91Ó°ÊÓ

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$5 \sqrt{-8}+3 \sqrt{-18}$$

Solve and check each equation with rational exponents. $$ (x+5)^{3 / 2}=8 $$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+5 x $$

Exercises \(31-50\) contain 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. $$ \frac{5}{x}=\frac{10}{3 x}+4 $$

According to the National Center for Health Statistics, in \(1990,28 \%\) of babies in the United States were born to parents who were not married. Throughout the 1990 s, this increased by approximately \(0.6 \%\) per year. Use this information to solve Exercises \(33-34\) If this trend continues, in which year will \(37 \%\) of babies be born out of wedlock?

Exercises \(31-50\) contain 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. $$ \frac{2}{x}+3=\frac{5}{2 x}+\frac{13}{4} $$

Solve and check each equation with rational exponents. $$ (x+5)^{3 / 2}=8 $$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{-x+2}{x-4} \geq 0 $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$(-2+\sqrt{-4})^{2}$$

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$8 x-11 \leq 3 x-13$$