91Ó°ÊÓ

By making an appropriate substitution. $$ x^{4}-13 x^{2}+36=0 $$

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$\frac{3 x}{10}+1 \geq \frac{1}{5}-\frac{x}{10}$$

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-9 x $$

Things did not go quite as planned. You invested \(\$ 12,000\), part of it in stock that paid \(14 \%\) annual interest. However, the rest of the money suffered a \(6 \%\) loss. If the total annual income from both investments was \(\$ 680,\) how much was invested at each rate?

Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind , solve the equation. \(\frac{2}{x-2}=\frac{x}{x-2}-2\)

Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$1-\frac{x}{2}>4$$

By making an appropriate substitution. $$ 9 x^{4}=25 x^{2}-16 $$

In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-\frac{2}{3} x $$

Things did not go quite as planned. You invested \(\$ 12,000\), part of it in stock that paid \(14 \%\) annual interest. However, the rest of the money suffered a \(6 \%\) loss. If the total annual income from both investments was \(\$ 680,\) how much was invested at each rate?

In Exercises \(29-44\), perform the indicated operations and write the result in standard form. $$ (3 \sqrt{-5})(-4 \sqrt{-12}) $$