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12.4.2: Chapter 2

  • Page ID
    119023
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    Be Prepared

    2.1

    112 112

    2.2

    180 , 096 180 , 096

    2.3

    807 807

    2.4

    expression

    2.5

    1 , 024 1 , 024

    2.6

    73 73

    2.7

    19 19

    2.8

    42 42

    2.9

    x 8 x 8

    2.10

    44 and 215215

    2.11

    15 15

    2.12

    2 , 3 , 5 , 6 , 10 2 , 3 , 5 , 6 , 10

    2.13

    prime

    2.13

    2 4 2 4

    Try It

    2.1
    1. 18 plus 11; the sum of eighteen and eleven
    2. 27 times 9; the product of twenty-seven and nine
    3. 84 divided by 7; the quotient of eighty-four and seven
    4. p minus q; the difference of p and q
    2.2
    1. 47 minus 19; the difference of forty-seven and nineteen
    2. 72 divided by 9; the quotient of seventy-two and nine
    3. m plus n; the sum of m and n
    4. 13 times 7; the product of thirteen and seven
    2.3
    1. fourteen is less than or equal to twenty-seven
    2. nineteen minus two is not equal to eight
    3. twelve is greater than four divided by two
    4. x minus seven is less than one
    2.4
    1. nineteen is greater than or equal to fifteen
    2. seven is equal to twelve minus five
    3. fifteen divided by three is less than eight
    4. y minus three is greater than six
    2.5
    1. >
    2. <
    2.6
    1. <
    2. >
    2.7
    1. equation
    2. expression
    2.8
    1. expression
    2. equation
    2.9

    415

    2.10

    79

    2.11
    1. 4 · 4 · 4 · 4 · 4 · 4 · 4 · 4
    2. a · a · a · a · a · a · a
    2.12
    1. 8 · 8 · 8 · 8 · 8 · 8 · 8 · 8
    2. b · b · b · b · b · b
    2.13
    1. 125
    2. 1
    2.14
    1. 49
    2. 0
    2.15
    1. 2
    2. 14
    2.16
    1. 35
    2. 99
    2.17

    18

    2.18

    9

    2.19

    16

    2.20

    23

    2.21

    86

    2.22

    1

    2.23

    81

    2.24

    75

    2.25
    1. 10
    2. 19
    2.26
    1. 4
    2. 12
    2.27
    1. 13
    2. 5
    2.28
    1. 8
    2. 16
    2.29

    64

    2.30

    216

    2.31

    64

    2.32

    81

    2.33

    33

    2.34

    10

    2.35

    40

    2.36

    9

    2.37

    The terms are 4x, 3b, and 2. The coefficients are 4, 3, and 2.

    2.38

    The terms are 9a, 13a2, and a3, The coefficients are 9, 13, and 1.

    2.39

    9 and 15; 2x3 and 8x3; y2 and 11y2

    2.40

    4x3 and 6x3; 8x2 and 3x2; 19 and 24

    2.41

    16x + 17

    2.42

    17y + 7

    2.43

    4x2 + 14x

    2.44

    12y2 + 15y

    2.45
    1. 47 − 41
    2. 5x ÷ 2
    2.46
    1. 17 + 19
    2. 7x
    2.47
    1. x + 11
    2. 11a − 14
    2.48
    1. j + 19
    2. 2x − 21
    2.49
    1. 4(p + q)
    2. 4p + q
    2.50
    1. 2x − 8
    2. 2(x − 8)
    2.51

    w − 5

    2.52

    l + 2

    2.53

    6q − 7

    2.54

    4n + 8

    2.55

    no

    2.56

    yes

    2.57

    yes

    2.58

    yes

    2.59

    x + 1 = 7; x = 6

    2.60

    x + 3 = 4; x = 1

    2.61

    x = 13

    2.62

    x = 5

    2.63

    y = 28

    2.64

    y = 46

    2.65

    x = 22

    2.66

    y = 4

    2.67

    a = 37

    2.68

    n = 41

    2.69

    7 + 6 = 13

    2.70

    8 + 6 = 14

    2.71

    6 ⋅ 9 = 54

    2.72

    21 ⋅ 3 = 63

    2.73

    2(x − 5) = 30

    2.74

    2(y − 4) = 16

    2.75

    x + 7 = 37; x = 30

    2.76

    y + 11 = 28; y = 17

    2.77

    z − 17 = 37; z = 54

    2.78

    x − 19 = 45; x = 64

    2.79
    1. yes
    2. no
    2.80
    1. no
    2. yes
    2.81
    1. yes
    2. no
    2.82
    1. no
    2. yes
    2.83
    1. no
    2. yes
    2.84
    1. yes
    2. no
    2.85
    1. yes
    2. no
    2.86
    1. no
    2. yes
    2.87

    Divisible by 2, 3, 5, and 10

    2.88

    Divisible by 2 and 3, not 5 or 10.

    2.89

    Divisible by 2, 3, not 5 or 10.

    2.90

    Divisible by 3 and 5.

    2.91

    1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

    2.92

    1, 2, 4, 5, 8, 10, 16, 20, 40, 80

    2.93

    composite

    2.94

    prime

    2.95

    2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5, or 24 ⋅ 5

    2.96

    2 ⋅ 2 ⋅ 3 ⋅ 5, or 22 ⋅ 3 ⋅ 5

    2.97

    2 ⋅ 3 ⋅ 3 ⋅ 7, or 2 ⋅ 32 ⋅ 7

    2.98

    2 ⋅ 3 ⋅ 7 ⋅ 7, or 2 ⋅ 3 ⋅ 72

    2.99

    2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5, or 24 ⋅ 5

    2.100

    2 ⋅ 2 ⋅ 3 ⋅ 5, or 22 ⋅ 3 ⋅ 5

    2.101

    2 ⋅ 3 ⋅ 3 ⋅ 7, or 2 ⋅ 32 ⋅ 7

    2.102

    2 ⋅ 3 ⋅ 7 ⋅ 7, or 2 ⋅ 3 ⋅ 72

    2.103

    36

    2.104

    72

    2.105

    60

    2.106

    105

    2.107

    440

    2.108

    360

    Section 2.1 Exercises

    1.

    16 minus 9, the difference of sixteen and nine

    3.

    5 times 6, the product of five and six

    5.

    28 divided by 4, the quotient of twenty-eight and four

    7.

    x plus 8, the sum of x and eight

    9.

    2 times 7, the product of two and seven

    11.

    fourteen is less than twenty-one

    13.

    thirty-six is greater than or equal to nineteen

    15.

    3 times n equals 24, the product of three and n equals twenty-four

    17.

    y minus 1 is greater than 6, the difference of y and one is greater than six

    19.

    2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six

    21.

    a is not equal to 7 times 4, a is not equal to the product of seven and four

    23.

    equation

    25.

    expression

    27.

    expression

    29.

    equation

    31.

    37

    33.

    x 5

    35.

    5x5x5

    37.

    2x2x2x2x2x2x2x2

    39.
    1. 43
    2. 55
    41.

    5

    43.

    34

    45.

    58

    47.

    6

    49.

    13

    51.

    4

    53.

    35

    55.

    10

    57.

    41

    59.

    81

    61.

    149

    63.

    50

    Section 2.2 Exercises

    69.

    22

    71.

    26

    73.

    144

    75.

    32

    77.

    27

    79.

    21

    81.

    41

    83.

    9

    84.

    225

    85.

    73

    87.

    54

    89.

    15x2, 6x, 2

    91.

    10y3, y, 2

    93.

    8

    95.

    5

    97.

    x3 and 8x3; 14 and 5

    99.

    16ab and 4ab; 16b2 and 9b2

    101.

    13x

    103.

    26a

    105.

    7c

    107.

    12x + 8

    109.

    10u + 3

    111.

    12p + 10

    113.

    22a + 1

    115.

    17x2 + 20x + 16

    117.

    8 + 12

    119.

    14 − 9

    121.

    9 ⋅ 7

    123.

    36 ÷ 9

    125.

    x − 4

    127.

    6y

    129.

    8x + 3x

    131.

    y ÷ 3

    133.

    8 (y − 9)

    135.

    5 (x + y)

    137.

    b + 15

    139.

    b − 4

    141.

    2n − 7

    143.

    He will pay $750. His insurance company will pay $1350.

    Section 2.3 Exercises

    147.
    1. yes
    2. no
    149.
    1. no
    2. yes
    151.
    1. yes
    2. no
    153.
    1. no
    2. yes
    155.
    1. no
    2. yes
    157.
    1. no
    2. yes
    159.

    x + 2 = 5; x = 3

    161.

    x + 3 = 6; x = 3

    163.

    a = 16

    165.

    p = 5

    167.

    r = 24

    169.

    x = 7

    171.

    p = 69

    173.

    d = 67

    175.

    y = 22

    177.

    u = 30

    179.

    f = 178

    181.

    n = 32

    183.

    p = 48

    185.

    y = 467

    187.

    8 + 9 = 17

    189.

    23 − 19 = 4

    191.

    3 ⋅ 9 = 27

    193.

    54 ÷ 6 = 9

    195.

    2(n − 10) = 52

    197.

    3y + 10 = 100

    199.

    p + 5 = 21; p = 16

    201.

    r + 18 = 73; r = 55

    203.

    d − 30 = 52; d = 82

    205.

    u − 12 = 89; u = 101

    207.

    c − 325 = 799; c = 1124

    209.

    $1300

    211.

    $460

    Section 2.4 Exercises

    215.

    2, 4, 6, 8, 10 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48

    217.

    4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

    219.

    6, 12, 18, 24, 30, 36, 42, 48

    221.

    8, 16, 24, 32, 40, 48

    223.

    10, 20, 30, 40

    225.

    Divisible by 2, 3, 4, 6

    227.

    Divisible by 3, 5

    229.

    Divisible by 2, 3, 4, 6

    231.

    Divisible by 2, 3, 4, 5, 6, 10

    233.

    Divisible by 2, 4

    235.

    Divisible by 3, 5

    237.

    Divisible by 2, 5, 10

    239.

    Divisible by 2, 5, 10

    241.

    Divisible by 3, 5

    243.

    1, 2, 3, 4, 6, 9, 12, 18, 36

    245.

    1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

    247.

    1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72,144

    249.

    1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588

    251.

    prime

    253.

    composite

    255.

    prime

    257.

    composite

    259.

    composite

    261.

    composite

    263. This table has nine rows and three columns. The first row is a header row that labels each column. The first column is labeled “Weeks after opening the account”, the second is labeled “Total number of dollars Gina put in the account”, and the last is labeled “Simplified Total”. Under the “Weeks after opening the account” column are the values: 0, 1, 2, 3, 4, 5, 6, 20, and the letter x. Under the “Total number of dollars Gina put in the account” column are the expressions: 75; 75 plus 20; 75 plus 20 times 2; 75 plus 20 times 3; 75 plus 20 times empty set of brackets; 75 plus empty set of brackets; the last three rows are blank. Under the “Simplified Total” column are the values: 75, 95, 115, the last six rows are blank.

    Section 2.5 Exercises

    267.

    2 ⋅ 43

    269.

    2 ⋅ 2 ⋅ 3 ⋅ 11

    271.

    3 ⋅ 3 ⋅ 7 ⋅ 11

    273.

    5 ⋅ 23

    275.

    3 ⋅ 3 ⋅ 5 ⋅ 5 ⋅ 11

    277.

    2 ⋅ 2 ⋅ 2 ⋅ 7

    279.

    2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 7

    281.

    17 ⋅ 23

    283.

    2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3

    285.

    2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 5

    287.

    2 ⋅ 3 ⋅ 5 ⋅ 5

    289.

    3 ⋅ 5 ⋅ 5 ⋅ 7

    291.

    2 ⋅ 2 ⋅ 3 ⋅ 3

    293.

    2 ⋅ 5 ⋅ 5 ⋅ 7

    295.

    24

    297.

    30

    299.

    120

    301.

    300

    303.

    24

    305.

    120

    307.

    420

    309.

    42

    311.

    120

    313.

    40

    Review Exercises

    317.

    3 times 8, the product of three and eight.

    319.

    24 divided by 6, the quotient of twenty-four and six.

    321.

    50 is greater than or equal to 47

    323.

    The sum of n and 4 is equal to 13

    325.

    equation

    327.

    expression

    329.

    23

    331.

    x 6

    333.

    8 ⋅ 8 ⋅ 8 ⋅ 8

    335.

    yyyyy

    337.

    81

    339.

    128

    341.

    20

    343.

    18

    345.

    74

    347.

    31

    349.

    58

    351.

    26

    353.

    12n2,3n, 1

    355.

    6

    357.

    3 and 4; 3x and x

    359.

    24a

    361.

    14x

    363.

    12n + 11

    365.

    10y2 + 2y + 3

    367.

    x − 6

    369.

    3n ⋅ 9

    371.

    5(y + 1)

    373.

    c + 3

    375.
    1. yes
    2. no
    377.
    1. yes
    2. no
    379.
    1. no
    2. yes
    381.

    x + 3 = 5; x = 2

    383.

    c = 6

    385.

    x = 11

    387.

    y = 23

    389.

    p = 34

    391.

    7 + 33 = 40

    393.

    4 ⋅ 8 = 32

    395.

    2(n − 3) = 76

    397.

    x + 8 = 35; x = 27

    399.

    q − 18 = 57; q = 75

    401.

    h = 42

    403.

    z = 33

    405.

    q = 8

    407.

    v = 56

    409.

    3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48

    411.

    8, 16, 24, 32, 40, 48

    413.

    2, 3, 6

    415.

    2, 3, 5, 6, 10

    417.

    1, 2, 3, 5, 6, 10, 15, 30

    419.

    1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

    421.

    prime

    423.

    composite

    425.

    2 ⋅ 2 ⋅ 3 ⋅ 7

    427.

    2 ⋅ 5 ⋅ 5 ⋅ 7

    429.

    45

    431.

    175

    433.

    Answers will vary

    Practice Test

    435.

    15 minus x, the difference of fifteen and x.

    437.

    equation

    439.
    1. n6
    2. 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 = 243
    441.

    36

    443.

    5

    445.

    45

    447.

    125

    449.

    36

    451.

    x + 5

    453.

    3(ab)

    455.

    n = 31

    457.

    y − 15 = 32; y = 47

    459.

    4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

    461.

    23 ⋅ 33 ⋅ 5


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