Chapter 12

Amalia and Cindy leave from the same point at the same time. Cindy bicycles east at a rate that is 2 miles per hour faster than Amalia, who bicycles south. After one hour they are 10 miles apart. a. Let \(r\) represent Amalia's rate in miles per hour. Write an expression for the distance each girl has traveled in one hour. b. Draw and label a diagram of the situation. c. Use the Pythagorean theorem to find how fast each person is traveling. d. Which method did you use to solve the quadratic equation? Give a reason for your choice.

Simplify the expression. $$\frac{\sqrt{3}}{\sqrt{3}-1}$$

Solve the equation by completing the square. $$5 x^{2}-20 x-20=5$$

Decide whether the ordered pair is a solution of the inequality. $$y>3 x^{2}+50 x+500 ;(-6,100)$$

Solve the equation. Check for extraneous solutions. $$\frac{1}{5} x=\sqrt{x-6}$$

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

Use the fact that a Pythagorean triple is a group of three integers, such as 3, 4, and 5, that could be the lengths of the sides of a right triangle. Find two other Pythagorean triples that are not multiples of 3, 4, 5 or of each other.

Simplify the expression. $$\frac{14}{60-\sqrt{578}}$$

Solve the equation by completing the square. $$3 x^{2}+4 x+4=3$$

Decide whether the ordered pair is a solution of the inequality. $$y \geq-x^{2}+3 x-\frac{15}{4} ;(2,-3)$$

Solve the equation. Check for extraneous solutions. $$\frac{2}{3} x=\sqrt{24 x-128}$$

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

Use the fact that a Pythagorean triple is a group of three integers, such as 3, 4, and 5, that could be the lengths of the sides of a right triangle. Notice that \(3 \cdot 4 \cdot 5=60 .\) Is the product of the three numbers in each Pythagorean triple evenly divisible by \(3 ?\) by \(4 ?\) by \(5 ?\)

Simplify the expression. $$\frac{12}{7-\sqrt{3}}$$

Solve the equation by completing the square. $$4 x^{2}+6 x-6=2$$

Solve the percent problem. How much is \(15 \%\) of \(\$ 15 ?\)

Two numbers and their geometric mean are given. Find the value of \(a\). 12 and \(a ; 27\)

Find the domain and the range of the function. Then sketch the graph of the function. $$y=\sqrt{x}-2$$

Simplify the expression. $$\frac{4+\sqrt{3}}{a-\sqrt{b}}$$

Solve the equation by completing the square. $$6 x^{2}+24 x-41=0$$

Solve the percent problem. 41 inches is what percent of 50 inches?

Two numbers and their geometric mean are given. Find the value of \(a\). 4 and \(a ; 16\)

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

Plot the ordered pairs in a coordinate plane. $$(2,5),(0,-1),(3,1)$$

Solve the equation by completing the square. $$20 x^{2}-120 x-109=0$$

Solve the percent problem. 100 is \(1 \%\) of what number?

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

Plot the ordered pairs in a coordinate plane. $$(2,-5),(2,4),(-3,0)$$

Choose a method to solve the quadratic equation. Explain your choice. $$x^{2}-5 x-1=0$$

Two numbers and their geometric mean are given. Find the value of \(a\). 4 and \(a ; 14\)

Solve the percent problem. 6 inches is what percent of 3 inches?

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

Plot the ordered pairs in a coordinate plane. $$(-1,-2),(-4,5),(0,2)$$

Choose a method to solve the quadratic equation. Explain your choice. $$4 x^{2}-12=0$$

Solve the percent problem. 1240 is \(80 \%\) of what number?

Find the domain and the range of the function. Then sketch the graph of the function. $$y=\sqrt{x+1}$$

Plot the ordered pairs in a coordinate plane. $$(1,4),(-2,-1),(3,-1)$$

Solve the quadratic equation. $$x^{2}+10 x+13=0$$

Choose a method to solve the quadratic equation. Explain your choice. $$n^{2}+5 n-24=0$$

Solve the percent problem. \(\$ 5\) is \(33 \%\) of what amount of money?

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

Plot the ordered pairs in a coordinate plane. $$(2,3),(-2,-3),(4,-2)$$

Solve the quadratic equation. $$x^{2}-4 x-6=0$$

Choose a method to solve the quadratic equation. Explain your choice. $$9 a^{2}-25=0$$

Use the following information. You and a friend go hiking. You hike 3 miles north and 2 miles west. Starting from the same point, your friend hikes 4 miles east and 1 mile south. How far apart are you and your friend? (Hint: Draw a diagram on a grid.)

Find the domain and the range of the function. Then sketch the graph of the function. $$y=2 \sqrt{4 x+10}$$

Plot the ordered pairs in a coordinate plane. $$(1,3),(-3,1),(3,-4)$$

solve the quadratic equation. $$x^{2}-4 x-15=0$$

Choose a method to solve the quadratic equation. Explain your choice. $$x^{2}-x-20=0$$

Use the following information. You and a friend go hiking. You hike 3 miles north and 2 miles west. Starting from the same point, your friend hikes 4 miles east and 1 mile south. If you and your friend want to meet for lunch, where could you meet so that both of you hike the same distance? How far do you have to hike?