{x-2}+\frac{x+4}{2}.\) Find the \(x\)-intercepts of the graph of \(g\).

Find each solution set. $$\left|\frac{x+2}{x-1}\right| \leq 3$$

Complete the square to find the \(x\) -intercepts of each function given by the equation listed. $$ g(x)=x^{2}+5 x+2 $$

Purchasing. A discount store bought a quantity of potted plants for 250 dollars and sold all but 15 at a profit of 3.50 dollars per plant. With the total amount received, the manager could buy 4 more than twice as many as were bought before. Find the cost per plant.

Total Profit. Derex, Inc., determines that its total profit function is given by $$P(x)=-3 x^{2}+630 x-6000.$$ a) Find all values of \(x\) for which Derex makes a profit. b) Find all values of \(x\) for which Derex loses money.

For over 2000 years, artists, sculptors, and architects have regarded the proportions of a "golden" rectangle as visually appealing. A rectangle of width \(w\) and length \(l\) is considered "golden" if $$ \frac{w}{l}=\frac{l}{w+l} $$ Solve for \(l\).

If the graphs of two quadratic functions have the same \(x\) -intercepts, will they also have the same vertex? Why or why not?

Solve. $$\frac{x}{x-1}-6 \sqrt{\frac{x}{x-1}}-40=0$$