91Ó°ÊÓ

Solve each equation with rational exponents in Exercises \(31-40\) Check all proposed solutions. $$(x+5)^{\frac{2}{3}}=4$$

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(D=R T\) for \(R\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(A=\frac{1}{2} b h\) for \(b\)

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}+3 x $$

In all exercises other than \(\varnothing\), use interval notation to express solution sets and graph each solution set on a number line. In Exercises \(27-50,\) solve each linear inequality. $$ 1-(x+3) \geq 4-2 x $$

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. $$\frac{1}{x-1}+5=\frac{11}{x-1}$$

Perform the indicated operations and write the result in standard form. $$ \frac{-6-\sqrt{-12}}{48} $$

Solve each equation with rational exponents in Exercises \(31-40\) Check all proposed solutions. $$\left(x^{2}-x-4\right)^{\frac{3}{4}}-2=6$$

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

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(V=\frac{1}{3} B h\) for \(B\)