Chapter 1

Express interval in set-builder notation and graph the interval on a number line. \((-\infty, 5) \cap[1,8)\)

Find each product and write the result in standard form. $$ (2+3 i)^{2} $$

Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=-\frac{1}{2} x $$

Solve each radical equation. Check all proposed solutions. $$\sqrt{2 x+19}-8-x$$

According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24 Over your lifetime, how many years will you spend on each of these activities?

Solve cach equation in Exercises \(15-34\) by the square root property. $$2 x^{2}-7=-15$$

Express interval in set-builder notation and graph the interval on a number line. \((-\infty, 6) \cap[2,9)\)

Find each product and write the result in standard form. $$ (5-2 i)^{2} $$

Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=-\frac{1}{2} x+2 $$

Solve each radical equation. Check all proposed solutions. $$\sqrt{2 x+15}-6-x$$

Solve cach equation in Exercises \(15-34\) by the square root property. $$(x+2)^{2}=25$$

Express interval in set-builder notation and graph the interval on a number line. \((-\infty, 5) \cup[1,8)\)

Divide and express the result in standard form. $$ \frac{2}{3-i} $$

Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=2|x| $$

Solve cach equation in Exercises \(15-34\) by the square root property. $$(x-3)^{2}=36$$

Express interval in set-builder notation and graph the interval on a number line. \((-\infty, 6) \cup[2,9)\)

Divide and express the result in standard form. $$ \frac{3}{4+i} $$

Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=-2|x| $$

In \(2000,31 \%\) of U.S. adults viewed a college education as essential for success. For the period 2000 through 2010 , the percentage viewing a college education as essential for success increased on average by approximately 2.4 each year. If this trend continues, by which year will \(67 \%\) of all American adults view a college education as essential for success?

Solve cach equation in Exercises \(15-34\) by the square root property. $$3(x-4)^{2}=15$$

Express interval in set-builder notation and graph the interval on a number line. \([3, \infty) \cap(6, \infty)\)

Divide and express the result in standard form. $$ \frac{2 i}{1+i} $$

Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=|x|+1 $$

Solve cach equation in Exercises \(15-34\) by the square root property. $$3(x+4)^{2}=21$$

Express interval in set-builder notation and graph the interval on a number line. \([2, \infty) \cap(4, \infty)\)

Divide and express the result in standard form. $$ \frac{5 i}{2-i} $$

Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=|x|-1 $$

Solve each radical equation. Check all proposed solutions. $$\sqrt{x+5}-\sqrt{x-3}-2$$

A new car worth \(\$ 24,000\) is depreciating in value by \(\$ 3000\) per year. a. Write a formula that models the car's value, \(y,\) in dollars, after \(x\) years. b. Use the formula from part (a) to determine after how many years the car's value will be \(\$ 9000\). c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then show your solution to part (b) on the graph.

Solve cach equation in Exercises \(15-34\) by the square root property. $$(x+3)^{2}=-16$$

Express interval in set-builder notation and graph the interval on a number line. \([3, \infty) \cup(6, \infty)\)

Divide and express the result in standard form. $$ \frac{8 i}{4-3 i} $$

Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=9-x^{2} $$

A new car worth \(\$ 45,000\) is depreciating in value by \(\$ 5000\) per year. a. Write a formula that models the car's value, \(y,\) in dollars, after \(x\) years. b. Use the formula from part (a) to determine after how many years the car's value will be \(\$ 10,000\). c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then show your solution to part (b) on the graph.

Solve cach equation in Exercises \(15-34\) by the square root property. $$(x-1)^{2}=-9$$

Express interval in set-builder notation and graph the interval on a number line. \([2, \infty) \cup(4, \infty)\)

Divide and express the result in standard form. $$ \frac{-6 i}{3+2 i} $$

Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=-x^{2} $$

Solve each radical equation. Check all proposed solutions. $$\sqrt{2 x-3}-\sqrt{x-2}-1$$

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(5 x+11<26\)

You are choosing between two health clubs. Club A offers membership for a fee of \(\$ 40\) plus a monthly fee of \(\$ 25 .\) Club \(B\) offers membership for a fee of \(\$ 15\) plus a monthly fee of \(\$ 30\). After how many months will the total cost at each health club be the same? What will be the total cost for each club?

Solve cach equation in Exercises \(15-34\) by the square root property. $$(x-3)^{2}=-5$$

Divide and express the result in standard form. $$ \frac{2+3 i}{2+i} $$

Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=x^{3} $$

Solve each radical equation. Check all proposed solutions. $$\sqrt{2 x+3}+\sqrt{x-2}-2$$

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(2 x+5<17\)

You need to rent a rug cleaner. Company A will rent the machine you need for \(\$ 22\) plus \(\$ 6\) per hour. Company \(B\) will rent the same machine for \(\$ 28\) plus \(\$ 4\) per hour. After how many hours of use will the total amount spent at each company be the same? What will be the total amount spent at each company?

Solve cach equation in Exercises \(15-34\) by the square root property. $$(x+2)^{2}=-7$$

Divide and express the result in standard form. $$ \frac{3-4 i}{4+3 i} $$

Graph each equation .Let $x=-3,-2,-1,0,1,2, and 3. $$ y=x^{3}-1 $$