91Ó°ÊÓ

Write the quotient in standard form. $$\frac{i}{(4-5 i)^{2}}$$

Write the quotient in standard form. $$\frac{5 i}{(2+3 i)^{2}}$$

Determine the intervals on which the polynomial is entirely negative and those on which it is entirely positive. $$3 x^{2}+8 x+6$$

Use the Quadratic Formula to solve the equation. Use a graphing utility to verify your solutions graphically. $$8 x=4-x^{2}$$

Solving an Equation Involving an Absolute Value Find all solutions of the equation algebraically. Check your solutions. $$\left|x^{2}+6 x\right|=3 x+18$$

You plan to invest \(\$ 12,000\) in two funds paying \(4 \frac{1}{2} \%\) and \(5 \%\) simple interest. (There is more risk in the \(5 \%\) fund.) Your goal is to obtain a total annual interest income of \(\$ 560\) from the investments. What is the least amount you can invest in the \(5 \%\) fund to meet your objective?

Determine any point(s) of intersection algebraically. Then verify your result numerically by creating a table of values for each function. $$\begin{aligned} &y=6-x\\\ &y=3 x-2 \end{aligned}$$

Use the Quadratic Formula to solve the equation. Use a graphing utility to verify your solutions graphically. $$20 x^{2}-20 x+5=0$$

A grocer mixes peanuts that cost \(\$ 2.50\) per pound and walnuts that cost \(\$ 8.00\) per pound to make 100 pounds of a mixture that costs \(\$ 5.25\) per pound. How much of each kind of nut is put into the mixture?

Solve the inequality and graph the solution on the real number line. Use a graphing utility to verify your solution graphically. $$x^{2}+4 x+4 \geq 9$$