Solution Manual for Intermediate Algebra for College Students, 7th Edition

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SOLUTIONSMANUALDANIELS.MILLERNiagara County Community CollegeINTERMEDIATEALGEBRAFORCOLLEGESTUDENTSSEVENTHEDITIONRobert BlitzerMiami Dade College

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TABLE OF CONTENTS for INSTRUCTOR SOLUTIONSINTERMEDIATEALGEBRA FORCOLLEGESTUDENTS7EChapter1:Algebra, Mathematical Models, and Problem Solving1Chapter2:Functions and Linear Functions67Chapter3:Systems of Linear Functions131Chapter4:Inequalities and Problem Solving251Chapter5:Polynomials, Polynomial Functions, and Factoring331Chapter6:Rational Expressions, Functions, and Equations423Chapter7:Radicals, Radical Functions, and Rational Exponents587Chapter8:Quadratic Equations and Functions677Chapter9:Exponential and Logarithmic Functions839Chapter 10:Conic Sections and Systems of Nonlinear Equations943Chapter 11:Sequences, Series, and the Binomial Theorem1051

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Chapter 1Algebra, Mathematical Models, and Problem Solving11.1 Check Points1.a.eight times a numberfive more8585xxb.the quotient of adecreased bynumber and seventwice the number2277xxxx2.replacewith 10230.12230.12(10)231.221.8xxAt age 10, the average neurotic level is 21.8.3.replacewith 1322286(3)86(133)86(10)86(100)8600608xx4.a.2010 is 10 years after 2000.replacewith 10224654117,65046(10)541(10)17,65046(100)541(10)17,6504600541017,65027,660xDxxDThe formula indicates that the mean student-loandebt for college students who graduated in 2010was $27,660.b.The model value, $27,660, is more than theactual data value, $26,682. Thus, themathematical model overestimates by $978.5.a.true; Because the number 13 is an element of theset of integers.b.true; Because 6 is not an element of{7, 8, 9, 10},the statement is true.6.a.8is less than2;trueb.7 is greater than3;truec.1is less than or equal to4;falsed.5 is greater than or equal to 5; truee.2 is greater than or equal to14;true7.a.25xxb.13.5xxc.1x x 1.1 Concept and Vocabulary Check1.variable2.expression3.bth to thenth power; base; exponent4.formula; modeling; models5.natural6.whole7.integers8.rational9.irrational10.rational; irrational11.left12.2; 5; 2; 513.greater than14.less than or equal to

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Chapter 1Algebra, Mathematical Models, and Problem Solving21.1 Exercise Set1.5x2.6x3.4x4.9x5.4x6.2x7.210x8.54x9.162x10.132x11.42x12.53x13.35x14.610x15.75(10)7505716.86 58303817.6(3)81881018.8 342442019.21111339931120.21111224421121.276(7)349423731022.287 8464564841223.3345(97)45(2)45(8)4404424.  3365 8665 265 86404625.283(82)643(6)64184626.284 83644 564204427.{1, 2, 3, 4}28.{1, 2, 3}29.{–7, –6, –5, –4}30.{–6, –5, –4, –3}31.{8, 9, 10, . . .}32.{10, 11, 12, . . .}33.{1, 3, 5, 7, 9}34.{1, 3, 5, 7}35.true; Seven is an integer.36.true; Nine is an integer.37.true; Seven is a rational number.38.true; Nine is a rational number.39.false; Seven is a rational number.40.false; Nine is not an irrational number.41.true; Three is not an irrational number.42.true; Five is not an irrational number.43.false;12is a rational number.44.false;14is a rational number.45.true;2is not a rational number.46.true;πis not a rational number.47.false;2is a real number.

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Section 1.1Algebraic Expressions, Real Numbers, and Interval Notation348.false;πis a real number.49.–6 is less than –2; true50.–7 is less than –3; true51.5 is greater than –7; true52.3 is greater than –8; true53.0 is less than –4; false. 0 is greater than –4.54.0 is less than –5; false. 0 is greater than –5.55.–4 is less than or equal to 1; true56.–5 is less than or equal to 1; true57.–2 is less than or equal to –6; false. –2 is greaterthan –6.58.–3 is less than or equal to –7; false. –3 is greaterthan –7.59.–2 is less than or equal to –2; true60.–3 is less than or equal to –3; true61.–2 is greater than or equal to –2; true62.–3 is greater than or equal to –3; true63.2 is less than or equal to12; false. 2 is greaterthan12.64.4 is less than or equal to12; false. 4 is greaterthan12.65.16xx66.24xx67.52xx68.43xx69.31xx70.25xx71.2x x72.3x x73.3x x 74.5x x 75.3x x76.2x x77.5.5x x78.3.5x x79.true80.true81.false;31, 2,3, 4.82.false;41, 2, 3, 4,5.

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Chapter 1Algebra, Mathematical Models, and Problem Solving483.true84.true85.false; The value of {x|xis an integer between3and 0} ={ 2,1}, not{ 3,2,1,0}.86.false; The value of {x|xis an integer between4and 0} ={ 3,2,1}, not{ 4,3,2,1, 0}.87.false; Twice the sum of a number and three isrepresented by23x, not23x.88.false; Three times the sum of a number and five isrepresented by35x, not35x.89.4.60.024.60.02(20)4.2RxThe average resistance to happiness at age 20 is 4.2.90.4.60.024.60.02(30)4.0RxThe average resistance to happiness at age 30 is 4.0.91.[4.60.02(30)][4.60.02(50)]4.03.60.4The difference between the average resistance tohappiness at age 30 and at age 50 is 0.4.92.[4.60.02(20)][4.60.02(70)]4.23.21.0The difference between the average resistance tohappiness at age 20 and at age 70 is 0.4.93.  22328.70.3328.7 40.3 43234.84.862SxxAccording to the formula, 67% of American adultsused smartphones to go online in 2013. The formulaunderestimated the actual value by 1%.94.  22328.70.3328.7 30.3 33226.12.755.4SxxAccording to the formula, 55.4% of Americanadults used smartphones to go online in 2012. Theformula overestimated the actual value by 0.4%.95.5 (5032)9C5 (18)10910°C is equivalent to 50°F.96.555(32)(8632)(54)30999CF30°C is equivalent to 86°F.97.2246016460(2)16(2)412016(4)4120641246460httTwo seconds after it was kicked, the ball’s heightwas 60 feet.98.2246016460(3)16(3)418016(9)418014418414440httThree seconds after it was kicked, the ball’s heightwas 40 feet.99. – 116.Answers will vary.117.does not make sense; Explanations will vary.Sample explanation: Many models work for a whileand then no longer are valid beyond a certain point.118.does not make sense; Explanations will vary.Sample explanation: Though this value is beyondthe capabilities of a calculator, it still exists. Thisparticular expression can be obtained via severalsoftware applications.119.makes sense120.does not make sense; Explanations will vary.Sample explanation: The model can be used toestimate the number in 2000 by letting0.x

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Section 1.2Operations with Real Numbers and Simplifying Algebraic Expression5121.false; Changes to make the statement true will vary.A sample change is: Every integer is a rationalnumber.122.false; Changes to make the statement true will vary.A sample change is: Some integers are not wholenumbers.123.true124.true125.Evaluate the two expressions.2 4202 24482 42082028Since the bird lover purchases17of the birds, theexpression has to be a multiple of 7. Since 48 in nota multiple of 7 and 28 is a multiple of 7, we knowthat the correct expression is2 420.126.2 33545127.824310or824310128.26 is not a perfect square and26cannot besimplified. Consider the numbers closest to 26,both smaller and larger, which are perfect squares.The first perfect square smaller than 26 is 25. Thefirst perfect square larger than 26 is 36. We knowthat the square root of 26 will lie between thesenumbers. We have362625.  If wesimplify, we have6265.  Therefore,26lies between –6 and –5.129.–5 and 5 are both a distance of five units from zeroon a real number line.130.4163(2)163(16)164864812(106)12(4)88131.2(35)2(3(4)5)2(125)2(17)34x6106(4)10241034x1.2 Check Points1.a.66because6is 6 units from 0.b.4.54.5because 4.5 is 4.5 units from 0.c.00because 0 is 0 units from 0.2.a.10( 18)28  b.0.20.90.7c.3165152101010  3.a.If8,x then( 8)8.x  b.If13,xthen13.x 4.a.7107( 10)3  b.4.3( 6.2)4.36.210.5 c.4141355555  5.a.2( 5)( 5)( 5)25b.25(5 5)25  c.3( 4)( 4)( 4)( 4)64 d.4333338155555625         6.a.3284 b.25248343515 7.2235122( 4)325122(16)3256(16)32596229674 

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Chapter 1Algebra, Mathematical Models, and Problem Solving68.343( 2)2(69)43( 8)2( 3)424232054  9.Commutative Property of Addition:4994xxCommutative Property of Multiplication:4949xx10.a.6(12)(612)18xxxb.7(4 )( 7 4)28xxx 11.4(72)288xx 12.22222231411(14)(311 )(141)(311)1514xxxxxxxxxxxx13.8(25)416404164401240xxxxxxx14.64[7(2)]64[72]64[9]6364424xxxxx1.2 Concept and Vocabulary Check1.negative number2.03.positive number4.positive number5.positive number6.negative number7.positive number8.divide9.subtract10.absolute value; 0;a11.a;a12.0; inverse; 0; identity13.ba14.()ab c15.abac16.simplified1.2 Exercise Set1.772.10103.444.13135.7.67.66.8.38.37.22ππ8.33ππ9.2210.3311.2255  12.771010  

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Section 1.2Operations with Real Numbers and Simplifying Algebraic Expression713.3( 8)11  14.5( 10)15  15.14104 16.1569 17.6.82.34.5 18.7.92.45.5 19.113119215515151520.747421051052781101010    21.2323949482735363636   22.34345757212041353535   23.3.7( 4.5)8.2  24.6.2( 5.9)12.1  25.0( 12.4)12.4  26.0( 15.3)15.3  27.12.4( 12.4)0 28.15.3( 15.3)0 29.1111xx 30.1313xx 31.55xx 32.99xx 33.00xx34.22xx 35.31531512  36.42042016  37.8( 10)81018 38.7( 13)71320 39.20( 5)20515   40.30( 10)301020   41.11111214242444 42.12121221051051052143101010    43.2.3( 7.8)2.37.85.5  44.4.3( 8.7)4.38.74.4  45.02022 46.03033 47.9( 10)90 48.8( 10)80 49.3113350.7117751.151511313 

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Solution Manual for Intermediate Algebra for College Students, 7th Edition - Page 11 preview image

Chapter 1Algebra, Mathematical Models, and Problem Solving852.111111313 53.20054.3 0055.421818 56.53215230 57.2( 3)( 1)( 2)( 4)( 6)( 1)( 2)( 4)(6)( 2)( 4)( 12)( 4)4858.32153615365330390  59.210101010060.28886461.2101010100  62.288864  63.322228 64.3333327 65.411111166.44444425667.Since a product with an odd number of negativefactors is negative,3311. 68.A product with an odd number of negative factors isnegative.3511 69.31111122228       70.311111444464       71.1234 72.3065 73.9045274.5511575.004.676.005.377.4.60is undefined.78.5.30is undefined.79.17199292714 80.1315525236 81.265306155122  82.289728369122  83.4( 5)6( 3)20( 18)20182    84.8( 3)5( 6)24( 30)24306   85.223( 2)4( 3)3(4)4(9)123624 86.225( 3)2( 2)5(9)2(4)45837

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Solution Manual for Intermediate Algebra for College Students, 7th Edition - Page 12 preview image

Section 1.2Operations with Real Numbers and Simplifying Algebraic Expression987.2281624364164 43644 43641634834588.221010052310010025 231004 23100839238989.2222225 235 299( 2)3( 2)109921111121  90. 2221023 453 45121736123 2126691.832(25)4(86)832( 3)4(2)83 68832861492.832(57)5(42)832( 2)5(2)83 41083 41083681826 93.22434128858333 94.64532415999101195. 222562 37124893 25893 512 48975187114142 96.222123 5 23123 5 497336736123 5 131036123 5(13)4 5(13)262620(13)260102626 97.153( 1)122 3154122 3152122 31526 315218131831 98.1752122 3177122 3177122 31776 317718101828 99.2222201105122011062201100362201642201822011637100. 2222435213243(3)1324922434842  101.Commutative Property of Addition410104xxCommutative Property of Multiplication410410xx102.Commutative Property of Addition530305xxCommutative Property of Multiplication530530xx103.Commutative Property of Addition7557xx Commutative Property of Multiplication7575xx

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Solution Manual for Intermediate Algebra for College Students, 7th Edition - Page 13 preview image

Chapter 1Algebra, Mathematical Models, and Problem Solving10104.Commutative Property of Addition3773xx Commutative Property of Multiplication3737xx105.4(6)(46)10xxx106.12(3)(123)15xxx107.7(3 )( 7 3)21xxx 108.10(5 )( 10 5)50xxx 109.11( 3 )333yyy 110.11( 4)444yyy 111.3(25)3 23 5615xxx112.5(47)5 45 72035xxx113.7(23)7 27 31421xxx   114.9(32)9 39 22718xxx   115.(36)1 31 636xxx    116.(63)1 61 363xxx   117.757512xxxx118.81081018xxxx119.22226615xxxx120.22229918xxxx121.2222226104264102641021012xxxxxxxxxxxx122.222295349354129xxxxxxxx123.8(35)68 38 562440624640246401840xxxxxxxxxx124.7(45)87 47 5828358288352035xxxxxxxx125.5(32)725 35 21 71 215107215710215712812yyyyyyyyyy 126.4(53)634 54 (3)1 61 3201263206151415yyyyyyyy 127.74 34574 34571216201625yyyy128.65 82465 82465 12265 1252660101054yyyyyy 129.2222222222221846251846125184671846718647186111211xxxxxxxxxxxx

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Solution Manual for Intermediate Algebra for College Students, 7th Edition - Page 14 preview image

Section 1.2Operations with Real Numbers and Simplifying Algebraic Expression11130.2222221457241457144145710xxxxxx22222214571014751014715715xxxxxx131.444xxxx 132.8828xxxxx133.6530xx 134.10440xx 135.523xxx136.62628xxxxx 137.83683656xxxxx138.8368318310xxx 139.21( 29)8  140.4( 10)6  141.21( 29)212950 142.4( 10)41014 143.3( 10)3107  The approval rating of France exceeds the approvalrating of China by 7.144.3( 29)32926  The approval rating of France exceeds the approvalrating of Iran by 26.145.10( 3)49333  The average approval rating of China, France, andIsrael is3.146.29( 10)2118336  The average approval rating of Iran, China, and theUK is6.147. 221.21.6(40)1.2 61.6(640)116.8DxxAccording to the model, college students spent$116.8 billion in 2013.The model underestimates the actual valuedisplayed in the graph by $0.2 billion.148. 221.21.6(40)1.2 41.6(440)89.6DxxAccording to the model, college students spent$89.6 billion in 2011.The model overestimates the actual value displayedin the graph by $2.6 billion.149.a.0.050.12 10,0000.0512000.1212000.07xxxxxb.0.05 60000.12 10,00060000.05 60000.12 400030048078012000.07 60001200420780The total interest will be $780.150.a.0.060.5(50)0.06250.5250.44tttttb.0.06(20)0.5(5020)0.06(20)0.5(30)1.21516.2250.44(20)258.816.2The total distance will be 16.2 miles.

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Solution Manual for Intermediate Algebra for College Students, 7th Edition - Page 15 preview image

Chapter 1Algebra, Mathematical Models, and Problem Solving12151. – 167.Answers will vary.168.makes sense169.makes sense170.does not make sense; Explanations will vary.Sample explanation: For terms to be considered liketerms they must have the same variables and thesame powers.171.does not make sense; Explanations will vary.Sample explanation: When there is no number infront of a variable, the coefficient has a value of 1.172.false; Changes to make the statement true will vary.A sample change is:164 24 28173.false; Changes to make the statement true will vary.A sample change is:62 4362 76148 174.false; Changes to make the statement true will vary.A sample change is:53(4)531237xxx175.false; Changes to make the statement true will vary.A sample change is:2xxx 176.true177.(82) 3414178.12 5109452179.229 4(16)(39)9 47( 6)1212556655213 9336125522736125363546397 180.104xx181.444102(5)102(75)102(2)102 16103242x182.true;12is not an irrational number.183.x24yx−324( 3)495y  −224( 2)440y −124( 1)413y 024(0)404y124(1)413y224(2)440y324(3)495y 184.x21yx−321( 3)198y  −221( 2)143y  −121( 1)110y 021(0)101y121(1)110y221(2)143y 321(3)198y 185.x1yx−44133y  −33122y  −22111y  −11100y 00111y11122y22133y

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Solution Manual for Intermediate Algebra for College Students, 7th Edition - Page 16 preview image

Section 1.3Graphing Equations131.3 Check Points1.2.Make a table:222222221( ,)31( 3)8( 3,8)21( 2)3( 2,3)11( 1)0( 1, 0)01(0)1(0,1)11(1)0(1, 0)21(2)3(2,3)31(3)8(3,8)xyxx yyyyyyyy=−−=− −= −−−−=− −= −−−−=− −=−=−==−==−= −−=−= −−3.Make a table:1( ,)44133( 4,3)33122( 3, 2)22111( 2,1)11100( 1,0)00111(0,1)11122(1, 2)22133(2,3)xyxx yyyyyyyy       4.a.The drug concentration is increasing from 0 to 3hours.b.The drug concentration is decreasing from 3 to13 hours.c.The drug’s maximum concentration is 0.05milligram per 100 milliliters, which occurs after3 hours.d.None of the drug is left in the body.5.The minimumx-value is –100, the maximumx-value is 100, and the distance between consecutivetick marks is 50. The minimumy-value is –100, themaximumy-value is 100, and the distance betweenconsecutive tick marks is 10.1.3 Concept and Vocabulary Check1.x-axis2.y-axis3.origin4.quadrants; four5.x-coordinate;y-coordinate6.solution; satisfies

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