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

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SOLUTIONSMANUALDAVIDATWOODRochester Community and Technical CollegeDEVELOPMENTALMATHEMATICSWITHAPPLICATIONSANDVISUALIZATIONPREALGEBRA,BEGINNINGALGEBRA,ANDINTERMEDIATEALGEBRASECONDEDITIONGary RockswoldMinnesota State University, MankatoTerry KriegerRochester Community and Technical CollegewithJessica Rockswold

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Table of ContentsChapter 1Whole Numbers1Chapter 2Integers43Chapter 3Algebraic Expressions and Linear Equations75Chapter 4Fractions129Chapter 5Decimals205Chapter 6Ratios, Proportions, and Measurement281Chapter 7Percent and Probability333Chapter 8Geometry371Chapter 9Linear Equations and Inequalities in One Variable401Chapter 10Graphing Equations439Chapter 11Systems of Linear Equations in Two Variables523Chapter 12Polynomials and Exponents577Chapter 13Factoring Polynomials and Solving Equations629Chapter 14Rational Expressions681Chapter 15Introduction to Functions757Chapter 16Systems of Linear Equations827Chapter 17Radical Expressions and Functions863Chapter 18Quadratic Functions and Equations923Chapter 19Exponential and Logarithmic Functions997Chapter 20Conic Sections1053Chapter 21Sequences and Series1093

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Section 1.1:Introduction to Whole Numbers1Chapter 1 Whole NumbersSection 1.1 Introduction to Whole Numbers1. counting2. 03. periods4. standard5. place value6. trillions7. word8. expanded9. graph10. bar graph, line graph11. 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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2Chapter 1 Whole Numbers35. 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 bewritten 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 as83,000,600,012.44. 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+650. 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+854. In expanded form, 17 is written as 10+7.55.a) 3<5b) 4>3c) 5>156.a) 3>2b) 5<8c) 2<557.a) 22>4b) 8<11c) 11<2258.a) 12<31b) 23<40c) 31<4059.a) 86>64b) 64>24c) 24>1060.a) 27<73b)98>15c) 15<73

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Section 1.1:Introduction to Whole Numbers361. 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 officereceipts.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 ascore 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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4Chapter 1 Whole Numbers96. 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 thenext.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, threehundred 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 canbe 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 hundredthousand.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; Perimeter1. addends2. sum.3. Yes,4. commutative5. associative6. identity7. addition8. minuend, subtrahend9. difference10. No11. identity12. subtraction13. solution14. solutions

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Section 1.2:Adding and Subtracting Whole Numbers; Perimeter515.11+ 172816.34+ 215517.534+6559918.742+5679819.624+ 26188520.322+ 51683821.7511+357786822.2128+671279923.137484124787224.133521539489125.1 116, 49110,57327, 064

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6Chapter 1 Whole Numbers26.1 1112, 45823,97536, 43327.11 128,52953, 29881,82728.11 1 1340,98272, 099413, 08129.1 1 1409,377654, 7821, 064,15930.1 1 11500,809499, 7651, 000,57431.23056023135896732.1 1 25286377832715, 23233.1 1 210, 66945,12732, 25588, 05134.1 2173, 41756,83022,804153, 05135. Commutative Property

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Section 1.2:Adding and Subtracting Whole Numbers; Perimeter736. Commutative Property37. Identity Property38. Identity Property39. Associative Property40. Associative Property41. 6642. 8343. 7044. 9245.24111346.55312447.4683743148.2826122149.1769347142250.3857554330351.3672352115152.8175804213353.2 14553432182316

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8Chapter 1 Whole Numbers54.4 1264523327312555.5 14 2 1156 , 43123,52632,90556.7 113 1781, 64758,32923,31857.7 12 1245, 83214,39931, 43358.0 17 1312 8 17184 , 29798, 42885,86959.4 16517, 056416, 029101, 02760.6 136 10873,870649,335224,53561.2 9 9 173007389261862.5 9 9 1460045765428

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Section 1.2:Adding and Subtracting Whole Numbers; Perimeter963.3 99 15 1340 , 06322,37817, 68564.6 99 1370 , 03667,8732 16365.0 9 916 9 13100 , 70389,82710,87666.3 9 910 9 12400 , 102398,5161 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 because936is a true statement.80. The solution is 4 because549is a true statement.81. The solution is 3 because835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 because241014is a true statement.85. The solution is 27 because876027is a true statement.86. The solution is 89 because 31+58=89 is a true statement.87. The solution is 151 because15110141is a true statement.88. The solution is 47 because 53+47=100 is a true statement.

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10Chapter 1 Whole Numbers89. The solution is 27 because 80+27=107 is a true statement.90. The solution is 72 because841272is a true statement.91. The solution is 529 because 150+379=529 is true statement.92. The solution is 116 because11610214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 smallestnumber 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 temporaryassistance.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 by6,000,000.116. 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 Concepts1. 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; Area113. Forty-eight million, two hundred thirty-nine thousand, six hundred ten can be written in standardform 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)1137365814317b)11 11204, 6335 897210,5307. a)7 1387831248659b)2 13 14713 , 448112,564600,8848. a) The corresponding mathematical expression is9745, 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 because29227. is a true statement.10. The perimeter is 28+26+20+14+8+12= 108 cm.Section 1.3 Multiplying and Dividing Whole Numbers; Area1. addition2. factors3. product4. commutative5. associative6. identity7. zero8. distributive9. multiplication10. subtraction11. dividend, divisor12. quotient13. identity14. 0, undefined15. long division16. division

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12Chapter 1 Whole Numbers17. 1 square unit18. area19. Associative property20. Associative property21. Commutative property22. Commutative property23. Identity property24. Identity property25. Distributive property26. Distributive property27. Zero property28. Zero property29.5 65 930.7 27 531.4 84 132.6 96 333.6 32 334.5 47 435.71736.0 9037.0 5038.1121239. 6(9) = 5440. (4)(8)=3241.548733642.183541543.130261812

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Section 1.3:Multiplying and Dividing Whole Numbers; Area1344.6 74798383245.71242841420170446.39418752940169247.2172146881720240848.12492231476984011,31649.1 2 12 3 214753573754425051, 625

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