12.4.2: Chapter 2
- Page ID
- 119023
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Be Prepared
expression
and
prime
Try It
- ⓐ 18 plus 11; the sum of eighteen and eleven
- ⓑ 27 times 9; the product of twenty-seven and nine
- ⓒ 84 divided by 7; the quotient of eighty-four and seven
- ⓓ p minus q; the difference of p and q
- ⓐ 47 minus 19; the difference of forty-seven and nineteen
- ⓑ 72 divided by 9; the quotient of seventy-two and nine
- ⓒ m plus n; the sum of m and n
- ⓓ 13 times 7; the product of thirteen and seven
- ⓐ fourteen is less than or equal to twenty-seven
- ⓑ nineteen minus two is not equal to eight
- ⓒ twelve is greater than four divided by two
- ⓓ x minus seven is less than one
- ⓐ nineteen is greater than or equal to fifteen
- ⓑ seven is equal to twelve minus five
- ⓒ fifteen divided by three is less than eight
- ⓓ y minus three is greater than six
- ⓐ >
- ⓑ <
- ⓐ <
- ⓑ >
- ⓐ equation
- ⓑ expression
- ⓐ expression
- ⓑ equation
415
79
- ⓐ 4 · 4 · 4 · 4 · 4 · 4 · 4 · 4
- ⓑ a · a · a · a · a · a · a
- ⓐ 8 · 8 · 8 · 8 · 8 · 8 · 8 · 8
- ⓑ b · b · b · b · b · b
- ⓐ 125
- ⓑ 1
- ⓐ 49
- ⓑ 0
- ⓐ 2
- ⓑ 14
- ⓐ 35
- ⓑ 99
18
9
16
23
86
1
81
75
- ⓐ 10
- ⓑ 19
- ⓐ 4
- ⓑ 12
- ⓐ 13
- ⓑ 5
- ⓐ 8
- ⓑ 16
64
216
64
81
33
10
40
9
The terms are 4x, 3b, and 2. The coefficients are 4, 3, and 2.
The terms are 9a, 13a2, and a3, The coefficients are 9, 13, and 1.
9 and 15; 2x3 and 8x3; y2 and 11y2
4x3 and 6x3; 8x2 and 3x2; 19 and 24
16x + 17
17y + 7
4x2 + 14x
12y2 + 15y
- ⓐ 47 − 41
- ⓑ 5x ÷ 2
- ⓐ 17 + 19
- ⓑ 7x
- ⓐ x + 11
- ⓑ 11a − 14
- ⓐ j + 19
- ⓑ 2x − 21
- ⓐ 4(p + q)
- ⓐ 4p + q
- ⓐ 2x − 8
- ⓑ 2(x − 8)
w − 5
l + 2
6q − 7
4n + 8
no
yes
yes
yes
x + 1 = 7; x = 6
x + 3 = 4; x = 1
x = 13
x = 5
y = 28
y = 46
x = 22
y = 4
a = 37
n = 41
7 + 6 = 13
8 + 6 = 14
6 ⋅ 9 = 54
21 ⋅ 3 = 63
2(x − 5) = 30
2(y − 4) = 16
x + 7 = 37; x = 30
y + 11 = 28; y = 17
z − 17 = 37; z = 54
x − 19 = 45; x = 64
- ⓐ yes
- ⓑ no
- ⓐ no
- ⓑ yes
- ⓐ yes
- ⓑ no
- ⓐ no
- ⓑ yes
- ⓐ no
- ⓑ yes
- ⓐ yes
- ⓑ no
- ⓐ yes
- ⓑ no
- ⓐ no
- ⓑ yes
Divisible by 2, 3, 5, and 10
Divisible by 2 and 3, not 5 or 10.
Divisible by 2, 3, not 5 or 10.
Divisible by 3 and 5.
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
1, 2, 4, 5, 8, 10, 16, 20, 40, 80
composite
prime
2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5, or 24 ⋅ 5
2 ⋅ 2 ⋅ 3 ⋅ 5, or 22 ⋅ 3 ⋅ 5
2 ⋅ 3 ⋅ 3 ⋅ 7, or 2 ⋅ 32 ⋅ 7
2 ⋅ 3 ⋅ 7 ⋅ 7, or 2 ⋅ 3 ⋅ 72
2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5, or 24 ⋅ 5
2 ⋅ 2 ⋅ 3 ⋅ 5, or 22 ⋅ 3 ⋅ 5
2 ⋅ 3 ⋅ 3 ⋅ 7, or 2 ⋅ 32 ⋅ 7
2 ⋅ 3 ⋅ 7 ⋅ 7, or 2 ⋅ 3 ⋅ 72
36
72
60
105
440
360
Section 2.1 Exercises
16 minus 9, the difference of sixteen and nine
5 times 6, the product of five and six
28 divided by 4, the quotient of twenty-eight and four
x plus 8, the sum of x and eight
2 times 7, the product of two and seven
fourteen is less than twenty-one
thirty-six is greater than or equal to nineteen
3 times n equals 24, the product of three and n equals twenty-four
y minus 1 is greater than 6, the difference of y and one is greater than six
2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six
a is not equal to 7 times 4, a is not equal to the product of seven and four
equation
expression
expression
equation
37
x 5
5x5x5
2x2x2x2x2x2x2x2
- ⓐ 43
- ⓑ 55
5
34
58
6
13
4
35
10
41
81
149
50
Section 2.2 Exercises
22
26
144
32
27
21
41
9
225
73
54
15x2, 6x, 2
10y3, y, 2
8
5
x3 and 8x3; 14 and 5
16ab and 4ab; 16b2 and 9b2
13x
26a
7c
12x + 8
10u + 3
12p + 10
22a + 1
17x2 + 20x + 16
8 + 12
14 − 9
9 ⋅ 7
36 ÷ 9
x − 4
6y
8x + 3x
y ÷ 3
8 (y − 9)
5 (x + y)
b + 15
b − 4
2n − 7
He will pay $750. His insurance company will pay $1350.
Section 2.3 Exercises
- ⓐ yes
- ⓑ no
- ⓐ no
- ⓑ yes
- ⓐ yes
- ⓑ no
- ⓐ no
- ⓑ yes
- ⓐ no
- ⓑ yes
- ⓐ no
- ⓑ yes
x + 2 = 5; x = 3
x + 3 = 6; x = 3
a = 16
p = 5
r = 24
x = 7
p = 69
d = 67
y = 22
u = 30
f = 178
n = 32
p = 48
y = 467
8 + 9 = 17
23 − 19 = 4
3 ⋅ 9 = 27
54 ÷ 6 = 9
2(n − 10) = 52
3y + 10 = 100
p + 5 = 21; p = 16
r + 18 = 73; r = 55
d − 30 = 52; d = 82
u − 12 = 89; u = 101
c − 325 = 799; c = 1124
$1300
$460
Section 2.4 Exercises
2, 4, 6, 8, 10 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
6, 12, 18, 24, 30, 36, 42, 48
8, 16, 24, 32, 40, 48
10, 20, 30, 40
Divisible by 2, 3, 4, 6
Divisible by 3, 5
Divisible by 2, 3, 4, 6
Divisible by 2, 3, 4, 5, 6, 10
Divisible by 2, 4
Divisible by 3, 5
Divisible by 2, 5, 10
Divisible by 2, 5, 10
Divisible by 3, 5
1, 2, 3, 4, 6, 9, 12, 18, 36
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72,144
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588
prime
composite
prime
composite
composite
composite
Section 2.5 Exercises
2 ⋅ 43
2 ⋅ 2 ⋅ 3 ⋅ 11
3 ⋅ 3 ⋅ 7 ⋅ 11
5 ⋅ 23
3 ⋅ 3 ⋅ 5 ⋅ 5 ⋅ 11
2 ⋅ 2 ⋅ 2 ⋅ 7
2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 7
17 ⋅ 23
2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3
2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 5
2 ⋅ 3 ⋅ 5 ⋅ 5
3 ⋅ 5 ⋅ 5 ⋅ 7
2 ⋅ 2 ⋅ 3 ⋅ 3
2 ⋅ 5 ⋅ 5 ⋅ 7
24
30
120
300
24
120
420
42
120
40
Review Exercises
3 times 8, the product of three and eight.
24 divided by 6, the quotient of twenty-four and six.
50 is greater than or equal to 47
The sum of n and 4 is equal to 13
equation
expression
23
x 6
8 ⋅ 8 ⋅ 8 ⋅ 8
y ⋅ y ⋅ y ⋅ y ⋅ y
81
128
20
18
74
31
58
26
12n2,3n, 1
6
3 and 4; 3x and x
24a
14x
12n + 11
10y2 + 2y + 3
x − 6
3n ⋅ 9
5(y + 1)
c + 3
- ⓐ yes
- ⓑ no
- ⓐ yes
- ⓑ no
- ⓐ no
- ⓑ yes
x + 3 = 5; x = 2
c = 6
x = 11
y = 23
p = 34
7 + 33 = 40
4 ⋅ 8 = 32
2(n − 3) = 76
x + 8 = 35; x = 27
q − 18 = 57; q = 75
h = 42
z = 33
q = 8
v = 56
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48
8, 16, 24, 32, 40, 48
2, 3, 6
2, 3, 5, 6, 10
1, 2, 3, 5, 6, 10, 15, 30
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
prime
composite
2 ⋅ 2 ⋅ 3 ⋅ 7
2 ⋅ 5 ⋅ 5 ⋅ 7
45
175
Answers will vary
Practice Test
15 minus x, the difference of fifteen and x.
equation
- ⓐ n6
- ⓑ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 = 243
36
5
45
125
36
x + 5
3(a − b)
n = 31
y − 15 = 32; y = 47
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
23 ⋅ 33 ⋅ 5