Chapter 1

Write an equation or an inequality to model the real-life situation. Ben's hourly wage \(b\) at his after school job is \(\$ 1.50\) less than Eileen's hourly wage \(e.\)

Evaluate the expression for the given value of the variable. $$ w^{3} \text { when } w=13 $$

If you are driving at a constant speed of 96 kilometers per hour, how long will it take you to travel 288 kilometers?

Evaluate the expression. $$\frac{5^{3} \cdot 2}{1+6^{2}-8}$$

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$5+5 x \geq 10 ; 1$$

Write an equation or an inequality to model the real-life situation. The distance \(s\) to school is \(\frac{1}{5}\) mile more than the distance \(c\) to the Community Center swimming pool.

Evaluate the expression for the given value of the variable. $$ p^{2} \text { when } p=2.5 $$

In Exercises \(40-42,\) use the following information. The number of calories burned while doing an activity can be expressed by \(\mathrm{rm},\) where \(r\) is the rate of calories burned and \(m\) is the number of minutes spent doing the activity. A 120 -pound student playing volleyball burns 2.7 calories per minute. If the student plays for 30 minutes, how many calories does the student burn?

Writing You decide to buy two rings from an outdoor vendor. One ring costs $$ 10.89 .\( The other ring costs $$ 12.48 . The sales tax is \)8 \% .\( The vendor uses a calculator to obtain the price including sales tax for both rings and gets $$ 24.37 .\) What mistake did the vendor make?

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$4 p-1 \geq 8 ; 2$$

Write an equation or an inequality to model the real-life situation. The length \(c\) of the Colorado River is three times the length \(r\) of the Connecticut River, plus 229 miles.

Evaluate the expression for the given values of the variables. $$ (x+y)^{2} \text { when } x=5 \text { and } y=3 $$

An in-line skater, who is the same weight as the student in Exercise 40 , burns 387 calories in 90 minutes. How many calories does the in-line skater burn per minute?

Which is correct? Explain. A. \(\frac{(9-7)^{2}+3}{5}=(9-7)^{2}+3 \div 5\) B. \(\frac{(9-7)^{2}+3}{5}=\left[(9-7)^{2}+3\right] \div 5\)

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$3 r-15<0 ; 5$$

Evaluate the expression for the given values of the variables. $$ m-n^{2} \text { when } m=25 \text { and } n=4 $$

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$11 x \leq x-7 ; 9$$

Write an equation or an inequality to model the real-life situation. The volume \(V\) of a cube with a side length \(s\) is less than or equal to thirty minus three.

Evaluate the expression for the given values of the variables. $$ (a-b)^{4} \text { when } a=4 \text { and } b=2 $$

Heidi Zimmer plans to climb the highest peak in each continent. She has already climbed summits in North America, Europe, Africa, and South America. Copy and complete the table. Convert \(h,\) the height in meters, to the height in feet by dividing each given value of \(h\) by \(0.3048 .\) The last column shows how much shorter each mountain is than Mt. Everest, which is 29,029 feet high. $$ \begin{array}{|l|c|c|c|} \hline \text { Mountain, Continent } & h & \frac{h}{0.3048} & 29,029-\frac{h}{0.3048} \\ \hline \text { Mt. McKinley, North America } & 6194 & ? & ? \\ \hline \text { Mt. Elbrus, Europe } & 5633 & ? & ? \\ \hline \text { Mt. Kilimanjaro, Africa } & 5963 & ? & ? \\ \hline \text { Mt. Aconcagua, South America } & 6959 & ? & ? \\ \hline \end{array} $$

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$6+y \leq 8 ; 3$$

Write an equation or an inequality to model the real-life situation. The product of \(\$ 25\) and the number \(m\) of club memberships is greater than or equal to \(\$ 500.\)

Evaluate the expression for the given values of the variables. $$ c^{3}+d \text { when } c=4 \text { and } d=16 $$

A baseball player's batting average is found by dividing the number of hits \(h\) by the official times at bat \(b .\) During the 1998 baseball season, Alex Rodriguez of the Seattle Mariners had 686 official times at bat and made 213 hits. Use a verbal model to find his batting average. Round your answer to the nearest thousandth.

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$29-4 b>5: 7$$

Write an equation or an inequality to model the real-life situation. The perimeter \(P\) of a square is equal to four times the difference of a number \(s\) and two.

Evaluate the expression for the given values of the variables. $$ (d-3)^{2} \text { when } d=13 $$

MULTIPLE CHOICE You drove 200 miles in 3 hours 20 minutes. Which expression represents your average speed if \(d\) represents distance and \(t\) represents time? A \(d t\) B \(\frac{d}{t}\) C \(\frac{t}{d}\) D \(d+t\)

Write the expression in exponential form. \(x\) raised to the sixth power

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$t^{2}+6>40 ; 6$$

Write an equation or an inequality to model the real-life situation. The simple interest earned on a principal of three hundred dollars at an annual interest rate of \(x\) percent is less than or equal to seventy-two dollars.

Evaluate the expression for the given values of the variables. $$ 16+x^{3} \text { when } x=2 $$

MULTIPLE CHOICE You invest \(\$ 300\) at a simple annual interest rate of \(4.5 \%\). How much simple interest will you earn in 10 years? A \(\$ 115\) B \(\$ 120\) C \(\$ 135\) D \(\$ 150\)

Write the expression in exponential form. nine cubed

Hotel RATES A hotel charges \( 49.99 \) per room per night for adults and \( 44.10\) per room per night for senior citizens. The expression \(2 \)x\( 49.99+ \)3 x 44.1 represents the total cost of five rooms for two adults and three senior citizens for an overnight stay. Where in the expression can you put grouping symbols to make sure it is evaluated correctly?

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$a-7 \geq 15 ; 22$$

Write an equation or an inequality to model the real-life situation. The area \(A\) of a trapezoid is equal to one half times the sum of seven and nine, times a number \(h\) plus seven.

MULTIPLE CHOICE A rectangular computer screen measures 28 centimeters by 21 centimeters. What is the perimeter of the screen? A \(49 \mathrm{cm}\) B \(98 \mathrm{cm}\) C \(294 \mathrm{cm}\) D) \(588 \mathrm{cm}\)

Write the expression in exponential form. \(y \cdot y \cdot y \cdot y \cdot y \cdot y \cdot y\)

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$6 x-16<20 ; 7$$

Write an equation or an inequality to model the real-life situation. The square of the length \(c\) of the hypotenuse of a right triangle is equal to four squared plus three squared.

Use a calculator to evaluate the power. For keystroke help see Student Help box on page 11. $$ 2^{10} $$

In baseball the pitcher's mound is 60.5 feet from home plate. The strike zone, or distance across the plate, is 17 inches. The time it takes for a baseball to reach home plate can be determined by dividing the distance the ball travels by the speed at which the pitcher throws the baseball. If a pitcher throws a baseball at 90 miles per hour, how many seconds does it take for the baseball to reach home plate?

Write the expression in exponential form. \(15 \cdot 15 \cdot 15 \cdot 15\)

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$y^{3}-2 \leq 8 ; 2$$

The science club is selling magazine subscriptions at \(\$ 15\) each. The club wants to raise \(\$ 315\) for science equipment. Write a verbal model that relates the number of subscriptions, the cost of each subscription, and the amount of money the club needs to raise.

Use a calculator to evaluate the power. For keystroke help see Student Help box on page 11. $$ 5^{9} $$

Evaluate the expression. \(\frac{3 b+3 c}{5}\) when \(b=1\) and \(c=9\)

CHECKING SOLUTIONS OF INEQUALTTIES Check whether the given number is a solution of the inequality. $$r+2 r<30 ; 9$$

The science club is selling magazine subscriptions at \(\$ 15\) each. The club wants to raise \(\$ 315\) for science equipment. Assign labels and write an algebraic model based on your verbal model.