(Solution Manual) Beginning Algebra

Messersmith, 1

Math & Statistics

Solution Manual

1st Edition

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Solution Manual for Beginning Algebra, The downloadable file consists of 695 pages, and the total size of the file is 4.25 MB. Purchase now only for highly discounted price.

Author(s): Messersmith

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Chapter 1: The Real Number System and Geometry 1Section 1.1: Exercises 1) a) 2 5 b) 42 63 c) 414 2) a) 1 3 b) 5 8 c) 31 62 3) 1 2 4) 1 3 5) a) 18 1 18 18 2 9 18 3 6 The factors of 18 are 1, 2, 3, 6, 9, and 18. b) 40 1 40 40 2 20 40 4 10 40 5 8   The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. c) 23 1 23 The factors of 23 are 1 and 23. 6) a) 20 1 20 20 2 10 20 4 5 The factors of 20 are 1, 2, 4, 5, 10, and 20. b) 17 1 17 The factors of 17 are 1 and 17. c) 60 1 60 60 2 30 60 3 2060 4 15 60 5 12 60 6 10     The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. 7) a) Composite b) Composite c) Prime 8) a) Prime b) Composite c) Composite 9) Composite. It is divisible by 2 and has other factors as well. 10) Composite. It is divisible by 5 and has other factors as well. 11) a) 18 2 3 3 b) 54 2 3 3 3 c) 42 2 3 7 d) 150 2 3 5 5 12) Answers may vary. 72 2 2 2 3 3 13) a) 93 33 12 2 2 3 4 b) 54 2 3 3 3 3 72 2 2 2 3 3 4  c) 84 2 2 3 7 12 2 or 235 5 7 5 5 d) 120 2 2 2 3 5 3 280 2 2 2 5 7 7   14) a) 21 3 7 3 35 5 7 5 b) 4 8 2222 3 3 8 0 2222 5 5 Section 1.1: Review of Fractions 2c) 125 5 5 5 1 500 2 2 5 5 5 4 d) 900 2 2 3 3 5 52450 2 3 3 5 5 15) a) 23 2 3 6 75 7 5 3 5  b) 155 26 1342 9 352 1 0 13 3 39 c) 1 2 1147 17 7 15 1 15 15 d) 426 55 5222 35 562 1 2 55 2 5 e) 14481 1 18 211 1 22 f) 12 4 96877 8 421 7 171 7 3or 141 4 4 16) a) 15 1 5 5 69 6 9 5 4  b) 9 20 1063 93 2 7 71 0 77 0 c) 121 25 1251 36 311 1 13 3 d) 303 49 7213 100 1033 9 71 0 7 0 e) 771015 15 3102 1 72 31 14 2 or 433  f) 55 5 471796 7 1142 9 1621211 17) She multiplied the whole numbers and multiplied the fractions. She should have converted the mixed numbers to improper fractions before multiplying. 11 1 1 7 1 1 77 7 55 2 or 12232 32 3 6 6   18) Convert mixed numbers to improper fractions and then multiply. 19) a) 12 1 42 7 42 671 11 1 26 2 1 2 b) 34 3 5 3 5 1 5 11 5 11 4 11 4 44   c) 18 9 18 35 102 35 7102 9 122 4 71 7 d) 14 2 14 15 157 15 1151 2 171711 Chapter 1: The Real Number System and Geometry 3e) 21 3 3 2 2 86151 55 1 5 32  8 5 1153 28 7 83 17 24 3 or 377  f) 44871 1 78 211 1 72 1 4 20) Convert the mixed numbers to improper fractions and then multiply the first fraction by the reciprocal of the second. 21) 10 2 5, 15 3 5  LCM of 10 and 15 is 2 3 5 30  22) 12 2 2 3, 9 3 3  LCM of 12 and 9 is 2 2 3 3 36  23) a) 10 2 5, 30 2 3 5  91 1LCD of and is 2 3 5 3010 30 b) 82 2 2 , 1 22 2 3  75LCD of and is 2 2 2 3 2481 2 c) 9 3 3, 6 2 3, 4 2 2   41 3LCD of , , and is 2 2 3 3 3696 4 24) a) 14 2 7, 7 1 7  32LCD of and is 2 7 1414 7 b) 25 5 5, 10 2 5  17 3LCD of and is 2 5 5 5025 10 c) 30 2 3 5, 4 2 2, 20 2 2 5   29 3 9LCD of , and is 2 2 3 5 6030 4 20 25) a) 626 28 11 11 11 11 b) 19 7 19 7 12 3 20 20 20 20 5  c) 4294 2 9 25 25 25 25 15 3 25 5  d) 21 4 3 4 3 7 961 81 8 1 8 1 8    e) 31 11 81 11 8 1 12 9 53 0 3 03 0 3 0 3 0  f) 13 2 13 12 13 12 1 18 3 18 18 18 18  g) 4 5 36 35 36 35 71 8or 17 9 63 63 63 63 63   h) 511 0 3 1 0 3 7 6 4 12 12 12 12  i) 37 367 1 5 10 20 4 20 20 20 671 5 20 28 7 2 or 120 5 5   Section 1.1: Review of Fractions 4j) 121 0 9 1 22 0 6 9 27 54 54 54 91 22 0 54 41 54      26) a) 858 531 99 9 9 3  b) 14 2 14 2 12 4 15 15 15 15 5  c) 11 13 11 13 24 2 36 36 36 36 3  d) 16 8 11 16 8 11 45 45 45 45 35 7 45 9  e) 15 3 15 12 15 12 3 1 6 4 1 6 1 61 61 6    f) 11 3 4 3 4 7 8 6 24 24 24 24    g) 5 2 45 16 45 16 29 8 9 72 72 72 72    h) 23 19 69 19 30 90 90 90 69 19 90 50 5 90 9   i) 112 2 3 8 6 4 3 12 12 12 238 12 13 1 or 112 12     j) 324 91 28 1 051 53 03 03 0 91 28 2 9 30 30     27) a) 52 5 2 7861 4 1 411 11 11 11  b) 13 1 3291 110 10 10 4211 1110 5  c) 11 5 11 5 6 1716 6 612 12 12 12 2  d) 11 4 532 3 25 4 20 20 45 95520 20   e) 241 0454 5 431 51 51 5 10 4115 621115 5   f) 5 3 25 129 59581 0 4 04 0 25 12 134440 40 Chapter 1: The Real Number System and Geometry 5g) 3 3 12 2146 4 67 4 28 28 12 211028 33 510 1128 28    h) 13 4 13 167720 5 20 20 13 16720 29 97820 20    28) a) 23 2 3 531 4 47 777  b) 53 5 3871 516 16 16 8115 1516 2  c) 13 5 13 553 220 20 20 822220 5  d) 81 1 6 610 2 10 29 3 18 18 16 6818 10 58818 9    e) 53 1 0912 1212 8 24 24 10 9 193324 24   f) 12 5 1 847 4 79 5 45 45 51 8 2 311 1145 45   g) 51 1 1 51 114 1 461 81 81 8 15 11 265518 18 846618 9   h) 7 2 35 16343 48 5 40 40 35 16740 51 117840 40    29) 25 7 3 2 1 171 7 433 1 5 5 5     Alex can make 4 whole bears. Determine amount of fabric used to make 4 bears: Amount of fabric remaining: 20 21 207 yds yds yds yds33 3 1 yd left over3    30) To make 24 cookies, 3 4 cup of brown sugar is required. Raphael wants make 48 cookies which is 2 times 24 cookies, so to determine the amount of brown sugar needed, multiply 3 4 by 2. 33 2 6 2 12 1 1 cups4 4 1 442  Section 1.1: Review of Fractions 631) 2 175175725 2 1 7 150 hits 32) 33 03056 3 15 118 children 33) Add the width of the frame twice to each dimension since it is being added to both sides of the picture. 311 3 1 118 2 2 22888 8 5228  111 21112 2 2 2 2 2488 888 211168 4116 1682 1516 in. by 22 in.28   34) 34 330 26 29 2644 4 43 133 i n .44  35) 2118 3 611 1 13 4 2 12 12 12 836212 17212 53 cups12     36) 1 3 1 261 5 5 10 10 10 10 261 10 9mile10   37) 3 3 15 1216 11 16 114 5 20 20 15 12520 35 gallons20   38) 11 734 4 3444 34  2 4 117 18 rows 39) 54 24267 5 16 135 problems 40) 1 117Deposit: $117339 1 1 3 1$39 Keep: $117 $39 $78  41) Add the total length welded so far: 13 2 914 10 14 106 4 12 12 29 1 124 2412 12   Subtract the total from the desired length: Chapter 1: The Real Number System and Geometry 771 1 2 12 232 24 32 2481 2 2 42 4 45 2231 2424 24 45 22724 237 i n .24    42) 2 150015003500 2 1 3 11000 teenagers 43) 3 400400580 3 1 5 1240 students Section 1.2: Exercises 1) a) base: 6; exponent: 4 b) base: 2; exponent: 3 c) base: 9 8; exponent: 5 2) a) base: 5; exponent: 1 b) base: 1; exponent: 8 c) base: 3 7; exponent: 2 3) a) 49999 9 b) 822222222 2 c) 3111 1 444 4 4) 7 is a factor which appears 5 times in the product 77777 . 5) a) 288 8 6 4 b) 211 11 11 121 c) 42 2222 1 6 d) 35 5 5 5 125 e) 43 3333 8 1 f) 212 12 12 144 g) 211 1 1 h) 233 3 9 10 10 10 100 i) 61 111111 1 2 222222 6 4 j)  20.3 0.3 0.3 0.09 6) a) 299 9 8 1 b) 213 13 13 169 c) 333 3 3 2 7 d) 52 22222 3 2 e) 344 4 4 6 4 f) 411 1 1 1 1 g) 266 6 3 6 h) 277 7 4 9 55 5 2 5 i) 42 2222 1 6 3 3333 8 1 Section 1.2: Exponents and Order of Operations 8j)   20.02 0.02 0.02 0.0004  7) 20.5 0.5 0.5 0.25 or 2 2 110.524 8) 1 raised to any power equals 1. 9) Answers may vary. 10) 20 12 5 32 5 27   11) 1 7241 541 9  12) 51 18 2 11 33 2 11 35 11 24   13) 4 821 4 2 41 4 3 8    14) 15 2 1 30 1 29  15) 2 03 29 2 069 14 9 23    16) 28 21 7 4 28 3 4 31 4 27      17) 381 2 89 1 74   18) 9527 1 27 159 15 1 14    19) 21 2 9 2 58 31 0 1 1 58 421 3 193 10 5 1311 2 20 5 20 20 13 20   20) 45 12 4 96 632 5 96 31 6 321 3 10 1 10 3 27 9 27 27 7 27  21) 232 3 42243 4 9 34 29 27 8 18 18 19 1 or 118 18     22) 2235 9 2 5 24 4 1 6 36 25 11 16 16 16      23) 25 11 2 1 25 22 1 31 4    24) 21 61 42 21 67 18 7 25     25)    3339 3 9 7 39 3 2 39 3 8 39 24 15   26)    2212 71 12 6 12 3 617 2 7 3     27) 60 15 5 3 4 15 19  Chapter 1: The Real Number System and Geometry 928)  2 227 10 7 8 3 27 3 8 3 27 9 8 3 32 4 2 7         29)  74 5 1 9 1 0 2 74 5 9 2 75 2 35 2 37       30)    3 36 3 14 12 10 63 2 1 0 63 8 1 0 61 1 1 0 66 10 56        31)       32 321232 1 16 125 5 1 2 125 25 12 5 11 0 1 1          32)  2 247 3 5 62 4         2 211 3 5 8 4 121 3 5 8 16 121 3 40 16 121 3 24 121 72 49          33)  22 247 2 4 5 42 5 12 8 3 144 24 120 100 10 5 120 12 6     34)  22 6684 2 1 2 2 78 69 5 6 5 4 144 64 3 80402    35)  33 249 6 43 42 4 23 8 4 1 (27) 28 7 27 6 or 377 36)   4473 1 08 73 2 61 021 1 651 1 73 1 6 22 74 8 5 5 5 22 22 2        Section 1.3: Exercises 1) Acute 2) Right 3) Straight 4) Obtuse 5) Supplementary; complementary 6) No. If both angles are obtuse then their sum will be great than 180°, so they cannot be supplementary. 7) 90 59 31 8) 90 84 6  9) 90 12 78  10) 90 40 50 11) 180 143 37  12) 180 62 118  Section 1.3: Geometry Review 1013) 180 38 142  14) 180 155 25  15) Angle Measure Reason 180 31 149 supplementary 31 vertical 149 verticalmA mB mC mA        16) Angle Measure Reason 180 84 96 supplementary 96 vertical 84 verticalmA mB mA mC        17) 180 18) the sum of the two known angles 90 68 158  the measure of the unknown angle 180 158 22  The triangle is right since it contains one right angle. 19) the sum of the two known angles 119 22 141  the measure of the unknown angle 180 141 39  The triangle is obtuse since it contains one obtuse angle. 20) the sum of the two known angles 47 71 118  the measure of the unknown angle 180 118 62  The triangle is acute since all three angles are acute. 21) the sum of the two known angles 90 51 141   the measure of the unknown angle 180 141 39  The triangle is right since it contains one right angle. 22) No. The sum of the angles in a triangle is 180. If a triangle had two obtuse angles, their sum would be greater than 180. 23) Equilateral 24) Scalene 25) Isosceles 26) Each of them is a 60 angle. 27) True 28) True 29) 210 8 80 ftAl w   22 21 0 28 20 16 36 ftPlw  30) 2(8)(3.7) 29.6 mmAb h   222(4) 2(8) 81 6 2 4 m mPa b    31)    21 2 114 cm 6 cm2 7 6 42 cmAb h   8 cm 14 cm 7.25 cm 29.25 cmP abc    32)    221 2 118 in. 5 in.2 9 5 in. 45 in.Ab h    Chapter 1: The Real Number System and Geometry 1113 in 18 in 7.8 in 38.8 inP abc   33)  2 26.5 mi 6.5 mi 42.25 miAs   4 4 6.5 mi 26 milesPs  34) 2 22217 ft 2 ft32 23 5 ft32 115 1 ft 19 ft66Al w       22 212 7 ft 2 2 ft32 23 5 4622 532 3 1115 5 20 ft33Plw          35)  12 21 2 112 11 162 6 27 162 inAh b b     13 in 11 in 12 in + 16 in 52 inP abcd  36) 2 22(3.8 cm) 14.44 cmAs  4 4(3.8 cm) 15.2 cmPs  37) a) 2 2 2 25 in 25 in 78.5 inAr      b) 2 25 i n 10 in 31.4 inCr     38) a) 2 2 221 ft ft 3.14 ftAr   b) 2 21 f t 2 ft 6.28 ftCr    39) a) 2 2 222.5 m 6.25 m 19.625 mAr     b) 2 22 . 5 m 5 m 15.7 mCr     40) a) 2 2 227 cm 49 cm 153.86 cmAr     b) 2 27 c m 14 cm 43.96 cmCr     41) 2 2 21m2 1 m4Ar     2 12 m2 mCr     Section 1.3: Geometry Review 1242) 2 2 24.5 in 20.25 inAr     2 2 4.5 in 9 i nCr    43) 2 2 27 ft 49 ftAr     2 27 f t 14 ftCr    44) 2 2 25.3 cm 28.09 cmAr     2 2 5.3 ft 10.6 ftCr    45)      22 223 m 13 m 11 m 7 m 299 m 77 m 376 mA    2 23 m 2 20 m 46 m 40 m 86 mP 46)      22 219 cm 5 cm 11 cm 12 cm 95 cm 132 cm 227 cmA    2 19 cm 2 17 cm 38 cm 34 cm 72 cmP   47)          222 220.5 in 4.8 in 5.7 in 8.4 in 11.2 in 4.9 in 98.40 in 47.88 in 54.88 in 201.16 inA     2 20.5 in 2 13.2 in 41 in 26.4 in 67.4 inP  48)     22 217 ft 6 ft 6 ft 4 ft2 42 ft 12 ft 54 ftA  7 ft 6 ft 7 ft 5 ft 5 ft 30 ftP  49)   22 214 in 12 in 10 in 8 in 168 in 80 in 88 inA  50)     22 210 m 11 m 7 m 8 m 110 m 56 m 54 mA  51)     22 24 ft 7 ft 1.5 ft 1.5 ft 28 ft 2.25 ft 25.75 ftA  52)      22 2115 ft 8 ft 2 3 ft 3 ft2 120 ft 9 ft 111 ftA    53)   22 22 216 cm 3.14 5 cm 256 cm 78.5 cm 177.5 cmA   54)  22 22 220 in 3.14 10 in 400 in 314 m 86 inA  55)   37 m 5 m 2 m 70 m Vl w h  56) 3 332 mm 8 mm Vs  57) a)  3 3 3 334 3 446 in 216 in33 4 72 in 288 inVr      Chapter 1: The Real Number System and Geometry 1358)     2 2 2 331 3 15 ft 16 ft3 125 ft 16 ft3 1 400400 ft ft33Vr h       59) 3 3 334 3 4 4 5005 ft 125 ft ft33 3Vr     60)     39.4 in 11 in 12 in 1240.8 in Vl w h  61)    2 2 2 34 cm 8.5 cm 16 cm 8.5 cm 136 cmVr h       62)    2 2 2 32 ft 2.3 ft 4 ft 2.3 ft 9.2 ftVr h       63) a)   29 ft 6.5 ft 58.5 ft A 258.5 ft 2$20 ft $1170 b) No, it would cost $1170 to use this glass. 64) 3(15 in) (10 in) (13.6 in) 2040 inVl w h   65) a)   2 2 33 ft 8 ft 3.14 9 ft 8 ft 226.08 ftV   b) Capacity (7.48)(226.08) 1691 gal  66) 25 ft 8 ft 40 ft A To find the cost multiply the area by the rate. The Alhambra would cost 240 ft 2$9.80 ft $392.00 The Sahara would cost 240 ft 2$12.20 ft $488.00 So, she could afford either one. 67) a)  2 10 in 20 3.14 in 62.8 inC  b)  2 2 210 in 3.14 100 in 314 inA  68) 17 in 8.5 in 12 in 12 in 8.5 in 58 inP   69)      330 ft 19 ft 1.5 ft 855 ft Capacity 855 7.48 6395.4 galV   70) 2 2 18 in 36 in 36 3.14 113.04 inCr       Section 1.3: Geometry Review 1471) First, find the area of the countertop; it is made of three sections: 113 1 1 1 121 0 2 29 2 2 244 4 4 6 2 4 15 2646 11 5 1 1 1 127 6 2 21 6 3 742 6 6 4 2 8A                      2 21The area of the countertop is 37 ft . 8 To find the total cost, multiply the area by the unit cost. 1Cost 37 ft ($80.00) =$2970.00 8 No, she cannot afford her first choice granite. The granite counterto p would cost $2970.00 72)     2 2 2 31.5 cm 2 cm (3.14) 2.25 cmt 2 cm 14.13 cmVr h     73)  2 24 . 6 i n 2(3.14) 4.6 in 28.9 inCr     74) (a)  3316 in 11 in 5 in42 387.75 inVl w h         (b) 3 3Capacity liters287.75 in 0.016 in 6.024 liters   75) 121) A ( )2ah b b 21(4f )(14f 8ft)2 2ft(22f ) 44ftt tt  ) First, find the perimeter of the garden 14ft 5ft 8ft 5ft 32ft To find the total cost, multiply the perimeter by unit cost Cost 32ft $23.50/ft $752b P      76) 211) (15.6 in.)(18 in.)22 140.4 in. ) P 3 3(18 in.) 54 inaA b h bb    77) 211(15.6 in.)(18 in.)22 140.4 in.Ab h  78) 2 22First, find the area A (10 ft.)(12 ft.) 120 ft. To find the total cost, multiply the area by unit cost. Cost 120 ft. $2.69/ft. $322.80lw    79) 22 3Use 3.14 for 11(3.14)(12 ft) (8 ft)33 1205.76 ftVr h   80) The volume of the solid is the sum of the volumes of a right circular cone and a hemi-(half) sphere. Use 3.14 for . Chapter 1: The Real Number System and Geometry 1523 23 33 311 32 11 4(3.14)(1 in.) (4 in.)+ (3.14)(1 in.)32 3 1(12.56 in. 6.28 in. ) 6.28 in.3Vr h r    Section 1.4: Exercises 1) Answers may vary. 2) Answers may vary. 3) a) 17 b) 17,0 c) 17,0, 25 d) 4117,3.8, ,0, 25,6.7, 258 e)10,9.721983... f) all numbers in the set. 4) a) 21 b) 21,0 c) 6, 21, 0 d) ____276, 21,5. 62 , 0.4,3 , 0,98 e) 23, 2.074816... f) all numbers in the set. 5) true 6) false 7) false 8) true 9) true 10) true 11) 12) 13) 14) 15) The distance of the number from zero 16) 0 17) 8 18) 6 19) 15 20) 1 21) 3 4 22) 4.7 23) 10 10 24) 99 25) 99 44 26) 55 66 27) 14 14  28) 27 27 29) 17 4 13 13 Section 1.5: Addition and Subtractio n of Real Numbers 1630) 10 6 4 4    31) 114477  32) 9.6 9.6 33) 910, 2, 0, , 3.8, 710 34) 375 , 1, , 2.06, 2.6,384 35) 156.51, 6.5, 5, 2,7 , 736  36) 31 51, , 0.5, 0, 4,42  37) True 38) True 39) False 40) False 41) False 42) True 43) False 44) False 45) 53 46) 36 million 47) 14 million 48) 58,000 49) 419,000 50) 2.1 Section 1.5: Exercises 1) Answers may vary. 2) Answers may vary. 3) Answers may vary. 4) 85 3  5) 61 1 5 6) 15 6  7)  27 9   8)  10 6 4 9)  81 57  10) 12 6 18   11) 31 1 1 4  12) 71 3 6  13) 31 54 23 14)  19 14 19 14 33   15)  26 15 26 15 11      16)  20 30 20 30 10     Chapter 1: The Real Number System and Geometry 1717) 352 498 850  18)  217 521 304   19) 73 7 9 21 12 4 12 12 12 6   20) 3 11 9 22 13 10 15 30 30 30   21) 17 4 2 1 2 5 1or 16 8 24 24 24 24        22) 2 2 10 18 28 9 5 45 45 45    23) 4 4 20 12 8 91 5 4 5 4 5 4 5       24) 13167 84888        25)  19.4 16.7 2.7  26)  31.3 19.82 31.3 19.82 11.48      27)  25.8 16.57 25.8 16.57 9.23      28)  7.3 21.9 7.3 21.9 14.6    29)  9 5 11 9 6 9 6 15     30)   2 3 8257      31)   1 6 4 1 10 11     32)   14 10 2 14 12 14 12 26     33)  31 8 6 4 2 42 2        34)   14 9 1 8 5 7 2       35) 16 4 3 10 12 3 10 91 0 1 9       36) 82 837 2 037 17 7 24      37)  53 0 1 4 2 5 3 0 1 4 2 35 14 2 21 2 23        38)  17 9 1 10 17 9 1 10 811 071 0 1 7          39) 42 5 81 2 1 5 93 61 8 1 8 1 8 82 7 18 18 19 1 or 118 18           40) 13 3 5 63 2 5 10 10 10 10 53 10 10 21 10 5                Section 1.5: Addition and Subtractio n of Real Numbers 1841) 11 31 82 46 31 2 1 84 24 24 24 24 91 4 5 24 24 24           42) 11 3 2 22 9 16 12 8 3 24 24 24 22 7 24 24 22 7 24 24 29 5 or 124 24            43)    2.7 3.8 1.4 6.9 6.5 5.5 6.5 5.5 12    44)   9.7 5.5 1.1 9.7 4.4 9.7 4.4 5.3        45)  71 1 6 1 3 4 7 471 1        46) 81 3 1 2 8 1 3 1 2 91 5 91 5 6       47)  2 3 258 23 2 3 12 3 16 7             48)  67 52 0 1 1 1 5 20 11 159 15 9 14 5 4 6       49) false 50) true 51) false 52) false 53) true 54) true 55) 18 6 12  His score in the 2005 Masters was 12. 56) 275.6 287.1 11.5 There were 11.5 million fewer visitors to the national parks in 2007 than in 1999. 57) 6,110,000 5,790,000 320,000   The carbon emissions in China were 320 thousand metric tons more than those of the United States. 58) 428,554, 470 22, 430 428,576,900  The budget was $428,576,900. 59) 881,566 45, 407 926,973 There were 926,973 flights at O’Hare in 2007. 60) 41 149 108 The highest temperature recorded in Minneapolis was 108° F. 61) a) 1745 1748 3 b) 1611 1745 134 c) 1480 1611 131 d) 1480 1763 283 62) a) 19 25 6 Chapter 1: The Real Number System and Geometry 19 b) 18 17 1 c) 14 18 4  d) 14 25 11  63) a) 2.1 2.8 0.7  b) 2.6 2.5 0.1 c) 2.5 2.1 0.4 d) 2.6 2.8 0.2  64) a) 136.2 181.3 45.1  b) 140.2 124.6 15.6 c) 109.1 140.2 31.4  d) 109.1 181.3 72.2  65) 571 2 66) 11 3 14 67) 10 16 6  68) 41 5 1 1  69) 98 1 7  70) 19 25 6   71) 21 13 8  72) 72 01 3  73) 20 30 10 74) 37 22 15  75) 23 19 4 76) 81 8 1 0  77) 5 11 18 6 18 12     78) 1 7 3 3 51 4 3 54 9   Section 1.6: Exercises 1) negative 2) positive 3) 87 5 6  4) 4 ( 9) 36  5) 15 ( 3) 45  6)  23 48 1104   7) 43(7 ) 1 2(7 ) 8 4     8)  51 ( 1 1 ) 5 ( 1 1 )5 5    9) 41 14 33 10 2 33 3111 10 52 15  10) 14 15 14 27 28   1 27 9155 28 25 18  11) ( 0.5)( 2.8) 1.4 12) ( 6.1)(5.7) 34.77  13)  9 5 ( 1) ( 3) 45 3 135    14)  1 6 (4) ( 2) (3) 24 ( 6) 144        15) 33(7 )( 8 )(1 )(5 )10 10     128028 841  16) 55(4 )03 0 066     17) when is negative k 18) when is positive k 19) when k0 Section 1.6: Multiplication and Division of Real Numbers 2020) 2 22 2( 8) means 8 ( 8) 64 8m e a n s 1 8 So, 1 8 1 64 64           21) 2(6 ) 3 6 22) 263 6  23) 35 125  24) 421 6 25) 239 26) 511  27) 274 9  28) 346 4  29) 523 2  30) 212 144 31) positive 32) negative 33) 50 ( 5) 10  34) 84 12 7  35) 64416 36) 5469 37) 2.480.3 38) 16320.5 39) 12 6 10 13 5 13  40) 15 28 120 or 973 3    41) 007 42) 006 43) 270 3 1or 1180 2 2 44) 64 1 320 5 45) 7 8( 5) 7 ( 40) 33    46) 4 021 0 2 01 0 3 0      47) 2 29 14 ( 3)(6) ( 5) ( 18) 25 18 43       48) 223 6 4 23 36 4 23 932     49) 3 310 2(1 4) 9 10 2( 3) 9 10 2( 27) 910 ( 54) 910 6 16        50)     4 474 8 6 5 74 2 5 74 1 6 5 28 16 5 7             51)       382 7 3 64 62 71 8 621 1 62 21 6                 Chapter 1: The Real Number System and Geometry 2152)                 523 4 5 9 3 0 7 32 3 4 5 9 30 7 32 3 4 5 21 7 32 3 4 5 3 32 12 15 5                             53)    46 3 12 46 36 524 4 0 10 1 40 4    54)      22 286 1 0 7 48 10 7 5 1 12 5 4 12 5 48 10 7 41 2 5 45 16 7 4559             55) 12 6 72   56) 80204 57)  9 7 5 9 35 44    58)   10 2 11 20 11 9      59) 6377 7 09  60) 5488 9 16     61)  4 8 19 32 19 13  62)   1 6 3 2 04 8 2 02 8     63)  10072 2 5 724    25 5 25 5 20     64)   35 3511 2 2255    72 21 5  65)  2 18 31 2 13 26    66)  2 5 15 2 5 15   21 0 2 0 67) 22273 3 279 18 68) 11302 2 3015 15 69) 112 5 36 60 18 422     70)  1118 21 532     1118 26 6 13 732   Section 1.7: Exercises 1) The constant is 4. 2Term Coeff. 77 66 44p p Section 1.7: Algebraic Expressions and Properties of Real Numbers 222) 5The constant is .6 Term Coeff. 88 55 66z 3) The constant is 11. 22Term Coeff. 1 22 1 11 11xy xy y 4) The constant is 5.  3 2Term. Coeff. 1 1 99 55w w w  5) The constant is 1.  5 4 2Term Coeff. 22 1 55 3.8 3.8 1 11g g g g  6) There is no constant. 2 2Term Coeff. 121 121 1c d 7) a) 43 w h e n 2cc 42 3 8 3 1 1    b) 43 w h e n 5cc  4( 5) 3 20 3 17    8) a) 85 w h e n 3mm  83 5 2 4 5 1 9  b) 85 w h e n 1mm  8 1 58 51 3    9) 43 4 ( 5 ) 3 2 01 7xy   10) 33 ( 2 ) ( 5 ) 6 5 1zy     11) 2 219 (2 ) ( 3 ) (5 ) 1 9 4 ( 15) 19 4 15 19 19 19 0zx y           12) 2 24 (3) (4)( 5)( 2) 9 (40) 49xy z     13) 33(3) 21 ( 2 ) ( 5 ) 1 27 27310 1 9x y     14) 33 22(2 ) 8 811( 3 ) 19 1 8z x     15) 22 2224 ( ) (2 ) (5 ) 2( 5) 4(3 2) 42 5 10 4(1)zy yx z     21 21 143 14 23 2 Chapter 1: The Real Number System and Geometry 2316) 34 3410 3( 2 ) 10 3( 5 (2)( 2)) (3) ( 2) 10 3( 9) 27 16 10 27 17 11 11yz xz        17) No, the exponents are different. 18) Yes, both are -terms n 19) 3Yes. both are -terms ab 20) Answers may vary. 21) 1 22) 0 23) 5 24) 1 8 25) distributive 26) associative 27) identity 28) inverse 29) commutative 30) distributive 31) associative 32) commutative 33) 19 p 34) 55mn 35) (8 1) 9 36) 2c 37) 32 1k 38) 91 0x 39) y 40) 2477 41) No. Subtraction is not commutative. 42) Yes. Addition is commutative. 43) 2(1 9) 2 1 2 9 2 18 20      44) 3(9 4) 3 9 3 4 27 12 39     45) 2 ( 57 ) 2 5( 2 ) 7 10 ( 14) 24          46) 5 ( 37 ) 5 3( 5 ) 7 15 ( 35) 50          47) 4(8 3) 4 8 4 ( 3) 32 ( 12) 20     48)  65 1 1 65 (6 ) 1 1 30 66 36          49)  10 4 10 4 6    50)  39 39 1 2     51)  83 8 8 3 8 2 4yy y   52)  41 1 4 4 1 1 4 4 4kk k   53)  10 6 10 ( 10) 6 10 60zz z      54)  75 7 ( 7 ) 5 7 3 5mm m      55) 3 ( 4 6 ) 3 (3 )(4) (3 )(6 ) 31 21 8xy x y xy           56)   62 5 1 62 6 5 6 1 12 30 6ab a b ab       57) ( 8 9 14) 8 9 14cd cd    58) (1 0 4 ) 1 0 4x yz x yz   59) 10 9 14 2 10 14 9 2 24 7pp p p p    60) 22 2 22 2 211 12 3 6 12 6 11 3 17 8kk k kk k k       Section 1.7: Algebraic Expressions and Properties of Real Numbers 2461) 22 2 22 2 218 2 19 2 13 18 2 19 2 13 19 30yy y yy y y            62) 73 1 96 2 73921 6 35xx x x xxxx x          63) 42 1 1 4 23393 5 5 9 3 15 1 4 6 55 9 9 16 2 59rr r r rr r       64) 31 36284 4 33 16284 4 4 8368 1 88 8 4 4 39 9 84aa a aaa aaa a          65) 23 5 6 1 0 61 0 71 0ww ww ww w    66) 22 22 286 3 7 861 8 7 21 1dd dd d        67)  94 3 4 3 91 2 4 4 3 449 1 2 3 00 0xx x x xx x          68)  11 3 2 5 1 11 6 15 1 61 1 1 5 1 73mm mmmm m        69)  38 3 5 3 8 3 5 52gg g g g      70)   6 4 10 11 8 5 2 64 0 4 44 0 1 6 40 40 6 44 16 06 6 6 6bb bb bb b            71)  52 1 0 2 51 0 1 0 25 2 10 103tt tttt t    72)   11 8 3 4 2 6 9 11 24 32 2 12 9 2 4 2 1 13 21 2922 24uu uu uuu          73)    325 7 1 1 47 31 0 1 4 1 1 2 8 4 31 0 3 2 8 4 30 9 28 4 30 4 9 28 26 37xx x x xx xx xx x             74)   22 6 5 2 3 7 16 22 6 10 15 7 16 22 6 10 15 7 16 10 7 22 6 15 16 17 15ww ww ww ww w                 Chapter 1: The Real Number System and Geometry 2575)  4121 0 352zz  81 3852 2 81 3852 2 16 5 16 3 10 10 2 2 11 13 10 2zz zz zzz      76)  2567 2531 2cc  14 5 25436 1 2 51 4 2 5463 1 2 24 5 56 25 6 6 12 12 29 31 61 2cccc ccc     77) 35 111 0 348 1 0tt    15 9 5 1124 8 1 6 15 5 9 1128 4 1 6 60 5 16 36 1 8 8 16 16 16 65 19 81 6tt tt tt t           78)  79 221 4315 10 5yy  79 98 6 15 5 10 5 5 98 7 9 6 5 5 15 10 5 9 8 14 27 36 5 5 30 30 30 17 23 53 0yy yy yy y      79)   2.5 4 1.2 3 8xx 2.5 10 3.6 9.6 2.5 3.6 10 9.6 1.1 19.6xxxx x      80)  9.4 3.8 2 5 0.6 1.9 aa   9.4 7.6 19 0.6 1.9 7.6 1.9 9.4 19 0.6 5.7 9aa aa a         81) 18x 82) 11x 83) 6x 84) 8x 85) 3x 86) 14x 87) 12 2 x 88) 65 6 5 1 1xx x 89)  32 7 2 37 2 4 x xx    90) 92 9 2 1 1xx x 91) 15 5 15 5 10xx x  92)  82 32 832 5 x xx      