Solution Manual For Intermediate Algebra For College Students, 6th Edition

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Chapter 1Algebra, Mathematical Models, and Problem Solving1.1 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 3 years after 2007.replacewith 3222.75.682.7(3)5.6(3)82.7(9)5.6(3)824.316.8849.1xSxxSb.The model value, 49.1, is the same as the actualdata value shown in the figure.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 to1

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Chapter 1:Algebra, Mathematical Models, and Problem Solving21.1 Exercise Set2.6x4.9x6.2x8.54x10.132x12.53x14.610x16.86 58303818. 8 342442020.21111224421122. 287 8464564841224. 3365 8665 265 86404626.284 83644 564204428.{1, 2, 3}30.{–6, –5, –4, –3}32.{10, 11, 12, . . .}34.{1, 3, 5, 7}36.true; Nine is an integer.38.true; Nine is a rational number.40.false; Nine is not an irrational number.42.true; Five is not an irrational number.44.false;14 is a rational number.46.true;is not a rational number.48.false;is a real number.50.–7 is less than –3; true52.3 is greater than –8; true54.0 is less than –5; false. 0 is greater than –5.56.–5 is less than or equal to 1; true58.–3 is less than or equal to –7; false. –3 is greaterthan –7.60.–3 is less than or equal to –3; true62.–3 is greater than or equal to –3; true64.4 is less than or equal to12; false. 4 is greaterthan12.66.24xx68.43xx70.25xx72.3x x74.5x x 76.2x x78.3.5x x80.true

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 4 preview image

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Intermediate Algebra for College Students 6ESection 1.282.false;41, 2,3, 4,5.84.true86.false; The value of {x|xis an integer between4and 0} = { 3,2,1}, not { 4,3,2,1, 0}.88.false; Three times the sum of a number and five isrepresented by35x, not 35x.90.4.60.024.60.02(30)4.0RxThe average resistance to happiness at age 30 is 4.0.92.[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 0.4.94.224.65.554.6(3)5.5(3)562.963GxxAccording to the formula, 63 new college programsin green studies were created in 2008. The formulaunderestimated the actual value by 3 programs.96.555(32)(8632)(54)30999CF30C is equivalent to 86F.98.2246016460(3)16(3)418016(9)418014418414440httThree seconds after it was kicked, the ball’s heightwas 40 feet.100. – 116.Answers will vary.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.120.does not make sense; Explanations will vary.Sample explanation: The model can be used toestimate the number in 2000 by letting0.x122.false; Changes to make the statement true will vary.A sample change is: Some integers are not wholenumbers.124.true126.2 33545128.26 is not a perfect square and26 cannot 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  3

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 5 preview image

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Chapter 1:Algebra, Mathematical Models, and Problem Solving4b.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 8.343( 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; identity

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 6 preview image

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Intermediate Algebra for College Students 6ESection 1.213.ba14.()ab c15.abac16.simplified1.2 Exercise Set2.10104.13136.8.38.38.3310.3312.771010  14.5( 10)15  16.1569 18.7.92.45.5 20.747421051052781101010 22.34345757212041353535   24.6.2( 5.9)12.1  26.0( 15.3)15.3  28.15.3( 15.3)0 30.1313xx 32.99xx 34.22xx 36.42042016  38.7( 13)71320 40.30( 10)301020   42.12121221051051052143101010 44.4.3( 8.7)4.38.74.4  46.03033 48.8( 10)80 50.7117752.111111313 54.3 0056.53215230 58. 32153615365330390  60.28886462.  288864  64.3333327 66.44444425668.A product with an odd number of negative factors isnegative.3511 5

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 7 preview image

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Chapter 1:Algebra, Mathematical Models, and Problem Solving670.311111444464       72.3065 74.5511576.005.378.5.30is undefined.80.1315525236 82.289728369122  84.8( 3)5( 6)24( 30)24306   86.225( 3)2( 2)5(9)2(4)4583788.221010052310010025 231004 23100839238990.2221023 453 45121736123 2126692.832(57)5(42)832( 2)5(2)83 41083 41083681826 94.64532415999101196.222123 5 23123 5 497336736123 5 131036123 5(13)4 5(13)262620(13)260102626 98.1752122 3177122 3177122 31776 317718101828 100. 2222435213243(3)1324922434842  102.Commutative Property of Addition530305xxCommutative Property of Multiplication530530xx104.Commutative Property of Addition3773xx Commutative Property of Multiplication3737xx106.12(3)(123)15xxx108.10(5 )( 10 5)50xxx  110.11( 4 )444yyy 112.5(47)5 45 72035xxx114.9(32)9 39 22718xxx   116.(63)1 61 363xxx   118.81081018xxxx120.22229918xxxx

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 8 preview image

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Intermediate Algebra for College Students 6ESection 1.2122.222295349354129xxxxxxxx124.7(45)87 47 5828358288352035xxxxxxxx126.4(53)634 54 (3)1 61 3201263206151415yyyyyyyy128. 65 82465 82465 12265 1252660101054yyyyyy 130.2222221457241457144145710xxxxxx22222214571014751014715715xxxxxx132.8828xxxxx134.10440xx 136.62628xxxxx 138.8368318310xxx 140.4( 10)6  142.4( 10)41014 144.3( 29)32926  The approval rating of France exceeds the approvalrating of Iran by 26.146.29( 10)2118336  The average approval rating of Iran, China, and theUK is6.148.220.25(12)0.2(3)5(312)73.2Dxx  According to the model, college students spent$73.2 billion in 2009.The model underestimates the actual valuedisplayed in the graph by $0.8 billion.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.152. – 166.Answers will vary.168.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.172.false; Changes to make the statement true will vary.A sample change is: 164 24 28174.false; Changes to make the statement true will vary.A sample change is:53(4)531237xxx176.true178.12 51094527

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 9 preview image

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Chapter 1:Algebra, Mathematical Models, and Problem Solving8180.104xx181.444102(5)102(75)102(2)102 16103242x182.true;12 is 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1.3 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        

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 10 preview image

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Intermediate Algebra for College Students 6ESection 1.34.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; satisfies1.3 Exercise Set2. – 10.12.x,x y33, 022,511,800,911,822,533, 014.x,x y33,122, 011,100, 211,322, 433,59

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 11 preview image

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Chapter 1:Algebra, Mathematical Models, and Problem Solving1016.x,x y33,1022,811,600,411,222, 033, 218.x,x y373, 222,3151, 200, 2131, 222,1313, 220.x,x y33, 222,111, 000,111, 022,133, 222.x,x y33,622,411,200, 011,222,433,6

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 12 preview image

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Intermediate Algebra for College Students 6ESection 1.324.( ,)93( 3,)22( 2,2)11( 1,)20(0, 0)11(1,)22(2,2)93(3,)2xx y26.x,x y33,2822,911,200,111, 022, 733, 2628.[–10, 10, 2] by [– 4, 4, 2]This matches graph d.30.[–40, 40, 20] by [–1000, 1000, 100]This matches graph a.32.The equation that corresponds to1Yin the table is(b),21yx. We can tell because all of the points( 3,9), ( 2, 4), ( 1,1), (0, 0) , (1,1) , (2, 4) , and(3,9) are on the graph2yx, but all are not onany of the others.34.Yes. It passes through the point (0, 0) .36.(0, 2)38.The values of1Yand2Yare the same when2x and1x.40.42yx42.22yx11

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 13 preview image

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Chapter 1:Algebra, Mathematical Models, and Problem Solving1244.( ,)3( 3,1)2( 2,1)1( 1,1)0(0,1)1(1,1)2(2,1)3(3,1)xx y46.( ,)122, 211,111 , 22211 ,33311 ,33311 ,22211,1122,2xx y48.The top marginal tax rate in 1925 was 25%.50.The lowest marginal tax rate occurred in 1990 andwas about 28%.52.During the five-year period from 1930 to 1935, thetop marginal tax rate increased about 38%.54.At age 65, men have the greatest number ofawakenings, averaging about 8 awakenings pernight.56.The difference between thenumber of awakeningsfor 18-year-old men and women is about 1.1.58.graph d60.graph c62.graph a64.graph b66. – 72.Answers will vary.74.does not make sense; Explanations will vary.Sample explanation: Most graphing utilities do notdisplay numbers on the axes.76.does not make sense; Explanations will vary.Sample explanation: There may or may not be amathematical model that perfectly describes thegraph’s data.78.false; Changes to make the statement true will vary.A sample change is: When a point lies on thex-axis,y= 0.80.false; Changes to make the statement true will vary.A sample change is: Substituting the coordinates of(2,5) into324yx gives 3(5)2(2)4 which simplifies to 114 which is false.82.Your car was parked more than six hours, but notexceeding eight hours.83.14.314.384.1213179610124941249416133  85.65 4310620151062015101425xxxxxx 

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 14 preview image

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Intermediate Algebra for College Students 6ESection 1.486.43564( 9)35( 9)63634563939xx  The statement is true for9.x 87.133(2)133673xxx88.311021031125(31)155xxxx1.4 Check Points1.4529455295424424446xxxxxThe solution set is {6}.Check:45294(6)529245292929x2.2126453121143114128888881xxxxxxxxxxx  The solution set is {–1}.Check:2126452( 1)12( 1)6( 1)45( 1)21216451515xxxx   3.2(3)17133(2)261713362237323723530530556xxxxxxxxxxxThe solution set is {6}.Check:2(3)17133(2)2(63)17133(62)2(3)17133(8)61713241111xx 4.5357414xx53528287414285283285171411445732 54207211011110111011111111111111xxxxxxxxxxxxxThe solution set is {1}.Check:5357414151357414625741424141028282810102828xx5.474(1)347443474171xxxxxx This equation is an inconsistent equation and thushas no solution.The solution set is { }.13

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 15 preview image

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Chapter 1:Algebra, Mathematical Models, and Problem Solving146.799(1)279992797999xxxxxxxxThis equation is an identity and all real numbers aresolutions.The solution set isis a real numberx xor(,) or.7.385312989043853129890431293855775385577538538538515TxxxxxxThe average cost of tuition and fees at publiccolleges will reach $8904 in the school year ending15 years after 2000, or 2015.1.4 Concept and Vocabulary Check1.linear2.equivalent3.bc4.bc5.apply the distributive property6.least common denominator; 127.inconsistent;8.identity;(,) 1.4 Exercise Set2.385034214xxxThe solution set is {14}.4.587258016xxxThe solution set is {16}.6.25683610818xxx  The solution set is {18}.8.528355283538353279xxxxxxxThe solution set is {9}.10.352135138xxxxThe solution set is {8}.12.742814371436xxxxxThe solution set is {6}.14.5292242441yyyyyThe solution set is {–1}.16.21331223332123413441xxxxxxxxxxx    The solution set is {–1}.18.2751332751337313343134164xxxxxxxxx The solution set is {–4}.

Solution Manual For Intermediate Algebra For College Students, 6th Edition - Page 16 preview image

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Intermediate Algebra for College Students 6ESection 1.420.52235522353245253xxxxxxxxxxxxThe solution set is {3}.22.2 346562 34653026530212530127304276xxxxxxxxxxxxxThe solution set is {6}.24.3224816694318616462646226242zzzzzzzzz    The solution set is {–2}.26.1563030156xxxx653030xxxThe solution set is {30}.28.152613030526615515015xxxxxxxxThe solution set is {15}.30.352434452423202020xxxxxxxx The solution set is {–20}.32.217272221714214722282 277 172847119247119171197xxxxxxxxxxxxxxxxThe solution set is {7}.34.11246311212124633124 233284331047310xxxxxxxxxxx771xxThe solution set is {1}.36.23538xx2324 524381208233120816391048391045959519xxxxxxxxxxx  The solution set is {–19}.15

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