Chapter 12

Use the following information. The lateral surface area \(S\) of a cone whose base has radius \(r\) can be found using the formula $$S=\pi \cdot r \sqrt{r^{2}+h^{2}}$$ where h is the height of the cone. Find the lateral surface area of a cone that has a height of 30 centimeters and whose base has a radius of 14 centimeters.

Which of the following is a solution of \(x=\sqrt{x+20} ?\) F. -5 G. -4 H. 4 J. 5

ESTIMATING AREA Estimate the area of a rectangle whose sides are given. First round each side length to the nearest whole number. Then multiply to find the area. $$ 100.4 \text { by } 7.0 $$

Simplify the expression. $$ \frac{35 x-7 x^{3}}{49 x} $$

Choose a method and solve the quadratic equation. Explain your choice. $$ x^{2}-x-12=0 $$

Solve the percent problem. What is \(30 \%\) of \(160 ?\)

Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ x^{2}=36 $$

Determine whether the number is prime or composite. If it is composite, give its prime factorization. $$ 99 $$

Find the domain of \(y=\frac{3}{\sqrt{x}-2}\)

ESTIMATING AREA Estimate the area of a rectangle whose sides are given. First round each side length to the nearest whole number. Then multiply to find the area. $$ 17.3 \text { by } 2.8 $$

Find the quotient. Divide \(\left(-4 x^{2}-24 x\right)\) by \(-4 x\)

Choose a method and solve the quadratic equation. Explain your choice. $$ x^{2}-9=0 $$

Solve the percent problem. 105 is what percent of \(240 ?\)

Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ x^{2}=11 $$

Determine whether the number is prime or composite. If it is composite, give its prime factorization. $$ 18 $$

ESTIMATING AREA Estimate the area of a rectangle whose sides are given. First round each side length to the nearest whole number. Then multiply to find the area. $$ 20.5 \text { by } 1.5 $$

Find the quotient. Divide \(\left(7 p^{5}+18 p^{4}\right)\) by \(p^{4}\)

Choose a method and solve the quadratic equation. Explain your choice. $$ x^{2}-4 x=8 $$

Solve the percent problem. 203 is what percent of 406?

Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ 7 x^{2}=700 $$

Determine whether the number is prime or composite. If it is composite, give its prime factorization. $$ 33 $$

Simplify the radical expression. $$\sqrt{24}$$

Find the quotient. Divide \(\left(9 a^{2}-27 a-36\right)\) by \((a+1)\)

Choose a method and solve the quadratic equation. Explain your choice. $$ x^{2}+5 x-14=0 $$

Solve the percent problem. What is \(70 \%\) of \(210 ?\)

Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ 25 x^{2}-9=91 $$

Determine whether the number is prime or composite. If it is composite, give its prime factorization. $$ 69 $$

Simplify the radical expression. $$\sqrt{60}$$

Find the quotient. Divide \(\left(4 n^{2}-41 n+45\right)\) by \((4 n-5)\)

Choose a method and solve the quadratic equation. Explain your choice. $$ x^{2}-2 x=2 $$

Solve the equation by factoring. $$ x^{2}-25=0 $$

Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ x^{2}-16=-7 $$

Determine whether the number is prime or composite. If it is composite, give its prime factorization. $$ 80 $$

Simplify the radical expression. $$\sqrt{175}$$

Simplify the expression. $$ \frac{3}{x}+\frac{x+9}{x} $$

Choose a method and solve the quadratic equation. Explain your choice. $$ 3 x^{2}+5 x-12=0 $$

Solve the equation by factoring. $$ x^{2}+2 x-15=0 $$

Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ -16 x^{2}+48=0 $$

Simplify the radical expression. $$\sqrt{360}$$

Simplify the expression. $$ \frac{8}{4 a+1}+\frac{5}{4 a+1} $$

Choose a method and solve the quadratic equation. Explain your choice. $$ x^{2}+5 x-6=0 $$

Solve the equation by factoring. $$ x^{2}-13 x=-42 $$

Find the product. $$ (x+5)^{2} $$

Simplify the radical expression. $$\sqrt{\frac{20}{25}}$$

Simplify the expression. $$ \frac{2}{2 x}+\frac{12}{x} $$

Choose a method and solve the quadratic equation. Explain your choice. $$ x^{2}-6 x+7=0 $$

Solve the equation by factoring. $$ x^{2}-26=11 x $$

Find the product. $$ (2 x-3)^{2} $$

Simplify the radical expression. $$\frac{1}{2} \sqrt{80}$$

Simplify the expression. $$ \frac{2 x}{x+1}+\frac{5}{x+3} $$