Chapter 12

Determine whether the ordered pair is a solution of the inequality. (Lesson 9.8) $$ y \geq 4 x^{2}-48 x+61,(1,17) $$

Use linear combinations to solve the linear system. Then check your solution. \(4 x+3 y=1\) \(2 x-3 y=1\)

Determine whether the given lengths are sides of a right triangle. Explain your reasoning. $$ 11,60,61 $$

Solve by completing the square. $$ x^{2}-2 x=5 $$

Simplify the variable expression. $$ x^{1 / 3} \cdot x^{1 / 2} $$

In Exercises 38 and \(39,\) use the following information. When a car skids to a stop, its speed \(S\) (in miles per hour) before the skid can be modeled by the equation \(S=\sqrt{30 d f} .\) where \(d\) is the length of the tires' skid marks (in feet) and \(f\) is the coefficient of friction for the road. In an accident, a car makes skid marks that are 147 feet long. The coefficient of friction is 0.4. A witness says that the driver was traveling under the speed limit of 35 miles per hour. Can the witness’s statement be correct? Explain your reasoning.

Write a radical equation that has a solution of 18.

Evaluate the expression. Write the answer as a fraction or as a mixed number in simplest form. (Skills Review pp. 764-765) $$ \frac{2}{3} \cdot \frac{2}{5}+\frac{1}{5} $$

Use linear combinations to solve the linear system. Then check your solution. \(3 x+5 y=6\) \(-4 x+2 y=5\)

Determine whether the given lengths are sides of a right triangle. Explain your reasoning. $$ 7,24,26 $$

What is the distance between \((-6,-2)\) and \((2,4) ?\) A. \(2 \sqrt{5}\) B. \(2 \sqrt{7}\) C. 10 D. 28

Solve by completing the square. $$ x^{2}+30 x-7=0 $$

Simplify the variable expression. $$ x \cdot \sqrt[3]{y^{6}}+y^{2} \cdot \sqrt[3]{x^{3}} $$

Find the domain of the function. Then sketch its graph and find the range. $$y=7 \sqrt{x}$$

Solve the equation. Check for extraneous solutions. $$ \sqrt{x}-3=4 $$

Evaluate the expression. Write the answer as a fraction or as a mixed number in simplest form. (Skills Review pp. 764-765) $$ \frac{2}{7} \div \frac{1}{14}-\frac{5}{4} $$

Use linear combinations to solve the linear system. Then check your solution. \(2 x+3 y=1\) \(5 x-4 y=14\)

Determine whether the given lengths are sides of a right triangle. Explain your reasoning. $$ 3,9,10 $$

The vertices of a right triangle are \((0,0),(0,6),\) and (6, 0). What is the length of the hypotenuse? F. 6 G. \(6 \sqrt{2}\) H. 36 J. 72

Solve by completing the square. $$ x^{2}-4 x-1=0 $$

Simplify the variable expression. $$ \left(y^{1 / 6}\right)^{3} \cdot \sqrt{x} $$

Simplify the radical expression. $$ \frac{5}{\sqrt{7}} $$

Find the domain of the function. Then sketch its graph and find the range. $$y=4 \sqrt{x}$$

Solve the equation. Check for extraneous solutions. $$ \sqrt{x}-6=0 $$

Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. \(2 x+y=3\) \(4 x+2 y=8\)

Evaluate the expression. Write the answer as a fraction or as a mixed number in simplest form. (Skills Review pp. 764-765) $$ \frac{11}{2}\left(\frac{1}{10}-\frac{1}{4}\right) $$

Factor the expression. $$ m^{2}-25 $$

Solve by completing the square. $$ x^{2}+20 x+3=0 $$

Simplify the variable expression. $$ \left(36 x^{3}\right)^{1 / 2} $$

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

Find the domain of the function. Then sketch its graph and find the range. $$y=5 \sqrt{x}$$

Solve the equation. Check for extraneous solutions. $$ \sqrt{x}+5=1 $$

Evaluate the expression. Write the answer as a fraction or as a mixed number in simplest form. (Skills Review pp. 764-765) $$ \frac{5}{3}-\left(\frac{2}{9} \cdot \frac{3}{4}+\frac{7}{12}\right) $$

Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. \(2 x+2 y=3\) \(4 x+2 y=6\)

Factor the expression. $$ 81 x^{2}-144 $$

Solve by completing the square. $$ x^{2}+14 x-2=0 $$

Simplify the radical expression. $$ \frac{3}{\sqrt{48}} $$

Simplify the variable expression. $$ \left(y \cdot y^{1 / 3}\right)^{3 / 2} $$

Find the domain of the function. Then sketch its graph and find the range. $$y=6 \sqrt{x}$$

Solve the equation. Check for extraneous solutions. $$ 6+\sqrt{3 x}=-3 $$

Evaluate the expression. Write the answer as a fraction or as a mixed number in simplest form. (Skills Review pp. 764-765) $$ \frac{1}{2}+\frac{2}{3}-\frac{3}{4} \cdot \frac{4}{5} $$

Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. \(2 x+y=-4\) \(y+2 x=8\)

Factor the expression. $$ 16 t^{2}-49 $$

Solve the quadratic equation. $$ x^{2}+4 x+5=0 $$

Simplify the radical expression. $$ \frac{5}{\sqrt{13}} $$

Simplify the variable expression. $$ \left(x^{1 / 3} \cdot y^{1 / 2}\right)^{6} \cdot \sqrt{x} $$

Find the domain of the function. Then sketch its graph and find the range. $$y=\sqrt{3 x}$$

Solve the equation. Check for extraneous solutions. $$ \sqrt{x+5}=7 $$

Evaluate the expression. Write the answer as a fraction or as a mixed number in simplest form. (Skills Review pp. 764-765) $$ \left(\frac{3}{8}-\frac{2}{3}\right) \div \frac{1}{3} $$

Complete the statement using \(<,>,\) or \(=\). \(54 \% ? 0.54\)