Chapter 1

Determine whether each statement is true or false. $$ 11 \nsubseteq \mathbb{Q} $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. the product of \(d\) and \(4,\) decreased by 15

Solve each equation. Check each result. See Example 3. $$ -\frac{9}{8} s=3 $$

Complete each statement so that the indicated property is illustrated. See Example 1. \(h+(-h)=______ \) Additive inverse property

Determine whether each statement is true or false. $$ \mathbb{Q} \nsubseteq \mathbb{Z} $$

Perform the operations. See Example 3 . $$ -0.4(-0.6) $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. the quotient of the base and twice the height

Find the volume of each figure to the nearest hundredth. See Example 4. (Answers may vary slightly depending on which approximation of is used.) A rectangular solid with dimensions \(2.51 \mathrm{ft}, 3.71 \mathrm{ft},\) and \(10.21 \mathrm{ft}\)

Vertical Angles. When two lines intersect, four angles are formed. Angles that are side-by-side, such as \(\angle 1\) (angle 1 ) and \(\angle 2,\) are called adjacent angles. Angles that are nonadjacent, such as \(\angle 1\) and \(\angle 3\) or \(\angle 2\) and \(\angle 4,\) are called vertical angles. From geometry, we know that if two lines intersect, vertical angles have the same measure. If \(\angle 1=3 x+10^{\circ}\) and \(\angle 3=5 x-10^{\circ},\) find \(x\)

List the elements of $$ \left\\{-3,-\frac{8}{5}, 0, \frac{2}{3}, 1, \sqrt{3}, 2, \pi, 4.75,916 . \overline{6}\right\\} $$ that belong to the following sets. Natural numbers

Perform the operations. See Example 3 . $$ -5(6)(-2) $$

Entrepreneurs. Last year, a women's professional organization made two small- business loans totaling \(\$ 28,000\) to young women beginning their own businesses. The money was lent at \(7 \%\) and \(10 \%\) simple interest rates. If the annual income the organization received from these loans was \(\$ 2,560,\) what was each loan amount?

Solve each equation. Check each result. See Example 3. $$ -\frac{5}{8} a-20=-10 $$

Find the volume of each figure to the nearest hundredth. See Example 4. (Answers may vary slightly depending on which approximation of is used.) A pyramid whose base is a square with each side measuring \(2.57 \mathrm{cm}\) and with a height of \(12.32 \mathrm{cm}\)

List the elements of $$ \left\\{-3,-\frac{8}{5}, 0, \frac{2}{3}, 1, \sqrt{3}, 2, \pi, 4.75,916 . \overline{6}\right\\} $$ that belong to the following sets. Whole numbers

Perform the operations. See Example 3 . $$ -9(-1)(-3) $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. 14 less than eleven-ninths of a number

Paula used some of the money that she received from an inheritance to invest in a certificate of deposit paying \(7 \%\) annual interest and the rest of the money in a promising biotech company offering an annual return of \(10 \%\). She invested twice as much in the \(10 \%\) investment as she did in the \(7 \%\) investment. Her combined annual income from the two investments was \(\$ 4,050 .\) A. How much did she invest in each account? B. How much did she inherit?

Solve each equation. Check each result. See Example 3. $$ \frac{5}{6} k-7.5=7.5 $$

e-Readers. The perimeter of the rectangular display screen of Amazon's Kindle 3 is 16.8 inches. If the height is 1.2 inches greater than the width, find the dimensions of the screen. (IMAGE CANNOT COPY)

List the elements of $$ \left\\{-3,-\frac{8}{5}, 0, \frac{2}{3}, 1, \sqrt{3}, 2, \pi, 4.75,916 . \overline{6}\right\\} $$ that belong to the following sets. Integers

Perform the operations. See Example 3 . $$ \left(-\frac{3}{5}\right)\left(\frac{10}{7}\right) $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. one-hundredth of the distance

Solve each equation. Check each result. See Example 3. $$ \frac{2}{5} c-12.2=1.8 $$

U.S. Currency. The perimeter of a one-dollar bill is 17.5 inches and the length is 0.92 in. more than twice the width. Find the dimensions of a one-dollar bill.

List the elements of $$ \left\\{-3,-\frac{8}{5}, 0, \frac{2}{3}, 1, \sqrt{3}, 2, \pi, 4.75,916 . \overline{6}\right\\} $$ that belong to the following sets. Rational numbers

Perform the operations. See Example 3 . $$ \left(-\frac{6}{7}\right)\left(-\frac{5}{12}\right) $$

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. double the difference of a number and 18

Solve each formula for the specified variable. See Example 5. $$ d=r t \quad \text { for } t $$

List the elements of $$ \left\\{-3,-\frac{8}{5}, 0, \frac{2}{3}, 1, \sqrt{3}, 2, \pi, 4.75,916 . \overline{6}\right\\} $$ that belong to the following sets. Irrational numbers

Perform the operations. See Examples 4 and 5 . $$ \frac{-8}{4} $$

Translate each verbal model into a mathematical model. Answers may vary depending on the variables chosen. The cost each semester is the sum of \(\$ 13\) times the number of units taken and a student services fee of \(\$ 24\)

Solve each equation. Check each result. See Example 4. $$ 9 n+36=6 n $$

Quilting. Throughout history, most artists and designers have felt that golden rectangles with a length 1.618 times as long as their width have the most visually attractive shape. A woman is planning to make a quilt in the shape of a golden rectangle. She has exactly 22 feet of a special lace that she plans to sew around the edge of the quilt. What should the length and width of the quilt be? Round both answers up to the nearest hundredth.

Solve each formula for the specified variable. See Example 5. $$ E=m c^{2} \text { for } m $$

Perform the operations. See Examples 4 and 5 . $$ \frac{16}{-4} $$

List the elements of $$ \left\\{-3,-\frac{8}{5}, 0, \frac{2}{3}, 1, \sqrt{3}, 2, \pi, 4.75,916 . \overline{6}\right\\} $$ that belong to the following sets. Real numbers

Translate each verbal model into a mathematical model. Answers may vary depending on the variables chosen. The yearly salary is \(\$ 25,000\) plus \(\$ 75\) times the number of years of experience.

Solve each equation. Check each result. See Example 4. $$ 60 t-50=15 t-5 $$

Ranching. \(\quad\) A farmer has 624 feet of fencing to enclose a pasture. Because a river runs along one side, fencing will be needed on only three sides. Find the dimensions of the pasture if its length is double its width. (IMAGE CANNOT COPY)

Solve each formula for the specified variable. See Example 5. \(V=\) Iwh for \(h\)

Perform the operations. See Examples 4 and 5 . $$ \frac{84}{-6} $$

List the elements of $$ \left\\{-3,-\frac{8}{5}, 0, \frac{2}{3}, 1, \sqrt{3}, 2, \pi, 4.75,916 . \overline{6}\right\\} $$ that belong to the following sets. Even natural numbers

Translate each verbal model into a mathematical model. Answers may vary depending on the variables chosen. The quotient of the number of clients and seventy-five gives the number of social workers needed.

An airplane leaves Los Angeles bound for Caracas, Venezuela, flying at an average rate of 500 mph. At the same time, another airplane leaves Caracas bound for Los Angeles, averaging 550 mph. If the airports are \(3,675\) miles apart, when will the air traffic controllers have to make the pilots aware that the planes are passing each other?

Solve each equation. Check each result. See Example 4. $$ 100 s-75=50 s+75 $$

Multiply. See Example 2 . $$-6 s(-4 t)(-1)$$

Solve each formula for the specified variable. See Example 5. $$ I=P r t \quad \text { for } t $$

List the elements of $$ \left\\{-3,-\frac{8}{5}, 0, \frac{2}{3}, 1, \sqrt{3}, 2, \pi, 4.75,916 . \overline{6}\right\\} $$ that belong to the following sets. Odd integers

Perform the operations. See Examples 4 and 5 . $$ \frac{-78}{6} $$