Chapter 2

Solve the inequality. Write the solution in interval notation. $$|2.1 x-5| \leq 8$$

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. \(15 x-y=30\)

Rainfall Suppose that during a storm rain is falling at a rate of 1 inch per hour. The water coming from a circular roof with a radius of 20 feet is running down a downspout that can accommodate 400 gallons of water per hour. See the figure. (a) Determine the number of cubic inches of water falling on the roof in 1 hour. (b) One gallon equals about 231 cubic inches. Write a formula for a function \(g\) that computes the gallons of water landing on the roof in \(x\) hours. (c) How many gallons of water land on the roof during a 2.5 -hour rain storm? (d) Will one downspout be sufficient to handle this type of rainfall? How many downspouts should there be? (IMAGE CANT COPY)

Solve the linear inequality graphically. Write the solution set in set-builder notation. Approximate endpoints to the nearest hundredth whenever appropriate. $$ 1.238 x+0.998 \leq 1.23(3.987-2.1 x) $$

Solve the inequality. Write the solution in interval notation. $$|2 x-3|>1$$

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. $$ 6 x-7 y=-42 $$

Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. $$ 3 \leq 5 x-17<15 $$

Solve the linear equation with the intersection-of-graphs method. Approximate the solution to the nearest thousandth whenever appropriate. $$ \sqrt{2} x=4 x-6 $$

Solve the inequality. Write the solution in interval notation. $$|5 x-7|>2$$

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. $$ 5 x+2 y=-20 $$

Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. $$ -4<\frac{55-3.1 x}{4}<17 $$

Solve the linear equation with the intersection-of-graphs method. Approximate the solution to the nearest thousandth whenever appropriate. $$ 3.1(x-5)=\frac{1}{5} x-5 $$

Solve the inequality. Write the solution in interval notation. $$|-3 x+8| \geq 3$$

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. $$ y-3 x=7 $$

Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. $$ 1.5 \leq 9.1-0.5 x \leq 6.8 $$

Solve the linear equation with the intersection-of-graphs method. Approximate the solution to the nearest thousandth whenever appropriate. $$ 65=8(x-6)-5.5 $$

Solve the inequality. Write the solution in interval notation. $$|-7 x-3| \geq 5$$

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. $$ 4 x-3 y=6 $$

Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. $$ 0.2 x<\frac{2 x-5}{3}<8 $$

Solve the linear equation with the intersection-of-graphs method. Approximate the solution to the nearest thousandth whenever appropriate. $$ \frac{6-x}{7}=\frac{2 x-3}{3} $$

Solve the inequality. Write the solution in interval notation. $$|0.25 x-1|>3$$

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. $$ 0.2 x+0.4 y=0.8 $$

First-Class Mail In March 2008 , the retail flat rate in dollars for first- class mail weighing up to 5 ounces could be computed by the piece wise- constant function \(P\), where \(x\) is the number of ounces. $$ P(x)=\left\\{\begin{array}{ll} 0.80 & \text { if } 0

Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. $$ x-4<2 x-5<6 $$

Solve the linear equation with the intersection-of-graphs method. Approximate the solution to the nearest thousandth whenever appropriate. $$ \pi(\mathbf{x}-\sqrt{2})=1.07 \mathbf{x}-6.1 $$

Solve the inequality. Write the solution in interval notation. $$|-0.5 x+5| \geq 4$$

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. $$ \frac{2}{3} y-x=1 $$

Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. $$ -3 \leq 1-x \leq 2 x $$

Domain and Range If \(f(k)=-6,\) what is the value of \(1 f(k) | ?\)

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. $$ y=8 x-5 $$

Use tables to solve the equation numerically to the nearest tenth. $$ 1-6 x=7 $$

Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Graph the equation. $$ y=-1.5 x+15 $$

Use tables to solve the equation numerically to the nearest tenth. $$ 2 x-7.2=10 $$

The intercept form of a line is \(\frac{x}{a}+\frac{y}{b}=1\) Determine the \(x\) -and y-intercepts on the graph of the equation. Draw a conclusion about what the constants a and b represent in this form. $$ \frac{x}{5}+\frac{y}{7}=1 $$

Exercises \(69-74:\) Complete the following for \(f(x)\) (a) Determine the domain of \(f\) (b) Evaluate \(f(-2), f(0),\) and \(f(3)\) (c) Graph \(f\) (d) Is \(f\) continuous on its domain? $$ f(x)=\left\\{\begin{array}{ll} 2 & \text { if }-5 \leq x \leq-1 \\ x+3 & \text { if }-1

Use tables to solve the equation numerically to the nearest tenth. $$ 5.8 x-8.7=0 $$

The intercept form of a line is \(\frac{x}{a}+\frac{y}{b}=1\) Determine the \(x\) -and y-intercepts on the graph of the equation. Draw a conclusion about what the constants a and b represent in this form. $$ \frac{x}{2}+\frac{y}{3}=1 $$

Exercises \(69-74:\) Complete the following for \(f(x)\) (a) Determine the domain of \(f\) (b) Evaluate \(f(-2), f(0),\) and \(f(3)\) (c) Graph \(f\) (d) Is \(f\) continuous on its domain? $$ f(x)=\left\\{\begin{array}{ll} 2 x+1 & \text { if }-3 \leq x<0 \\ x-1 & \text { if } \quad 0 \leq x \leq 3 \end{array}\right. $$

The intercept form of a line is \(\frac{x}{a}+\frac{y}{b}=1\) Determine the \(x\) -and y-intercepts on the graph of the equation. Draw a conclusion about what the constants a and b represent in this form. $$ \frac{2 x}{3}+\frac{4 y}{5}=1 $$

Exercises \(69-74:\) Complete the following for \(f(x)\) (a) Determine the domain of \(f\) (b) Evaluate \(f(-2), f(0),\) and \(f(3)\) (c) Graph \(f\) (d) Is \(f\) continuous on its domain? $$ f(x)=\left\\{\begin{array}{ll} 3 x & \text { if }-1 \leq x<1 \\ x+1 & \text { if } \quad 1 \leq x \leq 2 \end{array}\right. $$

Solve each inequality numerically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth when appropriate. $$ -4 x-6>0 $$

The intercept form of a line is \(\frac{x}{a}+\frac{y}{b}=1\) Determine the \(x\) - and \(y\) -intercepts on the graph of the equation. Draw a conclusion about what the constants a and b represent in this form. $$ \frac{5 x}{6}-\frac{y}{2}=1 $$

Exercises \(69-74:\) Complete the following for \(f(x)\) (a) Determine the domain of \(f\) (b) Evaluate \(f(-2), f(0),\) and \(f(3)\) (c) Graph \(f\) (d) Is \(f\) continuous on its domain? $$ f(x)=\left\\{\begin{array}{ll} -2 & \text { if }-6 \leq x<-2 \\ 0 & \text { if }-2 \leq x<0 \\ 3 x & \text { if } \quad 0 \leq x \leq 4 \end{array}\right. $$

Solve each inequality numerically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth when appropriate. $$ 1-2 x \geq 9 $$

Use tables to solve the equation numerically to the nearest tenth. $$ 0.5-0.1(\sqrt{2}-3 x)=0 $$

Exercises \(69-74:\) Complete the following for \(f(x)\) (a) Determine the domain of \(f\) (b) Evaluate \(f(-2), f(0),\) and \(f(3)\) (c) Graph \(f\) (d) Is \(f\) continuous on its domain? $$ f(x)=\left\\{\begin{array}{ll} x & \text { if }-3 \leq x \leq-1 \\ 1 & \text { if }-1

Solve each inequality numerically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth when appropriate. $$ 1 \leq 3 x-2 \leq 10 $$

Exercises \(69-74:\) Complete the following for \(f(x)\) (a) Determine the domain of \(f\) (b) Evaluate \(f(-2), f(0),\) and \(f(3)\) (c) Graph \(f\) (d) Is \(f\) continuous on its domain? $$ f(x)=\left\\{\begin{array}{ll} 3 & \text { if }-4 \leq x \leq-1 \\ x-2 & \text { if }-1

Solve each inequality numerically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth when appropriate. $$ -5<2 x-1<15 $$

Exercises \(75-82:\) Solve the equation (to the nearest tenth) (a) symbolically, (b) graphically, and (c) numerically. $$ 5-(x+1)=3 $$