Chapter 1

Evaluate the expression for the given value of the variable. $$ 5 y^{5} \text { when } y=2 $$

EQUATIONS AND INEQUALITIES Match the verbal sentence with its mathematical representation. The product of 16 and \(x\) is less than 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. Use mental math to solve the equation. What does the solution represent?

Evaluate the expression for the given value of the variable. (Review 1.1) $$\frac{4}{3} \cdot x \text { when } x=\frac{1}{6}$$

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

The girls' basketball team scored 544 points in 17 games last year. This year the coach has set a goal for the team to score at least 5 more points per game. If 18 games are scheduled for this year, write an inequality that represents the total number of points the team must equal or exceed to meet their season goal.

The area of a square is \(s^{2} .\) Show the relationship between the side length of a square and its area by copying and completing the following table. $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Side length, } s & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Area, } s^{2} & ? & ? & ? & ? & ? \\ \hline \end{array} $$

Evaluate the expression when \(x=2\). \(2 x\)

Evaluate the expression for the given value of the variable. (Review 1.1) \(9 d\) when \(d=0.5\)

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

Translate the phrase "a number decreased by the quotient of three and four." (A)\(n-\frac{3}{4}\) (B) \(=\frac{3}{4}-n\) (C) \(\frac{n-3}{4}\) (D) \(\frac{3}{4-n}\)

Copy and complete the table. What pattern do you see? $$\begin{array}{|l|l|l|l|l|} \hline \text { Power } & 10^{2} & 100^{2} & 1000^{2} & 10,000^{2} \\ \hline \text { Evaluate } & 100 & ? & ? & ? \\\ \hline \end{array} $$

Evaluate the expression when \(x=2\). $$ (x)(x) $$

Evaluate the expression for the given value of the variable. (Review 1.1) $$\frac{5}{16}-p \text { when } p=\frac{3}{8}$$

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

Give the correct algebraic translation of "Howard's hourly wage \(h\) is \(\$ 2\) greater than Marla's hourly wage \(m\)." (A)\(h < m+2\) (B) \(h=m+2\) (C) \(m=h+2\) (D) \(h > m+2\)

One room in Jean's apartment is a square measuring 12.2 feet along the base of each wall. How many square feet of wall-to-wall carpet does Jean need to carpet the room?

Evaluate the expression for the given value of the variable. (Review 1.2) $$(6 w)^{2} \text { when } w=5$$

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

A jet is flying nonstop from Baltimore, Maryland, to Jacksonville, Florida, at a speed \(r\) of 500 miles per hour. The distance \(d\) between the two cities is about 680 miles. Which equation models the number of hours \(t\) the flight will take? (A)\(t=\frac{680}{500}\) (B) \(t=680(500)\) (C) \(680=\frac{t}{500}\) (D) \(t=\frac{500}{680}\)

In 1997 the artist Jon Kuhn of North Carolina created a cubic sculpture called Crystal Victory, shown at the left. Each edge of the solid glass cube is 9.5 inches in length. How much liquid glass did Kuhn need to make the cube?

Evaluate the expression for the given value of the variable. (Review 1.2) $$4\left(t^{3}\right) \text { when } t=3$$

Your school is building a new computer center. Four hundred square feet of the center will be available for computer stations. Each station requires 20 square feet. You want to find how many computer stations can be placed in the new center. You write the equation \(20 x=400\) to model the situation. What do \(20, x,\) and 400 represent? Solve the equation. Check your solution.

Use the following information. You are in charge of the music for a school dance. The school's budget allows only \(\$ 300\) for music, which is enough to hire a disc jockey for 4 hours. You would rather hire a live band, but the band charges \(\$ 135\) per hour. Your school does not allow students to be charged an admission fee. To raise the money for a live band, you obtain permission for a voluntary contribution of \(\$ 1.25\) per person. How much extra money do you need to raise?

Each dimension of the cubical storage space inside a fireproof safe is 12 inches. What is the volume of the storage space?

Evaluate the expression for the given value of the variable. (Review 1.2) $$9 b^{2} \text { when } b=8$$

You are playing a new computer game. For every eight screens you complete, you receive a bonus. You want to know how many bonuses you will receive after completing 96 screens. You write the equation \(8 x=96\) to model the situation. What do \(8, x,\) and 96 represent? Solve the equation. Check your solution.

Use the following information. You are in charge of the music for a school dance. The school's budget allows only \(\$ 300\) for music, which is enough to hire a disc jockey for 4 hours. You would rather hire a live band, but the band charges \(\$ 135\) per hour. Your school does not allow students to be charged an admission fee. To raise the money for a live band, you obtain permission for a voluntary contribution of \(\$ 1.25\) per person. How many students must contribute \(\$ 1.25\) to cover the cost of a live band?

A swimming pool is 50 meters long, 19.5 meters wide, and 3 meters deep. Use the formula for the volume of a rectangular prism to find the volume of water in the pool. The formula is the length times the width times the height.

Evaluate the expression for the given value of the variable. (Review 1.2) $$5 x^{2} \text { when } x=16$$

You are taking a trip by automobile with the family of a friend. You have \(\$ 65\) to help pay for gas. It costs \(\$ 15\) to fill the tank. Can you completely fill the gas tank four times? You use the inequality \(15 x \leq 65\) to model the situation. What do \(15, x,\) and 65 represent?

Compare using \(<,=,\) or \(>.\) $$0.3 \underline{?} 0.30$$

The formula for the volume of a pyramid is \(\frac{1}{3}\) times the height times the area of the base. The Rain Forest Pyramid in Mood Gardens near Galveston, Texas, is 100 feet high and 200 feet along each side of its square base. What is the volume of space inside the Rain Forest Pyramid?

Evaluate the expression for the given value of the variable. (Review 1.2) $$(7 x)^{3} \text { when } x=2$$

You are budgeting money to buy a violin and bow that cost \(\$ 250\) including tax. If you save \(\$ 5\) per week, will you have enough money in a year? You write the inequality \(5 n \geq 250\) to model the situation. What do \(5, n,\) and 250 represent? Solve the inequality.

Compare using \(<,=,\) or \(>.\) $$21.1 \underline{?} 20 .99$$

Evaluate the expression for the given value of the variable. (Review 1.2) $$6 y^{5} \text { when } y=4$$

Match the problem with the formula needed to solve the problem. Then use the Guess, Check, and Revise strategy or another problem-solving strategy to solve the problem. Area of a rectangle \(\quad A=l w \quad\) Distance \(\quad d=r t\) Simple interest \(\quad I=P r t \quad\) Volume of a cube Temperature \(\quad C=\frac{5}{9}(F-32)\) Surface area of a cube \(S=6 s^{2}\) What is the average speed of a runner who completes a \(10,000\) -meter race in 25 minutes?

Compare using \(<,=,\) or \(>.\) $$6.7 \underline{?} 6 .079$$

Copy the table. $$ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text { Power } & 9^{1} & 9^{2} & 9^{3} & 9^{4} & 9^{5} & 9^{6} & 9^{7} & 9^{8} \\ \hline \text { Evaluate } & ? & ? & ? & ? & ? & ? & ? & ? \\ \hline \end{array} $$ Evaluate the powers of 9 in the table. What pattern do you see for the last digit of each product?

PINTEREST EARNED You deposit \(\ 120\) in a savings account that pays an annual interest rate of \(2.5 \% .\) How much simple interest would you earn in 2 years? (Review 1.1 )

Match the problem with the formula needed to solve the problem. Then use the Guess, Check, and Revise strategy or another problem-solving strategy to solve the problem. Area of a rectangle \(\quad A=l w \quad\) Distance \(\quad d=r t\) Simple interest \(\quad I=P r t \quad\) Volume of a cube Temperature \(\quad C=\frac{5}{9}(F-32)\) Surface area of a cube \(S=6 s^{2}\) How long must \(\$ 1000\) be invested at an annual interest rate of \(3 \%\) to earn \(\$ 300\) in simple interest?

Compare using \(<,=,\) or \(>.\) $$5.68 \underline{?}=5.678$$

Copy the table. $$ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text { Power } & 9^{1} & 9^{2} & 9^{3} & 9^{4} & 9^{5} & 9^{6} & 9^{7} & 9^{8} \\ \hline \text { Evaluate } & ? & ? & ? & ? & ? & ? & ? & ? \\ \hline \end{array} $$ Make a table like the one shown for powers of \(8 .\) Describe any patterns.

If you are driving at a constant speed of 68 miles per hour, how long will it take you to travel 170 miles? (Review 1.1 )

Match the problem with the formula needed to solve the problem. Then use the Guess, Check, and Revise strategy or another problem-solving strategy to solve the problem. Area of a rectangle \(\quad A=l w \quad\) Distance \(\quad d=r t\) Simple interest \(\quad I=P r t \quad\) Volume of a cube Temperature \(\quad C=\frac{5}{9}(F-32)\) Surface area of a cube \(S=6 s^{2}\) A car travels 60 miles per hour for a distance of 300 miles. How long did the trip take?

Compare using \(<,=,\) or \(>.\) $$0.333 \underline{?} 0.3333$$

Copy the table. $$ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text { Power } & 9^{1} & 9^{2} & 9^{3} & 9^{4} & 9^{5} & 9^{6} & 9^{7} & 9^{8} \\ \hline \text { Evaluate } & ? & ? & ? & ? & ? & ? & ? & ? \\ \hline \end{array} $$ Make a table for powers of \(7 .\) Describe any patterns.

Compare using \(<,=,\) or \(>.\) $$18.45 \underline{?} 18.5$$

Match the problem with the formula needed to solve the problem. Then use the Guess, Check, and Revise strategy or another problem-solving strategy to solve the problem. Area of a rectangle \(\quad A=l w \quad\) Distance \(\quad d=r t\) Simple interest \(\quad I=P r t \quad\) Volume of a cube Temperature \(\quad C=\frac{5}{9}(F-32)\) Surface area of a cube \(S=6 s^{2}\) You measure the temperature of a substance in a chemistry lab at \(32^{\circ} \mathrm{F}\). What is the temperature in degrees Celsius?