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Solution Manual for Developmental Mathematics with Applications and Visualization: Prealgebra, Beginning Algebra, and Intermediate Algebra, 2nd Edition

Solution Manual for Developmental Mathematics with Applications and Visualization: Prealgebra, Beginning Algebra, and Intermediate Algebra, 2nd Edition is an essential tool for mastering your textbook, offering detailed solutions and helpful explanations.

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    S OLUTIONS M ANUAL D AVID A TWOOD Rochester Community and Technical College D EVELOPMENTAL M ATHEMATICS WITH A PPLICATIONS AND V ISUALIZATION P REALGEBRA , B EGINNING A LGEBRA , AND I NTERMEDIATE A LGEBRA S ECOND E DITION Gary Rockswold Minnesota State Unive rsity, Mankato Terry Krieger Rochester Community and Technical College with Jessica Rockswold

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    Table of Contents Chapter 1 Whole Numbers 1 Chapter 2 Integers 43 Chapter 3 Algebraic Expressions and Linear Equations 75 Chapter 4 Fractions 129 Chapter 5 Decimals 205 Chapter 6 Ratios, Proportions, and Measurement 281 Chapter 7 Percent and Probability 333 Chapter 8 Geometry 371 Chapter 9 Linear Equations and Inequalities in One Variable 401 Chapter 10 Graphing Equations 439 Chapter 11 Systems of Linear Equations in Two Variables 523 Chapter 12 Polynomials and Exponents 577 Chapter 13 Factoring Polynomials and Solving Equations 629 Chapter 14 Rational Expressions 681 Chapter 15 Introduction to Functions 757 Chapter 16 Systems of Linear Equations 827 Chapter 17 Radical Expressions and Functions 863 Chapter 18 Quadratic Functions and Equations 923 Chapter 19 Exponential and Logarithmic Functions 997 Chapter 20 Conic Sections 1053 Chapter 21 Sequences and Series 1093

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    Section 1.1 : Introduction to Whole Numbers 1 Chapter 1 Whole Numbers Section 1.1 Introduction to Whole Numbers 1. counting 2. 0 3. periods 4. standard 5. place value 6. trillions 7. word 8. expanded 9. graph 10. bar graph, line graph 11. The digit 8 is the fourth digit from the right. It is in the thousands place. 12. The digit 8 is the second digit from the right. It is in the tens place. 13. The digit 8 is the eighth digit from the right. It is in the ten-millions place. 14. The digit 8 is the sixth digit from the right. It is in the hundred-thousands place. 15. The digit 8 is the third digit from the right. It is in the hundreds place. 16. The digit 8 is the fifth digit from the right. It is in the ten-thousands place. 17. The digit 8 is the first digit from the right. It is in the ones place. 18. The digit 8 is the seventh digit from the right. It is in the millions place. 19. The digit 8 is the ninth digit from the right. It is in the hundred-millions place. 20. The digit 8 is the tenth digit from the right. It is in the billions place. 21. The hundreds place is the third place from the right. The digit is 7. 22. The ten-thousands place is the fifth place from the right. The digit is 1. 23. The hundred-thousands place is the sixth place from the right. The digit is 8. 24. The ones place is the first place from the right. The digit is 5. 25. The billions place is the tenth place from the right. The digit is the 3. 26. The millions place is the seventh place from the right. The digit is 9. 27. The tens place is the second place from the right. The digit is 2. 28. The thousands place is the fourth place from the right. The digit is 6. 29. The hundred-millions place is the ninth place from the right. The digit is 4. 30. The ten-millions place is the eighth place from the right. The digit is 0. 31. In word form, the number 472,500 is written as four hundred seventy-two thousand, five hundred. 32. In word form, the number 79 is written as seventy-nine. 33. In word form, the number 93,206 is written as ninety-three thousand, two hundred six. 34. In word form, the number 10,000,015 can be written as ten-million, fifteen.

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    2 Chapter 1 Whole Numbers 35. In word form, the number 1651 can be written as one thousand, six hundred fifty one. 36. In word form, the number 632 can be written as six hundred thirty two. 37. Two thousand fifty-five is written in standard form as 2055. 38. Four hundred seventy-one is written in standard form as 471. 39. Five hundred ninety-nine million, six hundred sixteen thousand, four hundred twenty three can be written as 599,616,423. 40. Four thousand, one hundred thirty-five miles can be written as 4135. 41. Thirty-nine million, four hundred ten thousand can be written in standard form as 39,410,000. 42. Fifty-two thousand, three hundred sixty-seven can be written in standard form as 52,367. 43. Eighty-three billion, six hundred thousand, twelve can be written in standard form as 83,000,600,012. 44. One million, four hundred two thousand, eighty-one can be written in standard form as 1,402,081. 45. 300,000+40,000+2000+500+60+3 can be written in standard form as 342,563. 46. 5000+500+50+1 can be written in standard form as 5551. 47. 7,000,000+900,000+5000+300+70+7 can be written in standard form as 7,905,377. 48. 4,000,000+500,000+7000+200+9 can be written in standard form as 4,507,209. 49. In expanded form, 2,510,036 is written as 2,000,000+500,000+10,000+30+6 50. In expanded form, 8004 is written as 8000+4. 51. In expanded form, 629 is written as 600+20+9. 52. In expanded form, 63,907 is written as 60,000+3000+900+7. 53. In expanded form, 603,138 is written as 600,000+3000+100+30+8 54. In expanded form, 17 is written as 10+7. 55. a) 3<5 b) 4>3 c) 5>1 56. a) 3>2 b) 5<8 c) 2<5 57. a) 22>4 b) 8<11 c) 11<22 58. a) 12<31 b) 23<40 c) 31<40 59. a) 86>64 b) 64>24 c) 24>10 60. a) 27<73 b)98>15 c) 15<73

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    Section 1.1 : Introduction to Whole Numbers 3 61. 34>0, since 34 is to the right of 0. 62. 0<56, since 0 is to the left of 56. 63. 45<54, since 45 is to the left of 54. 64. 72>27, since 72 is to the right of 27. 65. 300>299, since 300 is to the right of 299. 66. 175>155, since 175 is to the right of 155. 67. 30,000<300,000, since 30,000 is to the left of 300,000. 68. 2100>2001, since 2100 is to the right of 2001. 69. 50,101<51,010, since 50,101 is to the left of 51,010. 70. 630,020<632,202, since 630,020 is to the left of 632,202. 71. According to the graph India had 81,000,000 Internet users in 2012. 72. According to the graph, there were 101,000,000 Internet users in Japan in 2012. 73. According to the graph, France had the fewest Internet users in 2012. 74. According to the graph, Brazil had more Internet users in 2012 than Russia. 75. According to the graph, the longest river in Canada is the Mackenzie. 76. According to the graph, the St. Lawrence River is the 3058 kilometers long. 77. According to the graph, the Nelson River is 2575 km long. 78. According to the graph, the Yukon River is longer than the Nelson River. 79. According to the graph, in 2014 Guardians of the Galaxy took in the smallest amount in box office receipts. 80. According to the graph, The Avengers had box office receipts of $623,000,000. 81. According to the graph, in 2014 Guardian of the Galaxy had box office receipts of $315,000,000. 82. According to the graph, The Hunger Games had higher gross box office receipts than Toy Story 3. 83. According to the graph, the minimum wage has increased over the time period. 84. According to the graph, the minimum wage in 1990 was 380 cents or $3.80. 85. According to the graph, the largest increase occurred from 1990 to 2010. 86. According to the graph, in 1950 the minimum wage was 75 cents. 87. According to the chart, Web Site Design had the highest score. 88. According to the chart, product pricing had a satisfaction score of 7. 89. Since each line in the chart represents a multiple of 2, then the web security score is 4. 90. According to the chart, people are not satisfied with shipping costs. 91. According to the charts, the Power Tools site had a higher score than the Electronics site. 92. According to the chart, Web Site Design had a score of 3. 93. According to the charts, the Power Tool site had an overall score of 38 and the Electronics site had a score of 37. 94. According to the chart, people are satisfied with the security of the site. 95. According to the table, in 2006 females had an average score of 502.

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    4 Chapter 1 Whole Numbers 96. According to the table, in 2004 males earned the highest average score. 97. According to the table, in 2008 males had a higher average score than females. 98. According to the table, in 2008 and 2010 males recorded an identical average score. 99. According to the table, in 2010 public colleges cost $8174. 100. According to the table, in 2012 private colleges cost $25,593. 101. According to the table, in 2011 public colleges had a cost of $8557. 102. According to the table, the cost of public and private colleges never decreased from one year to the next. 103. In expanded form 1124 can be written as 1000+100+20+4. 104. In expanded form 186,282 can be written as 100,000+80,000+6000+200+80+2. 105. Thirty-four billion, three hundred fifty-nine million, seven hundred thirty-eight thousand, three hundred seventy-eight can be written in standard form as 34,359,738,378. 106. One billion, seventy-three million, seven hundred forty-one thousand, eight hundred twenty-four can be written in standard form as 1,073,741,824. 107. In word form, the number 423,000,000,000 can be written as four hundred twenty-three billion. 108. In word form, the number 98,700,000 can be written as ninety-eight million, seven hundred thousand. 109. The truck driver earns more since 41,804 is to the right of 41,627 on a number line. 110. The white dish has fewer bacteria since 12,678,453 is to the left of 12,687,435 on a number line. Section 1.2 Adding and Subtracting Whole Numbers; Perimeter 1. addends 2. sum. 3. Yes, 4. commutative 5. associative 6. identity 7. addition 8. minuend, subtrahend 9. difference 10. No 11. identity 12. subtraction 13. solution 14. solutions

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    Section 1.2 : Adding and Subtracting Whole Numbers; Perimeter 5 15. 11 + 17 28 16. 34 + 21 55 17. 534 + 65 599 18. 742 + 56 798 19. 624 + 261 885 20. 322 + 516 838 21. 7511 + 357 7868 22. 2128 + 671 2799 23. 1 3748 4124 7872  24. 1 3352 1539 4891  25. 1 1 16, 491 10,573 27, 064 

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    6 Chapter 1 Whole Numbers 26. 1 11 12, 458 23,975 36, 433  27. 1 1 1 28,529 53, 298 81,827  28. 1 1 1 1 340,982 72, 099 413, 081  29. 1 1 1 409,377 654, 782 1, 064,159  30. 1 1 1 1 500,809 499, 765 1, 000,574  31. 230 5602 3135 8967  32. 1 1 2 528 6377 8327 15, 232  33. 1 1 2 10, 669 45,127 32, 255 88, 051  34. 1 2 1 73, 417 56,830 22,804 153, 051  35. Commutative Property

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    Section 1.2 : Adding and Subtracting Whole Numbers; Perimeter 7 36. Commutative Property 37. Identity Property 38. Identity Property 39. Associative Property 40. Associative Property 41. 66 42. 83 43. 70 44. 92 45. 24 11 13  46. 55 31 24  47. 468 37 431  48. 282 61 221  49. 1769 347 1422  50. 3857 554 3303  51. 3672 3521 151  52. 8175 8042 133  53. 2 14 5534 3218 2316 

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    8 Chapter 1 Whole Numbers 54. 4 12 6452 3327 3125  55. 5 14 2 11 56 , 431 23,526 32,905  56. 7 11 3 17 81, 647 58,329 23,318  57. 7 12 12 45, 832 14,399 31, 433  58. 0 17 13 12 8 17 184 , 297 98, 428 85,869  59. 4 16 517, 056 416, 029 101, 027  60. 6 13 6 10 873,870 649,335 224,535  61. 2 9 9 17 3007 389 2618  62. 5 9 9 14 6004 576 5428 

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    Section 1.2 : Adding and Subtracting Whole Numbers; Perimeter 9 63. 3 9 9 15 13 40 , 063 22,378 17, 685  64. 6 9 9 13 70 , 036 67,873 2 163  65. 0 9 9 16 9 13 100 , 703 89,827 10,876  66. 3 9 9 10 9 12 400 , 102 398,516 1 586  67. The corresponding mathematical expression is 22+57, which results in $79. 68. The corresponding mathematical expression is 107—39, which results in 68 songs. 69. The corresponding mathematical expression is 793—54,which results in 739 photos. 70. The corresponding mathematical expression is 1011+873, which results in 1884 toothpicks. 71. The corresponding mathematical expression is 62—19, which results in 43 eggs. 72. The corresponding mathematical expression is 13+89+104, which results in 206 cell phone minutes. 73. The corresponding mathematical expression is 1200+300, which results in 1500 patients. 74. The corresponding mathematical expression is 107—89, which results in 18 degrees. 75. The corresponding mathematical expression is 645—3, which results in 642 DVDs. 76. The corresponding mathematical expression is 185—58, which results in 127 plates. 77. The corresponding mathematical expression is 39+71, which results in 110 web pages. 78. The corresponding mathematical expression is 539+267,which results in 806 downloads. 79. The solution is 9 because 9 3 6   is a true statement. 80. The solution is 4 because 5 4 9   is a true statement. 81. The solution is 3 because 8 3 5   is a true statement. 82. The solution is 3 because 3+7=10 is a true statement. 83. The solution is 20 because 20+14 = 34 is a true statement. 84. The solution is 10 because 24 10 14   is a true statement. 85. The solution is 27 because 87 60 27   is a true statement. 86. The solution is 89 because 31+58=89 is a true statement. 87. The solution is 151 because 151 10 141   is a true statement. 88. The solution is 47 because 53+47=100 is a true statement.

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    10 Chapter 1 Whole Numbers 89. The solution is 27 because 80+27=107 is a true statement. 90. The solution is 72 because 84 12 72   is a true statement. 91. The solution is 529 because 150+379=529 is true statement. 92. The solution is 116 because 116 102 14   is a true statement. 93. The perimeter is 13+20+23 = 56 feet. 94. The perimeter is 18+18+11+11 = 58 inches. 95. The perimeter is 5+9+3+12+6 = 35 cm. 96. The perimeter is 7+7+7+10+8 = 39 miles. 97. The perimeter is 14+13+10+7+4+6 = 54 miles. 98. The perimeter is 25+10+13+13+12+23= 96 cm. 99. The perimeter is 8+21+18+5+10+16 = 78 inches. 100. The perimeter is 22+26+15+14+37+40 = 154 feet. 101. 16 – 4 = 12; Therefore, the iPhone camera has 12 megapixels. 102. 3 + 3 = 6, The screen size of the Samsung phone is 6 inches. 103. 83 – 40 = 43 Therefore, Gaedel’s height is 43 inches. 104. 131+32 = 163 Therefore, Groth’s record serve is 163 mph. 105. 553+69 = 622 deaths in 2011 and 2012. 106. 2,400,000—1,331,500 = 1,068,500. Therefore, the difference between the largest and smallest number of fires is 1,068,500. 107. 70+60=130 Therefore, the iPhone 5 can withstand 130 pounds of pressure. 108. 150 – 60 = 90. Therefore, the iPhone 6 can withstand 90 pounds of pressure. 109. 52 – 17 = 35. Therefore, Gretzky was 17 years old when he began his professional career. 110. 40+32 =72. Therefore, the team scoring record is 72 points. 111. 722 +380 = 1102. Therefore, the bench shirt world record is 1102 pounds. 112. 9390 – 936 = 8454. Therefore, the value of the Dow at the start of the day was 8454. 113. 12,000,000 – 6,000,000 = 6,000,000. In 2000 there were 6,000,000 who received temporary assistance. 114. 4,000,000+1,000,000 = 5,000,000. In 2004 there were 5,000,000 who received temporary assistance. 115. 12,000,000-6,000,000 = 6,000,000. Therefore, we must decrease the number of recipients by 6,000,000. 116. 4,000,000+2,000,000 = 6,000,000. In the year 2000 the number of recipients will be 6,000,000. Sections 1.1 and 1.2 Checking Basic Concepts 1. a) The digit 3 is the fifth digit from the right. It is in the tens-thousand place. b) The digit 3 is the third digit from the right. It is in the hundreds place. 2. In expanded form 74,293 can be written as 70,000+4000+200+90+3.

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    Section 1.3 : Multiplying and Dividing Whole Numbers; Area 11 3. Forty-eight million, two hundred thirty-nine thousand, six hundred ten can be written in standard form as 48,239,610. 4. . . 5. a) 67>25 since 67 is to the right of 25 on the number line. b) 15<51 since 15 is to the left of 51 on the number line. 6. a) 11 3736 581 4317  b) 11 11 204, 633 5 897 210,530  7. a) 7 13 8783 124 8659  b) 2 13 14 713 , 448 112,564 600,884  8. a) The corresponding mathematical expression is 97 45  , which results in 52. b) The corresponding mathematical expression is 106+73, which results in 179. 9. a) The solution is 5 because 3+5 = 8 is a true statement. b) The solution is 29 because 29 22 7   . is a true statement. 10. The perimeter is 28+26+20+14+8+12= 108 cm. Section 1.3 Multiplying and Dividing Whole Numbers; Area 1. addition 2. factors 3. product 4. commutative 5. associative 6. identity 7. zero 8. distributive 9. multiplication 10. subtraction 11. dividend, divisor 12. quotient 13. identity 14. 0, undefined 15. long division 16. division

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    12 Chapter 1 Whole Numbers 17. 1 square unit 18. area 19. Associative property 20. Associative property 21. Commutative property 22. Commutative property 23. Identity property 24. Identity property 25. Distributive property 26. Distributive property 27. Zero property 28. Zero property 29. 5 6 5 9    30. 7 2 7 5    31. 4 8 4 1    32. 6 9 6 3    33. 6 3 2 3    34. 5 4 7 4    35. 7 1 7   36. 0 9 0   37. 0 5 0   38. 1 12 12   39. 6(9) = 54 40. (4)(8)=32 41. 5 48 7 336  42. 1 83 5 415  43. 1 302 6 1812 

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    Section 1.3 : Multiplying and Dividing Whole Numbers; Area 13 44. 6 7 479 8 3832  45. 71 24 284 1420 1704  46. 3 94 18 752 940 1692  47. 2 172 14 688 1720 2408  48. 1 2 492 23 1476 9840 11,316  49. 1 2 1 2 3 2 1475 35 7375 44250 51, 625 

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