91Ó°ÊÓ

Solve the quadratic equation by factoring. $$ 4 x^{2}=5 x $$

For each of the following exercises, solve the equation for \(y\) in terms of \(x\) . $$5 x+2 y=0$$

For exercises 17 and 18, use this scenario: A retired woman has \(\$ 50,000\) to invest but needs to make \(\$ 6,000\) a year from the interest to meet certain living expenses. One bond investment pays 15\(\%\) annual interest. The rest of it she wants to put in a CD that pays 7\(\% .\) If we let \(x\) be the amount the woman invests in the 15\(\%\) bond, how much will she be able to invest in the CD?

For the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation. $$ |3 x-1|>11 $$

Solve the quadratic equation by factoring. $$ 7 x^{2}+3 x=0 $$

Solve the inequality involving absolute value. Write your final answer in interval notation. $$ |3 x-1|>11 $$

For the following exercises, solve the following polynomial equations by grouping and factoring. $$ m^{3}+m^{2}-m-1=0 $$

Solve each rational equation for x. State all x-values that are excluded from the solution set. \(2-\frac{3}{x+4}=\frac{x+2}{x+4}\)

For the following exercises, solve each rational equation for \(x\). State all \(x\) -values that are excluded from the solution set. $$ 2-\frac{3}{x+4}=\frac{x+2}{x+4} $$

For each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers. $$(-4,1) \text { and }(3,-4)$$