Chapter 8

GRAPHING LINEAR SYSTEMS Use the graphing method to solve the linear system and describe its solution(s). $$ \begin{aligned} &3 x-2 y=0\\\ &3 x-2 y=-4 \end{aligned} $$

Use the following information. The power generated by a windmill can be modeled by the equation \(w=0.015 s^{3},\) where \(w\) is the power measured in watts and \(s\) is the wind speed in miles per hour. Find the ratio of the power generated by a windmill when the wind speed is 20 miles per hour to the power generated when the wind speed is 10 miles per hour.

Solve the inequality. Then sketch a graph of the solution on a number line. $$|x+2|-1 \leq 8 $$

Sketch the graph of the inequality in a coordinate plane. $$ y \leq \frac{x}{2} $$

GRAPHING Graph the system of linear inequalities. $$ \begin{aligned} &2 x+y \leq 1\\\ &-2 x+y \leq 1 \end{aligned} $$

Use the following information. The power generated by a windmill can be modeled by the equation \(w=0.015 s^{3},\) where \(w\) is the power measured in watts and \(s\) is the wind speed in miles per hour. Write a general statement about how doubling the wind speed affects the amount of power generated by a windmill.

Solve the inequality. Then sketch a graph of the solution on a number line. $$\text |3-x|-6>-4 \quad $$

Sketch the graph of the inequality in a coordinate plane. $$ \frac{3}{4} x+\frac{1}{4} y \geq 1 $$

GRAPHING Graph the system of linear inequalities. $$ \begin{aligned} &x+2 y<3\\\ &x-3 y>1 \end{aligned}$$

Use the following information. The power generated by a windmill can be modeled by the equation \(w=0.015 s^{3},\) where \(w\) is the power measured in watts and \(s\) is the wind speed in miles per hour. Part A of a test has 10 true-false questions. Part B has 10 multiple-choice questions. Each of the multiple-choice questions has 4 possible answers. There are \(2^{10}\) ways to answer the 10 questions in Part A. There are \(4^{10}\) ways to answer the 10 questions in Part B. a. How many ways are there to answer all 20 questions? b. If you guess the answer to each question, what is the probability that you will get them all right?

Solve the inequality. Then sketch a graph of the solution on a number line. $$|9-2 x|+3<4 \quad $$

Decide whether the ordered pair is a solution of the system. $$\begin{aligned}&2 x+4 y=2\\\&-x+5 y=13 \quad(-3,2)\end{aligned}$$

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

Suppose you put one red marble, one green marble, and one blue marble in each of six bags. There are \(3^{6}\) possible orderings of the colors of the marbles you can get when you choose one marble from each bag. Suppose you put one red marble, one green marble, and one blue marble in each of six bags. There are \(3^{6}\) possible orderings of the colors of the marbles you can get when you choose one marble from each bag.

Solve the inequality. Then sketch a graph of the solution on a number line. $$|3 x+2|+9 \geq-1$$

Decide whether the ordered pair is a solution of the system. $$ \begin{aligned} &x-5 y=9\\\ &3 x+y=11 \quad(1,-4) \end{aligned} $$

SIMPLIFYING EXPRESSIONS Simplify the expression. $$ 2^{-4} $$

Suppose you put one red marble, one green marble, and one blue marble in each of six bags. There are \(3^{6}\) possible orderings of the colors of the marbles you can get when you choose one marble from each bag. If you use 14 bags, how many different orderings of colors are there? What is the probability that the marbles you choose will all be red?

Draw a box-and-whisker plot of the data. \(48,10,48,25,40,42,44,23,21,13,50,17\)

Decide whether the ordered pair is a solution of the system. \begin{aligned} &8 a+4 b=6\\\ &4 a+b=3\left(\frac{3}{4}, 0\right) \end{aligned}

SIMPLIFYING EXPRESSIONS Simplify the expression. $$ \left(\frac{1}{10}\right)^{-3} $$

Draw a box-and-whisker plot of the data. \(85,61,55,78,79,86,30,76,76,87,68,82\)

Decide whether the ordered pair is a solution of the system. \begin{aligned} &3 c-8 d=11\\\ &c+6 d=8 \quad\left(5,-\frac{1}{2}\right) \end{aligned}

SIMPLIFYING EXPRESSIONS Simplify the expression. $$ \frac{1}{(2 x)^{-2}} $$

Use substitution to solve the system. $$\begin{aligned}&2 x-y=-2\\\&4 x+y=5\end{aligned}$$

Use linear combinations to solve the system. $$ \begin{aligned} &x-y=4\\\ &x+y=12 \end{aligned} $$

SIMPLIFYING EXPRESSIONS Simplify the expression. $$ \frac{7^{4} \cdot 7}{7^{7}} $$

Use substitution to solve the system. $$\begin{aligned}&-3 x+y=4\\\&-9 x+5 y=10\end{aligned}$$

Use linear combinations to solve the system. $$ \begin{aligned} &-x+2 y=12\\\ &x+6 y=20 \end{aligned} $$

Write a convincing argument to show that the power of a product property is true.

Use substitution to solve the system. $$\begin{aligned}&x+4 y=300\\\&x-2 y=0\end{aligned}$$

Use linear combinations to solve the system. $$ \begin{aligned} &2 a+3 b=17\\\ &3 a+4 b=24 \end{aligned} $$

Evaluate the expression. \(b^{2}\) when \(b=8\)

Use substitution to solve the system. $$\begin{aligned}&2 x-3 y=10\\\&3 x+3 y=15\end{aligned}$$

Evaluate the expression. \((5 y)^{4}\) when \(y=2\)

Use substitution to solve the system. $$\begin{aligned}&x+15 y=6\\\&-x-5 y=84\end{aligned}$$

Evaluate the expression. \(\frac{1}{2} n^{3}\) when \(n=-2\)

Use substitution to solve the system. $$\begin{aligned}&4 x-y=5\\\&2 x+4 y=15\end{aligned}$$

Evaluate the expression. \(\frac{1}{y^{2}}\) when \(y=5\)

Evaluate the expression. \(\frac{24}{x^{3}}\) when \(x=2\)

Evaluate the expression. \(\frac{45}{a^{2}}\) when \(a=2\)

Use a table of values to graph the equation. $$ y=x+2 $$

Use a table of values to graph the equation. $$ y=-(x-4) $$

Use a table of values to graph the equation. $$ y=\frac{1}{2} x-5 $$

Use a table of values to graph the equation. $$y=\frac{3}{4} x+2$$

Use a table of values to graph the equation. $$y=2$$

Use a table of values to graph the equation. $$y=2$$

Sketch the graph of the inequality. $$x<4$$

Sketch the graph of the inequality. $$x>15$$

Sketch the graph of the inequality. $$x \geq-9$$