Chapter 2

Write each decimal as a percent. $$ 5 $$

In your own words, explain why a solution of a word problem should be checked using the original wording of the problem and not the equation written from the wording.

The graph shows the number of U.S. Starbucks locations from 2002 to \(2008 .\) The height of the graph for each year shown corresponds to the number of Starbucks locations in the United States. Use this graph to answer . (We study graphs such as this further in Section 6.1.) Between which two years did the greatest increase in the number of Starbucks locations occur?

Match each equation in the first column with its solution in the second column. Items in the second column may be used more than once. a. all real numbers b. no solution C. 0 $$ 2 x-6 x-10=-4 x+3-10 $$

Use the addition property to fill in the blank so that the middle equation simplifies to the last equation. See the Concept Check in this section. $$ \begin{aligned} x-4 &=-9 \\ x-4+(\quad) &=-9+(\quad) \\ x &=-5 \end{aligned} $$

Write each algebraic expression described. Simplify if possible. See Example \(11 .\) If \(x\) represents the first of two consecutive odd integers, express the sum of the two integers in terms of \(x\).

Solve. \(N=R+\frac{V}{G}\) for \(V\) (Urban forestry: tree plantings per year)

Give an example of how you recently solved a problem using mathematics.

Use the addition property to fill in the blank so that the middle equation simplifies to the last equation. See the Concept Check in this section. $$ \begin{aligned} a+9 &=15 \\ a+9+(\quad) &=15+(\quad) \\ a &=6 \end{aligned} $$

Write each algebraic expression described. Simplify if possible. See Example \(11 .\) If \(x\) is the first of three consecutive even integers, write their sum as an algebraic expression in \(x\).

Solve. B=\frac{F}{P-V} \text { for } V

Match each equation in the first column with its solution in the second column. Items in the second column may be used more than once. a. all real numbers b. no solution C. 0 $$ 9 x-20=8 x-20 $$

Write each algebraic expression described. Simplify if possible. See Example \(11 .\) If \(x\) is the first of four consecutive integers, express the sum of the first integer and the third integer as an algebraic expression containing the variable \(x\).

The formula \(V=l w h\) is used to find the volume of a box. If the length of a box is doubled, the width is doubled, and the height is doubled, how does this affect the volume? Explain your answer.

Match each equation in the first column with its solution in the second column. Items in the second column may be used more than once. a. all real numbers b. no solution C. 0 $$ -x+15=x+15 $$

Fill in the blanks with numbers of your choice so that each equation has the given solution. Note: Each blank will be replaced with a different number. \(x-\) ________ \(=\) _______; Solution: -10

Write each algebraic expression described. Simplify if possible. See Example \(11 .\) If \(x\) is the first of two consecutive integers, express the sum of 20 and the second consecutive integer as an algebraic expression containing the variable \(x\).

The formula \(A=b h\) is used to find the area of a parallelogram. If the base of a parallelogram is doubled and its height is doubled, how does this affect the area? Explain your answer.

Fill in the box with \(<,>, \leq,\) or \(\geq\). See the Concept Check in this section. Since \(3<5,\) then 3(-4)\(\square 5(-4)\)

Explain the difference between simplifying an expression and solving an equation.

The sum of the angles of a triangle is \(180^{\circ} .\) If one angle of a triangle measures \(x^{\circ}\) and a second angle measures \((2 x+7)^{\circ},\) express the measure of the third angle in terms of \(x\). Simplify the expression.

Write each algebraic expression described. Simplify if possible. See Example \(11 .\) Classrooms on one side of the science building are all numbered with consecutive even integers. If the first room on this side of the building is numbered \(x,\) write an expression in \(x\) for the sum of five classroom numbers in a row. Then simplify this expression.

Fill in the box with \(<,>, \leq,\) or \(\geq\). See the Concept Check in this section. If \(m \leq n,\) then \(2 m \square 2 n\)

On your own, write an expression and then an equation. Label each.

A quadrilateral is a four-sided figure (like the one shown in the figure) whose angle sum is \(360^{\circ} .\) If one angle measures \(x^{\circ},\) a second angle measures \(3 x^{\circ},\) and a third angle measures \(5 x^{\circ},\) express the measure of the fourth angle in terms of \(x\). Simplify the expression.

Write each algebraic expression described. Simplify if possible. See Example \(11 .\) Two sides of a quadrilateral have the same length, \(x\) while the other two sides have the same length, both being the next consecutive odd integer. Write the sum of these lengths. Then simplify this expression.

Find the temperature at which the Celsius measurement and the Fahrenheit measurement are the same number.

Fill in the box with \(<,>, \leq,\) or \(\geq\). See the Concept Check in this section. If \(m \leq n,\) then \(-2 m \square-2 n\)

In your own words, explain what is meant by the solution of an equation.

Simplify each expression. See Section \(1.8 .\) \(5 x+2(x-6)\)

In your own words, explain how to check a solution of an equation.

Simplify each expression. See Section \(1.8 .\) \(-7 y+2 y-3(y+1)\)

When solving an inequality, when must you reverse the direction of the inequality symbol?

Use a calculator to determine the solution of each equation. $$ 36.766+x=-108.712 $$

Simplify each expression. See Section \(1.8 .\) \(6(2 z+4)+20\)

Flying fish do not actually fly, but glide. They have been known to travel a distance of 1300 feet at a rate of 20 miles per hour. How many seconds would it take to travel this distance?

If both sides of the inequality \(-3 x<-30\) are divided by \(3,\) do you reverse the direction of the inequality symbol? Why or why not?

Simplify each expression. See Section \(1.8 .\) \(-(3 a-3)+2 a-6\)

A glacier is a giant mass of rocks and ice that flows downhill like a river. Exit Glacier, near Seward, Alaska, moves at a rate of 20 inches a day. Find the distance in feet the glacier moves in a year. (Assume 365 days a year.) Round to two decimal places.

Eric Daly has scores of \(75,83,\) and 85 on his history tests. Use an inequality to find the scores he can make on his final exam to receive a \(\mathrm{B}\) in the class. The final exam counts as two tests, and a \(\mathrm{B}\) is received if the final course average is greater than or equal to 80 .

Solve. $$ 1000(7 x-10)=50(412+100 x) $$

Simplify each expression. See Section \(1.8 .\) \(-(x-1)+x\)

Substitute the given values into each given formula and solve for the unknown variable. If necessary, round to one decimal place. $$ I=P R T ; \quad I=1,056,000, R=0.055, T=6 $$

Maria Lipco has scores of \(85,95,\) and 92 on her algebra tests. Use an inequality to find the scores she can make on her final exam to receive an A in the course. The final exam counts as three tests, and an \(\mathrm{A}\) is received if the final course average is greater than or equal to 90 . Round to one decimal place.

Solve. $$ 1000(x+40)=100(16+7 x) $$

Simplify each expression. See Section \(1.8 .\) \(8(z-6)+7 z-1\)

Substitute the given values into each given formula and solve for the unknown variable. If necessary, round to one decimal place. $$ I=P R T ; \quad I=3750, P=25,000, R=0.05 $$

Solve. $$ 0.035 x+5.112=0.010 x+5.107 $$

Fill in the blank with a number of your choice so that each equation has the given solution. 6 x= ____ ; solution: -8

Substitute the given values into each given formula and solve for the unknown variable. If necessary, round to one decimal place. $$ V=\frac{4}{3} \pi r^{3} ; \quad r=3 $$