Chapter 9

Simplify the radical expression. $$ \sqrt{40} $$

From 1994 to 1999, the sales for a chain of home furnishing stores increased by about the same annual rate. The sales \(S\) (in millions of dollars) in year \(t\) can be modeled by \(S=455\left(\frac{13}{10}\right)^{t}\) where \(t\) represents years since 1994 . Find the ratio of 1999 sales to 1995 sales.

TABLE TENNIS In Exercises \(72-75,\) use the following information. Suppose a table-tennis ball is hit in such a way that its path can be modeled by \(h=-4.9 t^{2}+2.07 t,\) where \(h\) is the height in meters above the table and \(t\) is the time in seconds. CRITICAL THINKING What factors would change the path of the table-tennis ball? What combination of factors would result in the table-tennis ball bouncing the highest? What combination of factors would result in the tabletennis ball bouncing the lowest?

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$6 s^{2}-12=0$$

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

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$5 a^{2}+10=20$$

Use a vertical motion model to find how long it will take for the object to reach the ground. You drop keys from a window 30 feet above ground to your friend below. Your friend does not catch them.

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

UNDERSTANDING GRAPHS Sketch the graphs of the three functions in the same coordinate plane. Describe how the three graphs are related. a. \(y=x^{2}+x+1\) \(y=\frac{1}{2} x^{2}+x+1\) \(y=2 x^{2}+x+1\) b. \(y=x^{2}-1 x+1\) \(y=x^{2}-5 x+1\) \(y=x^{2}-10 x+1\) c. \(y=x^{2}-x+1\) \(y=x^{2}-x+3\) \(y=x^{2}-x-2\)

Use a vertical motion model to find how long it will take for the object to reach the ground. An acorn falls 45 feet from the top of a tree.

Simplify the radical expression. $$ \sqrt{200} $$

How does a change in the value of \(a\) change the graph of \(y=a x^{2}+b x+c ?\)

A boulder falls off the top of a cliff during a storm. The cliff is 60 feet high. Find how long it will take for the boulder to hit the road below. Write the falling object model for \(s=60\)

Use a vertical motion model to find how long it will take for the object to reach the ground. A lacrosse player throws a ball upward from her playing stick with an initial height of 7 feet, at an initial speed of 90 feet per second.

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

How does a change in the value of \(b\) change the graph of \(y=a x^{2}+b x+c ?\)

Use a vertical motion model to find how long it will take for the object to reach the ground. You throw a ball downward with an initial speed of 10 feet per second out of a window to a friend 20 feet below. Your friend does not catch the ball.

Simplify the radical expression. $$ \frac{1}{3} \sqrt{27} $$

How does a change in the value of \(c\) change the graph of \(y=a x^{2}+b x+c ?\)

A boulder falls off the top of a cliff during a storm. The cliff is 60 feet high. Find how long it will take for the boulder to hit the road below. Solve the falling object model for \(h=0\)

A falcon dives toward a pigeon on the ground. When the falcon is at a height of 100 feet the pigeon sees the falcon, which is diving at 220 feet per second. Estimate the time the pigeon has to escape.

Simplify the radical expression. $$ \frac{1}{8} \sqrt{32} $$

GRAPHING Write the equation in slope-intercept form, and then graph the equation. Label the \(x\) - and \(y\) -intercepts on the graph. $$ -3 x+y+6=0 $$

A boulder falls off the top of a cliff during a storm. The cliff is 60 feet high. Find how long it will take for the boulder to hit the road below. Which problem solving method do you prefer? Why?

A hawk dives toward a snake. When the hawk is at a height of 200 feet the snake sees the hawk, which is diving at 105 feet per second. Estimate the time the snake has to escape.

GRAPHING Write the equation in slope-intercept form, and then graph the equation. Label the \(x\) - and \(y\) -intercepts on the graph. $$-x+y-7=0$$

Simplify the radical expression. $$ \frac{2}{3} \sqrt{300} $$

GRAPHING Write the equation in slope-intercept form, and then graph the equation. Label the \(x\) - and \(y\) -intercepts on the graph. $$4 x+2 y-12=0$$

At lunch, you order 2 pasta dishes and 1 type of salad. Your friend orders 1 pasta dish and 2 types of salads. The restaurant charges the same price for each pasta dish and the same price for each salad. Your bill is 13.85 dollars and your friend's bill is 9.85 dollars. How much did each pasta dish and each salad cost?

In parts (a)-(d), a batter hits a pitched baseball when it is 3 feet off the ground. After it is hit, the height \(h\) (in feet) of the ball at time \(t\) (in seconds) is modeled by$$h=-16 t^{2}+80 t+3$$where \(t\) is the time (inseconds). a.Find the time when the ball hits the ground in the outfield. b.Write a quadratic equation that you can use to find the time when the baseball is at its maximum height of 103 feet. Solve the quadratic equation. c.Use a graphing calculator to graph the function. Use the zoom feature to approximate the time when the baseball is at its maximum height. Compare your results with those you obtained in part (b). d.What factors change the path of a baseball? What factors would contribute to hitting a home run?

GRAPHING Write the equation in slope-intercept form, and then graph the equation. Label the \(x\) - and \(y\) -intercepts on the graph. $$x+2 y-7=5 x+1$$

GRAPHING LINEAR INEQUALITIES Graph the system of linear inequalities. $$\begin{aligned} &x-3 y \geq 3\\\ &x-3 y \leq 12 \end{aligned}$$

Writing Explain how you can use this two-part form of the quadratic formula $$x=\frac{-b}{2 a} \pm \frac{\sqrt{b^{2}-4 a c}}{2 a}$$ to find the distance between the axis of symmetry of a parabola and either of its \(x\) -intercepts.

GRAPHING LINEAR INEQUALITIES Graph the system of linear inequalities. $$\begin{aligned} &x+y \leq 5\\\ &x \geq 2\\\ &y \geq 0 \end{aligned}$$

(8) Home COMPUTER SALES The sales \(S\) (in millions of dollars) of home computers in the United States from 1988 to 1995 can be modeled by \(S=145.63 t^{2}+3327.56,\) where \(t\) is the number of years since \(1988 .\) Use this model to estimate the year in which sales of home computers will be 36,000 million dollars.

Evaluate the expression. x^{2} \text { when } x=-5

GRAPHING LINEAR INEQUALITIES Graph the system of linear inequalities. $$\begin{aligned} &x+y<10\\\ &2 x+y>10\\\ &x-y<2 \end{aligned}$$

The sales \(S\) (in millions of dollars) of computer software in the United States from 1990 to 1995 can be modeled by \(S=61.98 t^{2}+1001.15,\) where \(t\) is the number of years since \(1990 .\) Use this model to estimate the year in which sales of computer software will be 7200 million dollars.

Evaluate the expression. -y^{2} \text { when } y=-1

SIMPLIFYING EXPRESSIONS Simplify. Write your answer as a power or as an expression containing powers. (Review 8.1 ) $$4^{5} \cdot 4^{8}$$

Evaluate the expression. \(-4 x y\) when \(x=-2\) and \(y=-6\)

SIMPLIFYING EXPRESSIONS Simplify. Write your answer as a power or as an expression containing powers. $$\left(3^{3}\right)^{2}$$

Evaluate the expression. y^{2}-y \text { when } y=-2

SIMPLIFYING EXPRESSIONS Simplify. Write your answer as a power or as an expression containing powers. $$\left(3^{6}\right)^{3}$$

Solve the inequality and graph the solution. 2 \leq x<5

SIMPLIFYING EXPRESSIONS Simplify. Write your answer as a power or as an expression containing powers. $$a \cdot a^{5}$$

Solve the inequality and graph the solution. 8>2 x>-4

SIMPLIFYING EXPRESSIONS Simplify. Write your answer as a power or as an expression containing powers. $$\left(3 b^{4}\right)^{2}$$

Solve the inequality and graph the solution. -12<2 x-6<4

SIMPLIFYING EXPRESSIONS Simplify. Write your answer as a power or as an expression containing powers. $$6 x \cdot(6 x)^{2}$$