Chapter 2

Evaluate the expression. \(-1 \frac{3}{8}+4 \frac{3}{4}-7 \frac{1}{2}\)

Use a calculator to evaluate the expression. Round your answer to two decimal places. $$x^{2}+x-27.2 \text { when } x=-7$$

Evaluate the expression for the given value(s) of the variable(s). $$\frac{3 a-4 b}{a b} \text { when } a=-\frac{1}{3} \text { and } b=\frac{1}{4}$$

SIMPLIFYING EXPRESSIONS Simplify the expression by combining like terms. $$ 3 x^{2}+2 x^{2}-7 $$

Find the terms of the expression. $$-3 x+5-8 y$$

Decide whether the statement is true or false . If it is false, give a counterexample. $$(-a) \cdot(-b)=(-b) \cdot(-a)$$

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

SIMPLIFYING EXPRESSIONS Simplify the expression by combining like terms. $$ 9 x^{3}-4 x^{3}-2 $$

EVALUATING FUNCTIONS Evaluate the function for these values of \(x:-2,-1,0,\) and \(1 .\) Organize your results in a table. $$y=x-8$$

Decide whether the statement is true or false . If it is false, give a counterexample. The product \((-a) \cdot(-1)\) is always positive.

Find the domain of the function. $$y=\frac{3}{2-x}$$

Complete the statement using \(>,<, \geq,\) or \(\leq\). If \(3 \leq y,\) then \(y \geq 3\)

SIMPLIFYING EXPRESSIONS Simplify the expression by combining like terms. $$ 8 b+5-3 b $$

EVALUATING FUNCTIONS Evaluate the function for these values of \(x:-2,-1,0,\) and \(1 .\) Organize your results in a table. $$ y=12-x $$

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

Complete the statement using \(>,<, \geq,\) or \(\leq\). If \(m \leq 8\) then_8$=m.

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ (3 y+1)(-2)+y $$

EVALUATING FUNCTIONS Evaluate the function for these values of \(x:-2,-1,0,\) and \(1 .\) Organize your results in a table. $$ y=-x+12.1 $$

Formulate the following statement in terms of variables. Then decide whether it is true or false . The opposite of the sum of two numbers is equal to the sum of the opposites of the numbers. If false, give a counterexample. If true, give two examples involving negative numbers.

To promote sales, a grocery store advertises bananas for \(\mathbf{S} . \mathbf{2 5}\) per pound. The store loses \(\mathbf{S} . \mathbf{1 1}\) on each pound of bananas it sells. Write a verbal model that you can use to find the amount of money that the store loses depending on the number of pounds of bananas it sells.

Find the domain of the function. $$y=\frac{4}{x^{2}}$$

Complete the statement using \(>,<, \geq,\) or \(\leq\). If \(-7 \geq w\) then \(w\)__ -7

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ 4(2-a)-a $$

EVALUATING FUNCTIONS Evaluate the function for these values of \(x:-2,-1,0,\) and \(1 .\) Organize your results in a table. $$ y=-8.5-(-x) $$

Find the difference. $$\frac{4}{5}-\frac{2}{5}$$

To promote sales, a grocery store advertises bananas for \(\mathbf{S} . \mathbf{2 5}\) per pound. The store loses \(\mathbf{S} . \mathbf{1 1}\) on each pound of bananas it sells. The store sells 2956 pounds of bananas. How much money does the store lose on banana sales?

Write a positive number, a negative number, or zero to represent the elevation of the location. 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.

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ 12 s+(7-s) 2 $$

EVALUATING FUNCTIONS Evaluate the function for these values of \(x:-2,-1,0,\) and \(1 .\) Organize your results in a table. $$ y=27+x $$

Find the difference. $$\frac{8}{9}-\frac{2}{3}$$

To promote sales, a grocery store advertises bananas for \(\mathbf{S} . \mathbf{2 5}\) per pound. The store loses \(\mathbf{S} . \mathbf{1 1}\) on each pound of bananas it sells. The store also advertises apple juice for \(\$ 1.19\) per 64 -ounce bottle, and loses \(\$ .08\) per bottle sold. Use a verbal model to find how much the store loses on sales of 3107 bottles of apple juice.

You are scuba diving in the ocean. You dive down 22.5 feet in 9 seconds. What is your average velocity?

Write a positive number, a negative number, or zero to represent the elevation of the location. 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. View Orleans, Louisiana, 8 feet below sea level

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ (5-2 x)(-x)+x^{2} $$

Find the difference. $$\frac{3}{4}-\frac{5}{12}$$

Your aunt lends you \(\$ 175\) to buy a guitar. She will decrease the amount you owe by \(\$ 25\) for each day you help her by doing odd jobs. Write a verbal model that you can use to find the decrease in the amount you owe your aunt depending on the number of days you help her out.

Kareem Abdul-Jabbar scored \(38,387\) points and grabbed \(17,440\) rebounds in 1560 National Basketball Association games. How many points did he average per game? How many rebounds did he average per game? (Round your answers to the nearest tenth.) ) Source: NBA

Write a positive number, a negative number, or zero to represent the elevation of the location. 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. Death Valley. Califomia, 282 fect below sea level

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ 7 x-3 x(x+1) $$

Evaluate the expression. Use estimation to check your answer. $$ 5.3-(-2.5)-4.7 $$

Find the difference. $$\frac{7}{8}-\frac{1}{4}$$

Your aunt lends you \(\$ 175\) to buy a guitar. She will decrease the amount you owe by \(\$ 25\) for each day you help her by doing odd jobs. What is the change in the amount you owe your aunt after helping her out for 5 days? How much do you still owe her?

Write a positive number, a negative number, or zero to represent the elevation of the location. 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. Long Island Sound, Connecticut, sea level

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ -4(y+2)-6 y $$

Evaluate the expression. Use estimation to check your answer. $$ 8.9-(-2.1)-7.3 $$

Find the difference. $$4 \frac{2}{3}-2 \frac{1}{5}$$

You and your family take a summer vacation to Ireland. You discover that the number of Americans visiting Ireland is increasing by \(80,000\) visitors per year. Let \(x\) represent the number of visitors in 1997 . Write an expression for the number of visitors in 2000 .

COMBINING LIKE TERMS Apply the distributive property. Then simplify by combining like terms. $$ 3 t(t-5)+6 t^{2} $$

Evaluate the expression. Use estimation to check your answer. $$ -4.89+2.69-(-3.74) $$

Find the difference. $$\frac{5}{6}-\frac{1}{9}$$