Chapter 2

Find the terms of the expression. $$ -x-7 $$

Find the domain of the function. $$ y=\frac{1}{x+2} $$

Use the distributive property to rewrite the expression without parentheses. $$ -(6 y-5) $$

Determine whether the statement is true or false. If it is false, give a counterexample. If \(a>b,\) then \(a \cdot 0\) is greater than \(b \cdot 0\)

Find the sum. $$\frac{1}{7}+(-2)+\left(-\frac{5}{7}\right)$$

Write the numbers in increasing order. \(4.8,-2.6,0,-\frac{7}{2}, \frac{1}{2},-\frac{1}{2}\)

Find the terms of the expression. $$ -3 x+6 $$

Find the domain of the function. $$ y=\frac{1}{3 x} $$

You have 8 moving boxes that you can use to pack for college. Each box can hold 15 pounds of clothing or 60 pounds of books. Let c be the number of boxes that contain clothing. If 5 boxes contain clothing, how many pounds will you be moving?

Use the distributive property to rewrite the expression without parentheses. $$ (3 d-8)(-5) $$

You rappel down the side of a mountain at a rate of 2 feet per second. Write an algebraic model for your displacement d (in feet) after t seconds.

Find the sum. Use a calculator if you wish. $$-2.95+5.76+(-8.6)$$

The elevator in the Washington Monument in Washington, D.C., climbs at a rate of about 400 feet per minute. What is the elevator's speed?

Complete the statement using \(<\) or \(>\). If \(x>-4,\) then \(-4 ? x\)

Find the terms of the expression. $$ 9-28 x $$

Find the domain of the function. $$ y=\frac{x+6}{4} $$

You have \(\$ 58\) and you want to buy a pair of jeans and a \(\$ 20\) T-shirt. There is a 6% sales tax. Let x represent the cost of the jeans. The following inequality models how much you can spend on the jeans. $$x+20+0.06(x+20) \leq 58$$ Simplify the left side of the inequality.

Use the distributive property to rewrite the expression without parentheses. $$ (2.3-7 w)(-6) $$

Find the sum. Use a calculator if you wish. $$10.97+(-51.14)+(-40.97)$$

You rappel down the side of a mountain at a rate of 2 feet per second. What is your change in position after rappelling for 10 seconds?

Complete the statement using \(<\) or \(>\). If \(3

Find the terms of the expression. $$ -10+4 b $$

Find the domain of the function. $$ y=\frac{10-x}{7-x} $$

You have \(\$ 58\) and you want to buy a pair of jeans and a \(\$ 20\) T-shirt. There is a 6% sales tax. Let x represent the cost of the jeans. The following inequality models how much you can spend on the jeans. $$x+20+0.06(x+20) \leq 58$$ If the jeans cost $35, can you buy both the T-shirt and the jeans? Explain.

Use the distributive property to rewrite the expression without parentheses. $$ -\frac{3}{8}(x+24) $$

Find the sum. Use a calculator if you wish. $$20.37+190.8+(-85.13)$$

Determine whether the statement is true or false. If it is false, give a counterexample. The opposite of \(|a|\) is never positive.

Elevation is represented by comparing a location to sea level, which is given a value of zero. A location above sea level has a positive elevation, and a location below sea level has a negative elevation. Granite Peak, Montana, \(12,799\) feet above sea level

Find the terms of the expression. $$ a-5 $$

Find the velocity of the object. A submarine descends 21 meters in 2 seconds.

Evaluate the expression for the given value of x. Then simplify the expression first and evaluate the expression again. Which way is easier? Explain. $$-x(8-x)+2 x \text { when } x=2$$

In Exercises 53 and \(54,\) find and correct the error. $$ \begin{aligned} 9(3-5) &=9(3)-5 \\ &=27-5 \\ &=22 \end{aligned} $$

Find the sum. Use a calculator if you wish. $$300.3+(-22.24)+78.713$$

Scientists estimate that a peregrine falcon can dive for its prey at a rate of about 300 feet per second. Write an algebraic model for the displacement d (in feet) of a peregrine falcon after t seconds.

Determine whether the statement is true or false. If it is false, give a counterexample. The expression \(|-a|\) is never negative.

The daily closing prices for a company's stock are given in the table. Find the change in the closing price since the previous day. $$ \begin{array}{|c|c|c|c|c|c|} \hline \text { Date } & {\text { Sept. } 11} & {\text { Sept. } 12} & {\text { Sept. } 13} & {\text { Sept. } 14} & {\text { Sept. } 15} \\ \hline \text { Closing Price } & {101.31} & {103.19} & {105.75} & {104.44} & {102.19} \\ \hline \text { Change } & {} & {?} & {?} & {?} & {?} \\ \hline \end{array} $$

Evaluate the expression for the given value of x. Then simplify the expression first and evaluate the expression again. Which way is easier? Explain. $$ 6(-x-3)-x(9+x) \text { when } x=4 $$

Find the velocity of the object. An airplane descends 20,000 feet in 25 minutes.

In Exercises 53 and \(54,\) find and correct the error. $$ \begin{aligned} -2(7-8) &=-2(7)-2(8) \\ &=-14-6 \\ &=-30 \end{aligned} $$

A company had the following profits and losses over a 4 -month period: April, 3,515 dollars May,5,674 dollars June,8,993 dollars July,907 dollars.Did the company make an overall profit or loss? Explain.

Scientists estimate that a peregrine falcon can dive for its prey at a rate of about 300 feet per second. What is a peregrine falcon’s change in position after diving for 2 seconds?

Determine whether the statement is always, sometimes, or never true. Explain. The absolute value of a number is the same as the absolute value of the opposite number. In other words, \(|x|=|-x|\)

A submarine is at a depth of 725 feet below sea level. Five minutes later it is at a depth of 450 feet below sea level. What is the change in depth of the submarine? Did it go up or down?

In the expression \(5+12 d-3 d^{2},\) what is the coefficient of the \(d^{2}\) -term? $$ (A)-3 $$ $$ (B) 3 $$ $$ (C) 2 $$ $$ (D) d $$

Use the distributive property and mental math to simplify the expression. $$ 4(6.11) $$

Determine whether the statement is always, sometimes, or never true. Explain. The opposite of the absolute value of a number is the same as the absolute value of the opposite of the number. In other words, \(-|x|=|-x|\)

Which expression is simplified? $$(F) 7+5k-5k$$ $$ (G)3 x-9+2 x^{2} $$ $$ (H)-8 g+5-8 g $$ $$ (J)11 z-4 z $$

Use mental math to solve the equation. $$ x+17=25 $$

Determine whether the following statement is true or false. If it is true, give two examples. If it is false, give a counter example. $$ \begin{aligned} &\text {The opposite of the sum of two numbers is equal to the sum of the}\\\ &\text { opposites of the numbers.} \end{aligned} $$

Use the distributive property and mental math to simplify the expression. $$ 10(7.25) $$