Chapter 1

Use a calculator to evaluate the power. For keystroke help see Student Help box on page 11. $$ 3^{11}$$

Perform the indicated operation. Simplify your answer, if possible. (Skills Review, pp. \(781-783)\) $$ 1 \frac{7}{8}+\frac{3}{4} $$

Evaluate the expression. \(6+\frac{x+2}{y}\) when \(x=7\) and \(y=3\)

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$a(3 a+2)>50 ; 4$$

The science club is selling magazine subscriptions at \(\$ 15\) each. The club wants to raise \(\$ 315\) for science equipment. Use mental math to solve the equation.

Use a calculator to evaluate the power. For keystroke help see Student Help box on page 11. $$ 8^{6} $$

$$ \frac{2}{5}-\frac{1}{10} $$

Evaluate the expression. \(3 y^{2}+w\) when \(y=8\) and \(w=27\)

The area A of a trapezoid with parallel bases of lengths \(b_{1}\) and \(b_{2}\) and height \(h\) is \(A=\frac{1}{2} h\left(b_{1}+b_{2}\right)\) Find the area of a trapezoid whose height is 2 meters and whose bases are 6 meters and 10 meters. (GRAPH CANNOT COPY)

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$\frac{c+5}{3} \leq 4 ; 3$$

The science club is selling magazine subscriptions at \(\$ 15\) each. The club wants to raise \(\$ 315\) for science equipment. How many subscriptions does the science club need to sell to raise \(\$ 315 ?\)

Use a calculator to evaluate the power. For keystroke help see Student Help box on page 11. $$ 12^{7} $$

$$ \frac{2}{5}-\frac{1}{10} $$

Evaluate the expression. \(2 s^{3}-3 t\) when \(s=4\) and \(t=6\)

Use the following information. The surface area of a cylinder equals the lateral surface area \((2 \pi r \cdot h)\) plus the area of the two bases \(\left(2 \cdot \pi r^{2}\right)\). Write the expression for the surface area of a cylinder.

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$\frac{25-d}{d} \geq 4 ; 5$$

Use a calculator to evaluate the power. For keystroke help see Student Help box on page 11. $$ 6^{8} $$

$$ 2 \frac{1}{5} \div \frac{4}{5} $$

Check whether the number is a solution of the equation or the inequality. \(7 y+2=4 y+8 ; 2\)

Use the following information. The surface area of a cylinder equals the lateral surface area \((2 \pi r \cdot h)\) plus the area of the two bases \(\left(2 \cdot \pi r^{2}\right)\). Evaluate the expression when \(h=10.5\) centimeters and \(r=2.5\) centimeters. Use 3.14 as an approximation for \(\pi .\)

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$x^{2}-10>16 ; 6$$

Use the following information. Jeff lives in a state in which speeders are fined \(\$ 20\) for each mile per hour (mi/h) over the speed limit. Jeff was given a ticket for \(\$ 260\) for speeding on a road where the speed limit is 45 miles per hour. Jeff wants to know how fast he was driving. Assign labels to the three parts of the verbal model.

Use a calculator to evaluate the power. For keystroke help see Student Help box on page 11. $$ 13^{5} $$

$$ 3 \frac{2}{3} \cdot 3 $$

Check whether the number is a solution of the equation or the inequality. \(5 x-1=3 x+2 ; 4\)

You are shopping for school supplies. A store is offering a \(10 \%\) discount on binders and a \(20 \%\) discount on packages of paper. You want to buy 5 binders originally marked $$ 2.50\( each and 10 packages of paper originally marked $$ 1.30 each. a. Write an expression that shows how much you will save after the discounts. b. Evaluate the expression. c. Writing If you have $$ 25\) to spend on supplies, how much money will you have left over? Explain how you arrived at your answer.

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$n(21-n)<100 ; 8$$

Use the following information. Jeff lives in a state in which speeders are fined \(\$ 20\) for each mile per hour (mi/h) over the speed limit. Jeff was given a ticket for \(\$ 260\) for speeding on a road where the speed limit is 45 miles per hour. Jeff wants to know how fast he was driving. Use the labels to translate the verbal model into an algebraic model.

Evaluate the expression for the given value of the variable. $$ (5 w)^{3} \text { when } w=5 $$

$$ \frac{6}{5} \div \frac{3}{10} $$

Check whether the number is a solution of the equation or the inequality. \(32-5 y>11 ; 3\)

CRITICALTHINKING Without grouping symbols, the expression \(2 \cdot 3^{3}+4\) has a value of 58. Insert grouping symbols in the expression \(2 \cdot 3^{3}+4\) to produce the indicated values. a. 62 b. 220 c. 4374 d. \(279,936\)

EQUATIONS AND INEQUALITIES Match the verbal sentence with its mathematical representation. The sum of \(x\) and 16 is less than 32.

Use the following information. Jeff lives in a state in which speeders are fined \(\$ 20\) for each mile per hour (mi/h) over the speed limit. Jeff was given a ticket for \(\$ 260\) for speeding on a road where the speed limit is 45 miles per hour. Jeff wants to know how fast he was driving. Use mental math to solve the equation. What does the solution represent?

Evaluate the expression for the given value of the variable. $$ 6 t^{4} \text { when } t=3 $$

$$ 4 \frac{5}{9}-\frac{1}{5} $$

Check whether the number is a solution of the equation or the inequality. \(7 m+2<12 ; 1\)

EQUATIONS AND INEQUALITIES Match the verbal sentence with its mathematical representation. The product of 16 and \(x\) is equal to 32

Use the following information. Jeff lives in a state in which speeders are fined \(\$ 20\) for each mile per hour (mi/h) over the speed limit. Jeff was given a ticket for \(\$ 260\) for speeding on a road where the speed limit is 45 miles per hour. Jeff wants to know how fast he was driving. Perform unit analysis to check that the equation is set up correctly.

Evaluate the expression for the given value of the variable. $$ 7 b^{2} \text { when } b=7 $$

$$ \text {} 8 \frac{9}{10}+1 \frac{1}{5} $$

Check whether the number is a solution of the equation or the inequality. \(s-7 \geq 12-s ; 9\)

Evaluate the expression for the given value of the variable. $$ 2 x^{2} \text { when } x=15 $$

EQUATIONS AND INEQUALITIES Match the verbal sentence with its mathematical representation. The difference of \(x\) and 16 is 32

You are running for class president. At 2: 30 on election day you have 95 votes and your opponent has 120 votes. Forty-five more students will be voting. Let \(x\) represent the number of students (of the 45) who vote for you. a. Write an inequality that shows the values of \(x\) that will allow you to win the election. b. What is the smallest value of \(x\) that is a solution of the inequality?

Check whether the number is a solution of the equation or the inequality. \(n+2 \leq 2 n-2 ; 4\)

Evaluate the expression for the given value of the variable. $$ (8 x)^{3} \text { when } x=2 $$

EQUATIONS AND INEQUALITIES Match the verbal sentence with its mathematical representation. The quotient of \(x\) and 16 is greater than or equal to 32

Use the following information. You are shopping for a mountain bike. A store sells two different models. The model that has steel wheel rims costs \(\$ 220 .\) The model with aluminum wheel rims costs \(\$ 480 .\) You have a summer job for 12 weeks. You save \(\$ 20\) per week, which would allow you to buy the model with the steel wheel rims. You want to know how much more money you would have to save each week to be able to buy the model with the aluminum wheel rims. Write a verbal model and an algebraic model for how much more money you would have to save each week.

A major athletic footwear company had about \(\$ 3750\) million in sales of athletic footwear during the year ending May 31,1997 . The company's sales fell to about \(\$ 3500\) million in \(1998 .\) By how much did the company's sales decrease?