?In Exercises 97–102, write each algebraic expression without parentheses.\(-(-14

Fill in each blank so that the resulting statement is true. A combination of numbers, variables, and operation symbols is called an algebraic _________.

Fill in each blank so that the resulting statement is true. If n is a counting number, \(b^{n}\) , read _____, indicates that there are n factors of b . The number b is called the _____ and the number n is called the _________. ________________ Equation Transcription: Text Transcription: b^n

Fill in each blank so that the resulting statement is true. An equation that expresses a relationship between two or more variables, such as \(H=\frac{9}{10}(220-a)\), is called a/an _______. The process of finding such equations to describe real-world phenomena is called mathematical ________. Such equations, together with the meaning assigned to the variables, are called mathematical_______. ________________ Equation Transcription: Text Transcription: H=9/10(220-a)

Fill in each blank so that the resulting statement is true. The set of elements common to both set A and set B is called the _______ of sets A and B , and is symbolized by _______.

Fill in each blank so that the resulting statement is true. The set of elements that are members of set A or set B or of both sets is called the _______ of sets A or B and is symbolized by _______.

Fill in each blank so that the resulting statement is true. The set {1, 2, 3, 4, 5, ...} is called the set of _______ numbers .

Fill in each blank so that the resulting statement is true. The set {0, 1, 2, 3, 4, 5, ...} is called the set of _______ numbers .

Fill in each blank so that the resulting statement is true. The set of numbers in the form ab , where a and bbelong to the set in Exercise 8 and b0, is called the set of numbers .

Fill in each blank so that the resulting statement is true. The set of numbers in the form \(\frac{a}{b}\) , where a and b belong to the set in Exercise 8 and \(b \neq 0\), is called the set of _______ numbers . ________________ Equation Transcription: Text Transcription: a/b b neq 0

Fill in each blank so that the resulting statement is true. The set of numbers whose decimal representations are neither terminating nor repeating is called the set of _______ numbers .

Fill in each blank so that the resulting statement is true. Every real number is either a/an number or a/an _______ number .

Fill in each blank so that the resulting statement is true. The notion |x| is read the ______ of x/ If \(x \geq 0\), then |x| = _____. If \(x<0\), then |x| = _____. ________________ Equation Transcription: Text Transcription: x geq 0 x<0

Fill in each blank so that the resulting statement is true. The commutative properties state that \(a+b=\) ______ and \(ab=\) _______. ________________ Equation Transcription: Text Transcription: a+b= ab=

Fill in each blank so that the resulting statement is true. The associative properties state the \((a+b)+c =\) ______ and _____ \(=a(bc)\). ________________ Equation Transcription: Text Transcription: (a+b)+c = =a(bc)

Fill in each blank so that the resulting statement is true. The distributive property states that \(a(b+c)= \) ______. ________________ Equation Transcription: Text Transcription: a(b+c)=

Fill in each blank so that the resulting statement is true. \(a+(-a)=\) ____: The sum of a real number and its additive _______ is ____, the additive _______. ________________ Equation Transcription: Text Transcription: a+(-a)=

Fill in each blank so that the resulting statement is true. \(a \cdot \frac{1}{a}=1, a \neq 0\): The product of a nonzero real number and its multiplicative _______ is _____, the multiplicative ________, ________________ Equation Transcription: Text Transcription: a time 1/a = 1, a neq 0

Fill in each blank so that the resulting statement is true. An algebraic expression is _________ when parentheses have been removed and like terms have been combined.

Fill in each blank so that the resulting statement is true. \(-(-a)=\) _____. ________________ Equation Transcription: Text Transcription: -(-a)=

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(7+5 x, \text { for } x=10\) ________________ Equation Transcription: Text Transcription: 7+5x, for x = 10

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(8+6 x, \text { for } x=5\) ________________ Equation Transcription: Text Transcription: 8+6x, for x = 5

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(6 x-y, \text { for } x=3 \text { and } y=8\) ________________ Equation Transcription: Text Transcription: 6x-y, for x = 3 and y = 8

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(8 x-y, \text { for } x=3 \text { and } y=4\) ________________ Equation Transcription: Text Transcription: 8x-y, for x = 3 and y = 4

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(x^{2}+3 x, \text { for } x=8\) ________________ Equation Transcription: Text Transcription: x^2+3x, for x = 8

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(x^{2}+5 x, \text { for } x=6\) ________________ Equation Transcription: Text Transcription: x^2+5x, for x = 6

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(x^{2}-6 x+3, \text { for } x=7\) ________________ Equation Transcription: Text Transcription: x^2-6x+3, for x = 7

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(x^{2}-7 x+4, \text { for } x=8\) ________________ Equation Transcription: Text Transcription: x^2-7x+4, for x = 8

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(4+5(x-7)^{3}, \text { for } x=9\) ________________ Equation Transcription: Text Transcription: 4+5(x-7)^3, for x = 9

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(6+5(x-6)^{3}, \text { for } x=8\) ________________ Equation Transcription: Text Transcription: 6+5(x-6)^3, for x = 8

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(x^{2}-3(x-y), \text { for } x=8 \text { and } y=2\) ________________ Equation Transcription: Text Transcription: x^2-3(x-y), for x = 8 and y = 2

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(x^{2}-4(x-y), \text { for } x=8 \text { and } y=3\) ________________ Equation Transcription: Text Transcription: x^2-4(x-y), for x = 8 and y = 3

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(\frac{5(x+2)}{2 x-14}, \text { for } x=10\) ________________ Equation Transcription: Text Transcription: 5(x+2)/2x-14, for x = 10

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(\frac{7(x-3)}{2 x-16}, \text { for } x=9\) ________________ Equation Transcription: Text Transcription: 7(x-3)/2x-16, for x = 9

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(\frac{2 x+3 y}{x+1}, \text { for } x=-2 \text { and } y=4\) ________________ Equation Transcription: Text Transcription: 2x+3y/x+1, for x = -2 and y = 4

In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). \(\frac{2 x+y}{x y-2 x} \text {, for } x=-2 \text { and } y=4\) ________________ Equation Transcription: Text Transcription: 2x+y/xy-2x, for x = -2 and y = 4

The formula \(C=\frac{5}{9}(F-32)\) expresses the relationship between Fahrenheit temperature, F,and Celsius temperature, C. In Exercises 17–18, use the formula to convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. 50°F ________________ Equation Transcription: Text Transcription: C=5/9(F-32)

The formula \(C=\frac{5}{9}(F-32)\) expresses the relationship between Fahrenheit temperature, F,and Celsius temperature, C. In Exercises 17–18, use the formula to convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. 86°F ________________ Equation Transcription: Text Transcription: C=5/9(F-32)

A football was kicked vertically upward from a height of \(4\) feet with an initial speed of \(60\) feet per second. The formula \(h=4+60 t-16 t^{2}\) describes the ball’s height above the ground, \(h\), in feet, \(t\) seconds after it was kicked. Use this formula to solve Exercises 19–20. What was the ball’s height \(2\) seconds after it was kicked? Equation Transcription: Text Transcription: 4 60 h=4+60t-16t^2 h t 2

A football was kicked vertically upward from a height of \(4\) feet with an initial speed of \(60\) feet per second. The formula \(h=4+60 t-16 t^{2}\) describes the ball’s height above the ground, \(h\), in feet, \(t\) seconds after it was kicked. Use this formula to solve Exercises 19–20. What was the ball’s height \(3\) seconds after it was kicked? Equation Transcription: Text Transcription: 4 60 h=4+60t-16t^2 h t 3

In Exercises 21–28, find the intersection of the sets. \(\{1,2,3,4\} \cap\{2,4,5\}\) Equation Transcription: Text Transcription: {1,2,3,4} \cap {2,4,5}

In Exercises 21–28, find the intersection of the sets. \(\{1,3,7\} \cap\{2,3,8\}\) Equation Transcription: Text Transcription: {1,3,7} \cap {2,3,8}

In Exercises 21–28, find the intersection of the sets. \(\{s, e, t\} \cap\{t, e, s\}\) Equation Transcription: Text Transcription: {s,e,t} \cap {t,e,s}

In Exercises 21–28, find the intersection of the sets. \(\{r, e, a, l\} \cap\{l, e, a, r\}\) Equation Transcription: Text Transcription: {r,e,a,l} \cap {l,e,a,r}

In Exercises 21–28, find the intersection of the sets. \(\{1,3,5,7\} \cap\{2,4,6,8,10\}\) Equation Transcription: Text Transcription: {1,3,5,7} \cap {2,4,6,8,10}

In Exercises 21–28, find the intersection of the sets. \(\{0,1,3,5\} \cap\{-5,-3,-1\}\) Equation Transcription: Text Transcription: {0,1,3,5} \cap {-5,-3,-1}

In Exercises 21–28, find the intersection of the sets. \(\{a, b, c, d\} \cap \varnothing\) Equation Transcription: ? Text Transcription: {a,b,c,d} \cap \varnothing

In Exercises 21–28, find the intersection of the sets. \(\{w, y, z\} \cap \varnothing\) Equation Transcription: ? Text Transcription: {w,y,z} \cap \varnothing

In Exercises 29–34, find the union of the sets. \(\{1,2,3,4\} \cup\{2,4,5\}\) Equation Transcription: Text Transcription: {1,2,3,4} \cup {2,4,5}

In Exercises 29–34, find the union of the sets. \(\{1,3,7,8\} \cup\{2,3,8\}\) Equation Transcription: Text Transcription: {1,3,7,8} \cup {2,3,8}

In Exercises 29–34, find the union of the sets. \(\{1,3,5,7\} \cup\{2,4,6,8,10\}\) Equation Transcription: Text Transcription: {1,3,5,7} \cup {2,4,6,8,10}

In Exercises 29–34, find the union of the sets. \(\{0,1,3,5\} \cup\{2,4,6\}\) Equation Transcription: Text Transcription: {0,1,3,5} \cup {2,4,6}

In Exercises 29–34, find the union of the sets. \(\{a, e, i, o, u\} \cup \varnothing\) Equation Transcription: ? Text Transcription: {a,e,i,o,u} \cup \varnothing

In Exercises 29–34, fi nd the union of the sets. \(\{e, m, p, t, y\} \cup \varnothing\) Equation Transcription: ? Text Transcription: {e,m,p,t,y} \cup \varnothing

In Exercises 35–38, list all numbers from the given set that are a. natural numbers, b. Whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. \(\left\{-9,-\frac{4}{5}, 0,0.25, \sqrt{3}, 9.2, \sqrt{100}\right\}\) Equation Transcription: Text Transcription: {-9,-4/5,0,0.25, sqrt 3,9.2, sqrt 100}

In Exercises 35–38, list all numbers from the given set that are a. natural numbers, b. Whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. \(\{-7,-0 . \overline{6}, 0, \sqrt{49,} \sqrt{50}\}\) Equation Transcription: Text Transcription: {-7,-0.\overline 6,0,sqrt 49, sqrt 50}

In Exercises 35–38, list all numbers from the given set that are a. natural numbers, b. Whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. \(\left\{-11,-\frac{5}{6}, 0,0.75, \sqrt{5}, \pi, \sqrt{64}\right\}\) Equation Transcription: Text Transcription: {-11,-5/6,0,0.75, sqrt 5, pi, sqrt 64}

In Exercises 35–38, list all numbers from the given set that are a. natural numbers, b. Whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. \(\{-5,-0 . \overline{3}, 0, \sqrt{2}, \sqrt{4}\}\) Equation Transcription: Text Transcription: {-11,-0.overline 3,0, sqrt 2, sqrt 4}

Give an example of a whole number that is not a natural number.

Give an example of a rational number that is not an integer.

Give an example of a number that is an integer, a whole number, and a natural number.

Give an example of a number that is a rational number, an integer, and a real number.

Determine whether each statement in Exercises 43–50 is true or false. \(-13 \leq-2\) ________________ Equation Transcription: Text Transcription: -13 leq -2

Determine whether each statement in Exercises 43–50 is true or false. \(-6>2\) ________________ Equation Transcription: Text Transcription: -6>2

Determine whether each statement in Exercises 43–50 is true or false. \(4 \geq-7\) ________________ Equation Transcription: Text Transcription: 4 geq -7

Determine whether each statement in Exercises 43–50 is true or false. \(-13<-5\) ________________ Equation Transcription: Text Transcription: -13<-5

Determine whether each statement in Exercises 43–50 is true or false. \(-\pi \geq-\pi\) ________________ Equation Transcription: Text Transcription: -pi geq -pi

Determine whether each statement in Exercises 43–50 is true or false. \(-3>-13\) ________________ Equation Transcription: Text Transcription: -3>-13

Determine whether each statement in Exercises 43–50 is true or false. \(0 \geq-6\) ________________ Equation Transcription: Text Transcription: 0 geq -6

Determine whether each statement in Exercises 43–50 is true or false. \(0 \geq-13\) ________________ Equation Transcription: Text Transcription: 0 geq -13

In Exercises 51–60, rewrite each expression without absolute value bars. \(|300|\) ________________ Equation Transcription: Text Transcription: |300|

In Exercises 51–60, rewrite each expression without absolute value bars. \(|-203|\) ________________ Equation Transcription: Text Transcription: |-203|

In Exercises 51–60, rewrite each expression without absolute value bars. \(|12-\pi|\) ________________ Equation Transcription: Text Transcription: |12-pi|

In Exercises 51–60, rewrite each expression without absolute value bars. \(|7-\pi|\) ________________ Equation Transcription: Text Transcription: |7-pi|

In Exercises 51–60, rewrite each expression without absolute value bars. \(|\sqrt{2}-5|\) ________________ Equation Transcription: Text Transcription: |sqrt 2-5|

In Exercises 51–60, rewrite each expression without absolute value bars. \(|\sqrt{5}-13|\) ________________ Equation Transcription: Text Transcription: |sqrt 5-13|

In Exercises 51–60, rewrite each expression without absolute value bars. \(\frac{-3}{|-3|}\) ________________ Equation Transcription: Text Transcription: -3/|-3|

In Exercises 51–60, rewrite each expression without absolute value bars. \(\frac{-7}{|-7|}\) ________________ Equation Transcription: Text Transcription: -7/|-7|

In Exercises 51–60, rewrite each expression without absolute value bars. \(||-3|-|-7||\) ________________ Equation Transcription: Text Transcription: ||-3| - |-7||

In Exercises 51–60, rewrite each expression without absolute value bars. \(||-5|-|-13||\) ________________ Equation Transcription: Text Transcription: ||-5| - |-13||

In Exercises 61–66, evaluate each algebraic expression for x = 2 and y = -5. \(|x+y|\) ________________ Equation Transcription: Text Transcription: |x+y|

In Exercises 61–66, evaluate each algebraic expression for x = 2 and y = -5. \(|x-y|\) ________________ Equation Transcription: Text Transcription: |x-y|

In Exercises 61–66, evaluate each algebraic expression for x = 2 and y = -5. \(|x|+|y|\) ________________ Equation Transcription: Text Transcription: |x|+|y|

In Exercises 61–66, evaluate each algebraic expression for x = 2 and y = -5. \(|x|-|y|\) ________________ Equation Transcription: Text Transcription: |x|-|y|

In Exercises 61–66, evaluate each algebraic expression for x = 2 and y = -5. \(\frac{y}{|y|}\) ________________ Equation Transcription: Text Transcription: y/|y|

In Exercises 61–66, evaluate each algebraic expression for x = 2 and y = -5. \(\frac{|x|}{x}+\frac{|y|}{y}\) ________________ Equation Transcription: Text Transcription: |x|/x+|y|/y

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 2 and 17

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 4 and 15

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. -2 and 5

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. -6 and 8

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. -19 and -4

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. -26 and -3

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. -3.6 and -1.4

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. -5.4 and -1.2

In Exercises 75–84, state the name of the property illustrated. \(6+(-4)=(-4)+6\) ________________ Equation Transcription: Text Transcription: 6+(-4)=(-4)+6

In Exercises 75–84, state the name of the property illustrated. \(11 \cdot(7+4)=11 \cdot 7+11 \cdot 4\) ________________ Equation Transcription: Text Transcription: 11 times (7+4)=11 times 7+11 times 4

In Exercises 75–84, state the name of the property illustrated. \(6+(2+7)=(6+2)+7\) ________________ Equation Transcription: Text Transcription: 6+(2+7)=(6+2)+7

In Exercises 75–84, state the name of the property illustrated. \(6 \cdot(2 \cdot 3)=6 \cdot(3 \cdot 2)\) ________________ Equation Transcription: Text Transcription: 6 times (2 times 3)=6 times (3 times 2)

In Exercises 75–84, state the name of the property illustrated. \((2+3)+(4+5)=(4+5)+(2+3)\) ________________ Equation Transcription: Text Transcription: (2+3)+(4+5)=(4+5)+(2+3)

In Exercises 75–84, state the name of the property illustrated. \(7 \cdot(11 \cdot 8)=(11 \cdot 8) \cdot 7\) ________________ Equation Transcription: Text Transcription: 7 times (11 times 8)=(11 times 8) times 7

In Exercises 75–84, state the name of the property illustrated. \(2(-8+6)=-16+12\) ________________ Equation Transcription: Text Transcription: 2(-8+6)=-16+12

In Exercises 75–84, state the name of the property illustrated. \(-8(3+11)=-24+(-88)\) ________________ Equation Transcription: Text Transcription: -8(3+11)=-24+(-88)

In Exercises 75–84, state the name of the property illustrated. \(\frac{1}{(x+3)}(x+3)=1, x \neq-3\) ________________ Equation Transcription: Text Transcription: 1/(x+3)(x+3)=1, x neq -3

In Exercises 75–84, state the name of the property illustrated. \((x+4)+[-(x+4)]=0\) ________________ Equation Transcription: Text Transcription: (x+4)+[-(x+4)]=0

In Exercises 85–96, simplify each algebraic expression. \(5(3 x+4)-4\) ________________ Equation Transcription: Text Transcription: 5(3x+4)-4

In Exercises 85–96, simplify each algebraic expression. \(2(5 x+4)-3\) ________________ Equation Transcription: Text Transcription: 2(5x+4)-3

In Exercises 85–96, simplify each algebraic expression. \(5(3 x-2)+12 x\) ________________ Equation Transcription: Text Transcription: 5(3x-2)+12x

In Exercises 85–96, simplify each algebraic expression. \(2(5 x-1)+14 x\) ________________ Equation Transcription: Text Transcription: 2(5x-1)+14x

In Exercises 85–96, simplify each algebraic expression. \(7(3 y-5)+2(4 y+3)\) ________________ Equation Transcription: Text Transcription: 7(3y-5)+2(4y+3)

In Exercises 85–96, simplify each algebraic expression. \(4(2 y-6)+3(5 y+10)\) ________________ Equation Transcription: Text Transcription: 4(2y-6)+3(5y+10)

In Exercises 85–96, simplify each algebraic expression. \(5(3 y-2)-(7 y+2)\) ________________ Equation Transcription: Text Transcription: 5(3y-2)-(7y+2)

In Exercises 85–96, simplify each algebraic expression. \(4(5 y-3)-(6 y+3)\) ________________ Equation Transcription: Text Transcription: 4(5y-3)-(6y+3)

In Exercises 85–96, simplify each algebraic expression. \(7-4[3-(4 y-5)]\) ________________ Equation Transcription: Text Transcription: 7-4[3-(4y-5)]

In Exercises 85–96, simplify each algebraic expression. \(6-5[8-(2 y-4)]\) ________________ Equation Transcription: Text Transcription: 6-5[8-(2y-4)]

In Exercises 85–96, simplify each algebraic expression. \(18 x^{2}+4-\left[6\left(x^{2}-2\right)+5\right]\) ________________ Equation Transcription: Text Transcription: 18x^2+4-[6(x^2-2)+5]

In Exercises 85–96, simplify each algebraic expression. \(14 x^{2}+5-\left[7\left(x^{2}-2\right)+4\right]\) ________________ Equation Transcription: Text Transcription: 14x^2+5-[7(x^2-2)+4]

In Exercises 97–102, write each algebraic expression without parentheses. \(-(-14 x)\) ________________ Equation Transcription: Text Transcription: -(-14x)

In Exercises 97–102, write each algebraic expression without parentheses. \(-(-17 y)\) ________________ Equation Transcription: Text Transcription: -(-17x)

In Exercises 97–102, write each algebraic expression without parentheses. \(-(2 x-3 y-6)\) ________________ Equation Transcription: Text Transcription: -(2x-3y-6)

In Exercises 97–102, write each algebraic expression without parentheses. \(-(5 x-13 y-1)\) ________________ Equation Transcription: Text Transcription: -(5x-13y-1)

In Exercises 97–102, write each algebraic expression without parentheses. \(\frac{1}{3}(3 x)+[(4 y)+(-4 y)]\) ________________ Equation Transcription: Text Transcription: 1/3(3x)+[(4y)+(-4y)]

In Exercises 97–102, write each algebraic expression without parentheses. \(\frac{1}{2}(2 y)+[(-7 x)+7 x]\) ________________ Equation Transcription: Text Transcription: 1/2(2y)+[(-7x)+7x]

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. \(|-6|\) ____ \(|-3|\) ________________ Equation Transcription: ___ Text Transcription: |-6| ___ |-3|

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. \(|-20|\) ____ \(|-50|\) ________________ Equation Transcription: ___ Text Transcription: |-20| ___ |-50|

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. \(\left|\frac{3}{5}\right|\) ____ \(|-0.6|\) ________________ Equation Transcription: ___ Text Transcription: |3/5| ___ |-0.6|

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. \(\left|\frac{5}{2}\right|\) ____ \(|-2.5|\) ________________ Equation Transcription: ___ Text Transcription: |5/2| ___ |-2.5|

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. \(\frac{30}{40}-\frac{3}{4}\) ____ \(\frac{14}{15} \cdot \frac{15}{14}\) ________________ Equation Transcription: ____ Text Transcription: 30/40-3/4 ____ 14/15 times15/14 \

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. \(\frac{17}{18} \cdot \frac{18}{17}\) ____ \(\frac{50}{60}-\frac{5}{6}\) ________________ Equation Transcription: ____ Text Transcription: 17/18 times 18/17 ____ 50/60-5/6

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. \(\frac{8}{13} \div \frac{8}{13}\) ____ \(|-1|\) ________________ Equation Transcription: ____ Text Transcription: 8/13 div 8/13 ____ |-1|

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. \(|-2|\) ____ \(\frac{4}{17} \div \frac{4}{17}\) ________________ Equation Transcription: ____ Text Transcription: |-2| ____ 4/17 div 4/17

In Exercises 111–120, use the order of operations to simplify each expression. \(8^{2}-16 \div 2^{2} \cdot 4-3\) ________________ Equation Transcription: Text Transcription: 8^2-16 div 2^24-3

In Exercises 111–120, use the order of operations to simplify each expression. \(10^{2}-100 \div 5^{2} \cdot 2-3\) ________________ Equation Transcription: Text Transcription: 10^2-100 times 5^22-3

In Exercises 111–120, use the order of operations to simplify each expression. \(\frac{5 \cdot 2-3^{2}}{\left[3^{2}-(-2)\right]^{2}}\) ________________ Equation Transcription: Text Transcription: 5 times 2-3^2[3^2-(-2)]^2

In Exercises 111–120, use the order of operations to simplify each expression. \(\frac{10 \div 2+3 \cdot 4}{(12-3 \cdot 2)^{2}}\) ________________ Equation Transcription: Text Transcription: 102+3 times 4(12-3 times 2)^2

In Exercises 111–120, use the order of operations to simplify each expression. \(8-3[-2(2-5)-4(8-6)]\) ________________ Equation Transcription: Text Transcription: 8-3[-2(2-5)-4(8-6)]

In Exercises 111–120, use the order of operations to simplify each expression. \(8-3[-2(5-7)-5(4-2)]\) ________________ Equation Transcription: Text Transcription: 8-3[-2(5-7)-5(4-2)]

In Exercises 111–120, use the order of operations to simplify each expression. \(\frac{2(-2)-4(-3)}{5-8}\) ________________ Equation Transcription: Text Transcription: 2(-2)-4(-3)/5-8

In Exercises 111–120, use the order of operations to simplify each expression. \(\frac{6(-4)-5(-3)}{9-10}\) ________________ Equation Transcription: Text Transcription: 6(-4)-5(-3)/9-10

In Exercises 111–120, use the order of operations to simplify each expression. \(\frac{(5-6)^{2}-2|3-7|}{89-3 \cdot 5^{2}}\) ________________ Equation Transcription: Text Transcription: (5-6)^2-2|3-7|/89-3 times 5^2

In Exercises 111–120, use the order of operations to simplify each expression. \(\frac{12 \div 3 \cdot 5\left|2^{2}+3^{2}\right|}{7+3-6^{2}}\) ________________ Equation Transcription: Text Transcription: 12 div 35|2^2+3^2|/7+3-6^2

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number A number decreased by the sum of the number and four

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number A number decreased by the difference between eight and the number

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number Six times the product of negative fi ve and a number

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number Ten times the product of negative four and a number

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number The difference between the product of five and a number and twice the number

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number The difference between the product of six and a number and negative two times the number

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number The difference between eight times a number and six more than three times the number

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number Eight decreased by three times the sum of a number and six

The following bar graph shows the target heart rate ranges for four types of exercise goals. The lower and upper limits of these ranges are fractions of the maximum heart rate, 220-a. Exercises 129–130 are based on the information in the graph. If your exercise goal is to improve cardiovascular conditioning, the graph shows the following range for target heart rate, H,in beats per minute: a. What is the lower limit of the heart range, in beats per minute, for a 20-year-old with this exercise goal? b. What is the upper limit of the heart range, in beats per minute, for a 20-year-old with this exercise goal?

The following bar graph shows the target heart rate ranges for four types of exercise goals. The lower and upper limits of these ranges are fractions of the maximum heart rate, 220-a. Exercises 129–130 are based on the information in the graph. If your exercise goal is to improve overall health, the graph shows the following range for target heart rate, H, in beats per minute: a. What is the lower limit of the heart range, in beats per minute, for a 30-year-old with this exercise goal? b. What is the upper limit of the heart range, in beats per minute, for a 30-year-old with this exercise goal?

The bar graph shows the average cost of tuition and fees at private four-year colleges in the United States. The formula \(T=26 x^{2}+819 x+15,527\) models the average cost of tuition and fees, T, at private U.S. colleges for the school year ending x years after 2000. Use this information to solve Exercises 131–132. a. Use the formula to find the average cost of tuition and fees at private U.S. colleges for the school year ending in 2010. b. By how much does the formula underestimate or overestimate the actual cost shown by the graph for the school year ending in 2010? c. Use the formula to project the average cost of tuition and fees at private U.S. colleges for the school year ending in 2013. ________________ Equation Transcription: Text Transcription: T=26x^2+819x+15,527

The bar graph shows the average cost of tuition and fees at private four-year colleges in the United States. The formula \(T=26 x^{2}+819 x+15,527\) models the average cost of tuition and fees, T, at private U.S. colleges for the school year ending x years after 2000. Use this information to solve Exercises 131–132. a. Use the formula to find the average cost of tuition and fees at private U.S. colleges for the school year ending in 2009. b. By how much does the formula underestimate or overestimate the actual cost shown by the graph for the school year ending in 2009? c. Use the formula to project the average cost of tuition and fees at private U.S. colleges for the school year ending in 2012. ________________ Equation Transcription: Text Transcription: T=26x^2+819x+15,527

You had $10,000 to invest. You put x dollars in a safe, government-insured certificate of deposit paying 5% per year. You invested the remainder of the money in noninsured corporate bonds paying 12% per year. Your total interest earned at the end of the year is given by the algebraic expression . a. Simplify the algebraic expression. b. Use each form of the algebraic expression to determine your total interest earned at the end of the year if you invested $6000 in the safe, government-insured certificate of deposit. ________________ Equation Transcription: Text Transcription: 0.05x+0.12(10,000-x)

It takes you 50 minutes to get to campus. You spend t minutes walking to the bus stop and the rest of the time riding the bus. Your walking rate is 0.06 mile per minute and the bus travels at a rate of 0.5 mile per minute. The total distance walking and traveling by bus is given by the algebraic expression \(0.06t+0.5(50-t)\). a. Simplify the algebraic expression. b. Use each form of the algebraic expression to determine the total distance that you travel if you spend 20 minutes walking to the bus stop. ________________ Equation Transcription: Text Transcription: 0.06t+0.5(50-t)

Read the Blitzer Bonus beginning on page 15. Use the formula \(B A C=\frac{600 n}{w(0.6 n+169)}\) and replace w with your body weight. Using this formula and a calculator, compute your BAC for integers from \(n=1\) to \(n=10\). Round to three decimal places. According to this model, how many drinks can you consume in an hour without exceeding the legal measure of drunk driving? ________________ Equation Transcription: Text Transcription: BAC=600n/w(0.6n+169) n=1 n=10

Writing about mathematics will help you learn mathematics. For all writing exercises in this book, use complete sentences to respond to the question. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. What is an algebraic expression? Give an example with your explanation.

Writing about mathematics will help you learn mathematics. For all writing exercises in this book, use complete sentences to respond to the question. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. If n is a natural number, what does \(b^{n}\) mean? Give an example with your explanation. ________________ Equation Transcription: Text Transcription: b^n

Writing about mathematics will help you learn mathematics. For all writing exercises in this book, use complete sentences to respond to the question. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. What does it mean when we say that a formula models real-world phenomena?

Writing about mathematics will help you learn mathematics. For all writing exercises in this book, use complete sentences to respond to the question. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. What is the intersection of sets A and B?

Writing about mathematics will help you learn mathematics. For all writing exercises in this book, use complete sentences to respond to the question. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. What is the union of sets A and B?

Writing about mathematics will help you learn mathematics. For all writing exercises in this book, use complete sentences to respond to the question. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. How do the whole numbers differ from the natural numbers?

Writing about mathematics will help you learn mathematics. For all writing exercises in this book, use complete sentences to respond to the question. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. Can a real number be both rational and irrational? Explain your answer.

Writing about mathematics will help you learn mathematics. For all writing exercises in this book, use complete sentences to respond to the question. Some writing exercises can be answered in a sentence; others require a paragraph or two. You can decide how much you need to write as long as your writing clearly and directly answers the question in the exercise. Standard references such as a dictionary and a thesaurus should be helpful. If you are given two real numbers, explain how to determine which is the lesser.

Make Sense? In Exercises 144–147, determine whether each statement makes sense or does not make sense, and explain your reasoning. My mathematical model describes the data for tuition and fees at public four-year colleges for the past ten years extremely well, so it will serve as an accurate prediction for the cost of public colleges in 2050.

Make Sense? In Exercises 144–147, determine whether each statement makes sense or does not make sense, and explain your reasoning. A model that describes the average cost of tuition and fees at private U.S. colleges for the school year ending x years after 2000 cannot be used to estimate the cost of private education for the school year ending in 2000.

Make Sense? In Exercises 144–147, determine whether each statement makes sense or does not make sense, and explain your reasoning. The humor in this cartoon is based on the fact that the football will never be hiked.

Make Sense? In Exercises 144–147, determine whether each statement makes sense or does not make sense, and explain your reasoning. Just as the commutative properties change groupings, the associative properties change order.

In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Every rational number is an integer.

In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some whole numbers are not integers.

In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some rational numbers are not positive.

In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Irrational numbers cannot be negative.

In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The term x has no coefficient.

In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(5+3(x-4)=8(x-4)=8x-32\) ________________ Equation Transcription: Text Transcription: 5+3(x-4)=8(x-4)=8x-32

In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(-x-x=-x+(-x)=0\) ________________ Equation Transcription: Text Transcription: -x-x=-x+(-x)=0

In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(x-0.02(x+200)=0.98x-4\) ________________ Equation Transcription: Text Transcription: x-0.02(x+200)=0.98x-4

In Exercises 156–158, insert either < or > in the shaded area between the numbers to make the statement true. \(\sqrt{2}\) ____ \(1.5\) ________________ Equation Transcription: ____ Text Transcription: sqrt 2 ____ 1.5

In Exercises 156–158, insert either < or > in the shaded area between the numbers to make the statement true. \(-\pi\) ____ \(-3.5\) ________________ Equation Transcription: ____ Text Transcription: -pi ____ -3.5

In Exercises 156–158, insert either < or > in the shaded area between the numbers to make the statement true. \(-\frac{3.14}{2}\) ____ \(-\frac{\pi}{2}\) ________________ Equation Transcription: ____ Text Transcription: -3.14/2 ____ -pi/2

Exercises 159–161 will help you prepare for the material covered in the next section. In parts (a) and (b), complete each statement. a. \(b^{4} \cdot b^{3}=(b \cdot b \cdot b \cdot b)(b \cdot b \cdot b)=b^{?}\) b. \(b^{5} \cdot b^{5}=(b \cdot b \cdot b \cdot b \cdot b)(b \cdot b \cdot b \cdot b \cdot b)=b^{?}\) c. Generalizing from parts (a) and (b), what should be done with the exponents when multiplying exponential expressions with the same base? ________________ Equation Transcription: Text Transcription: b^4 times b^3=(b times b times b times b)(b times b times b)=b? b^5 times b^5=(b times b times b times b times b)(b times b times b times b times b)=b?

Exercises 159–161 will help you prepare for the material covered in the next section. In parts (a) and (b), complete each statement. c. Generalizing from parts (a) and (b), what should be done with the exponents when multiplying exponential expressions with the same base?

Exercises 159–161 will help you prepare for the material covered in the next section. If 6.2 is multiplied by \(10^{3}\), what does this multiplication do to the decimal point in 6.2? ________________ Equation Transcription: Text Transcription: 10^3