Solution manual for intermediate algebra 1st edition by clark

Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ 1.1 Exercises Chapter 3.4 x − 8.2 = 15.6 3.4 x − 8.2 + 8.2 = 15.6 + 8.2 3.4 x = 23.8 Section 1.1 3.4 x 23.8 = 3.4 3.4 x=7 x + 10 = 40 x + 10 − 10 = 40 − 10 x = 30 x 30 = 2 x = 15 20 = 5.2 x − 0.8 20 + 0.8 = 5.2 x − 0.8 + 0.8 20.8 = 5.2 x 20.8 5.2 x = 5.2 5.2 4=x 3x + 14 = 35 3x + 14 − 14 = 35 − 14 3x = 21 x=4 3x 21 = 3 x=7 45 = −3.6c + 189 45 − 189 = −3.6c + 189 − 189 −144 = −3.6c −144 −3.6c = −3.6 −3.6 40 = c c = 40 −4t + = −32 −4t + − = −32 − −4t = −40 −4t −40 = −4 −4 t = 10 0.05 ( x − 200 ) = 240 0.05 x − 10 = 240 −7m + 20 = 48 −7m + 20 − 20 = 48 − 20 −7m = 28 −7m 28 = −7 −7 m = −4 0.05 x − 10 + 10 = 240 + 10 0.05 x = 250 0.05 x 250 = 0.05 0.05 x = 5000 10 0.03 ( n − 500 ) = 108 2.5 x + 7.5 = 32.5 2.5 x + 7.5 − 7.5 = 32.5 − 7.5 2.5 x = 25 0.03n − 15 = 108 0.03n − 15 + 15 = 108 + 15 0.03n = 123 2.5 x 25 = 2.5 2.5 x = 10 0.03n 123 = 0.03 0.03 n = 4100 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions 11 c a E = −17 w + 600 C = 10h + 20 E = −17(8) + 600 C = 10 (1) + 20 E = 464 C = 30 After weeks, enrollment in math classes at the college After hour of training, a new employee can make 30 will be 464 candies an hour 13 b a C = 10h = 20 N = −315.9t + 4809.8 C = 10 ( ) + 20 N = −315.9 ( ) + 4809.8 C = 40 + 20 = 60 After hour of training, a new employee can make 60 N = −631.8 + 4809.8 N = 4178 candies an hour In 1992, there were 4178 homicides of 15-19 year olds in c the United States Let C = 150 b 150 = 10h + 20 N = −315.9t + 4809.8 150 − 20 = 10h + 20 − 20 N = −315.9 (12 ) + 4809.8 130 = 10h N = −3790.8 + 4809.8 130 10h = 10 10 13 = h N = 1019 In 2002, there were 1019 homicides of 15-19 year olds in the United States A new employee can make 150 candies an hour after 13 c hours of training Let N = 7337 12 7337 − 4809.8 = −315.9t + 4809.8 − 4809.8 a 2527.2 = −315.9t E = −17 w + 600 2527.2 −315.9t = −315.9 −315.9 −8 = t E = −17(0) + 600 = 600 The total enrollment in math classes at the college was In 1982, there were 7337 homicides of 15-19 year olds in 600 at the beginning of the fall semester the United States b Let E = 430 14 430 = −17 w + 600 a p = 2.399 + 0.03w 430 − 600 = −17 w + 600 − 600 −170 = −17 w p = 2.399 + 0.03 ( ) −170 −17 w = −17 −17 10 = w p = 2.399 + 0.15 p = 2.549 Five weeks after the start of summer, the gas price is The total enrollment will be 430 ten weeks after the start $2.549 per gallon of the fall semester Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ 1.1 Exercises b b Let p = 2.759 P = 5.5(b) − 500.50 2.759 = 2.399 + 0.03w P = 5.5(200) − 500.50 2.759 − 2.399 = 2.399 − 2.399 + 0.03w P = 1100 − 500.50 0.360 = 0.03w P = $599.50 0.360 0.03w = 0.03 0.03 12 = w There is a $599.50 profit for selling 200 books c Let P = 3600 Twelve weeks after the start of summer, the gas price is P = 5.5b − 500.50 $2.759 per gallon 3600 = 5.5b − 500.50 15 3600 + 500.50 = 5.5b − 500.50 + 500.50 a 4100.5 = 5.5b P = 1.5t − 300 4100.5 5.5 = b 5.5 5.5 745.545 = b P = 1.5 (100 ) − 300 P = 150 − 300 P = −150 To make $3600 in profit, you must sell 746 books There is a loss of $150 for selling only 100 T-shirts 17 b a P = 1.5t − 300 C = 2.50 + 2.0m C = 2.50 + 2.0 ( 25 ) P = 1.5 ( 400 ) − 300 C = 2.50 + 50.0 P = 600 − 300 P = 300 C = 52.50 There is a profit of $300 for selling 400 T-shirts It costs $52.50 to take a 25-mile taxi ride in NYC c b Let P = 1000 100 = 2.50 + 2.0m 100 − 2.50 = 2.50 − 2.50 + 2.0m 1000 = 1.5t − 300 1000 + 300 = 1.5t − 300 + 300 97.50 = 2.0m 1300 = 1.5t 97.50 2.0m = 2.0 2.0 48.75 = m 1300 1.5t = 1.5 1.5 866.67 ≈ t For $100, you can take about a 48-mile taxi ride in NYC To make $1000 profit, you must sell 867 T-shirts 18 16 a a P = 35 − 0.07 s P = 35 − 0.07 (150 ) P = 5.5(b) − 500.50 P = 412.50 − 500.50 P = 35 − 10.5 P = 24.5 P = $ − 88.00 After 150 seconds, the pressure in the vacuum chamber There is a loss of $88 dollars for selling only 75 books will be 24.5 psi P = 5.5(75) − 500.50 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions b 23 P = 35 − 0.07 s a = 35 − 0.07 s P = 0.08 ( s − 1000 ) − 35 = 35 − 35 − 0.07 s P = 0.08 ( 2000 − 1000 ) −34 = −0.07 s P = 0.08 (1000 ) = 80 −34 −0.07 s = −0.07 −0.07 485.7 ≈ s On $2000 in sales, you will make $80 in commissions The pressure in the vacuum chamber will be psi after P = 0.08 ( s − 1000 ) about 486 seconds P = 0.08 ( 50, 000 − 1000 ) 19 P = 0.08 ( 49, 000 ) b a P = 3.5 This too few people This would mean that P = 3920 only 3500 people live in Kentucky On sales of $50,000, you will make $3920 in b P = 4200 This answer is most reasonable This commissions would mean that 4,200,000 people live in Kentucky c c P = −210 This not possible This would mean that P = 0.08 ( s − 1000 ) −210, 000 people live in Kentucky b R = −3000 Revenue must be ≥ so this is not 500 = 0.08s − 80 500 + 80 = 0.08s − 80 + 80 580 = 0.08s 580 0.08s = 0.08 0.08 7250 = s possible To make $500 per week, you will need $7250 in sales c R = $4500 This answer is most reasonable each week 21 24 a T = −50 This answer is most reasonable a b T = 75 This temperature is too warm for South Pole P = 0.06 ( s − 500 ) temperatures P = 0.06 ( 2000 − 500 ) c T = 82 This temperature is too warm for South Pole P = 0.06(1500) = 90 temperatures On $2000 in sales, you will make $90 in commissions 22 b a S = 10.50 This answer is too small to represent a P = 0.06 ( s − 500 ) cook’s monthly salary P = 0.06 ( 5000 − 500 ) b S = 1600 This answer is most reasonable for a cook’s P = 0.06(4500) = 270 monthly salary On $5000 in sales, you will make $270 in commissions 20 a R = 20 A $20 revenue for a two-day event seems too small c S = 28, 000 This answer is too large to represent a cook’s monthly salary Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ 1.1 Exercises c c P = 0.06 ( s − 500 ) Let C = 37 37 = 0.20m + 10 450 = 0.06 ( s − 500 ) 37 − 10 = 0.20m + 10 − 10 450 = 0.06s − 30 450+30 = 0.06s − 30 + 30 27 = 0.20m 480 = 0.06 s 480 0.06 = s 0.06 0.06 8000 = s 27 0.20 m = 0.20 0.20 135 = m If your June bill was $37, then you talked 135 minutes If you need at least $450 per week to pay your bills, you 27 must make $8000 in sales a P = 250 + 0.07 s 25 b a B = 29.95 + 0.55m Let s = 2000 P = 250 + 0.07 ( 2000 ) b B = 29.95 + 0.55 ( 75 ) P = 250 + 140 = 390 B = 29.95 + 41.25 If you have sales of $2000 in a week, your pay will be B = 71.20 $390 If you drive the 10-foot truck 75 miles, it will cost you c Let P = 650 $71.20 650 = 250 + 0.07 s c 650-250 = 250 − 250 + 0.07 s B = 29.95 + 0.55m 400 = 0.07 s 100 = 29.95 + 0.55m 400 0.07 s = 0.07 0.07 5714.29 = s 100 − 29.95 = 29.95 − 29.95 + 0.55m 70.05 = 0.55m 70.05 0.55m = 0.55 0.55 127.36 ≈ m To earn $650 per week, you must have $5714.29 in sales each week $37 will buy 135 minutes 28 For a total of $100, you can rent the 10-foot truck from a P = 300 + 0.05s Budget and drive it 127 miles b 26 Let s = 4000 P = 300 + 0.05(4000) a C = 0.20m + 10 P = 300 + 200 b P = $500 Let m = 200 Your paycheck will be $500 if you have $4000 in sales C = 0.20(200) + 10 C = 40 + 10 C = $50 The total monthly cost for talking 200 minutes is $50 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions c c Let P = 750 450 0.05 = s 0.05 0.05 $9000 = s C = 1000 + 400d 3500 = 1000 + 400d 3500 − 1000 = 1000 − 1000 + 400d 2500 = 400d 2500 400d = 400 400 6.25 = d For a paycheck of $750, the weekly sales would be $9000 For $3500 a family of four can take a trip to Orlando, 29 Let C be the total cost of a trip to Las Vegas for d Florida, for six days days 31 Let C be the total cost (in dollars) of shooting a a C = 125 + 100d wedding, and p be the number of proofs the b photographer edits and prints C = 125 + 100 ( 3) a C = 5.29 p + 400 C = 125 + 300 = 425 b 750 = 300 + 0.05s 750 + −300 = 300 + −300 + 0.05s 450 = 0.05s A three day trip to Las Vegas will cost $425 C = 5.29 (100 ) + 400 c C = 529 + 400 $700 = $350 C = 125 + 100d 350 = 125 + 100d 350 − 125 = 125 − 125 + 100d 225 = 100d 225 100d = 100 100 2.25 = d C = 929 If the photographer edits and prints 100 proofs the cost will be $929 c Let C = 1250 1250 = 5.29 p + 400 1250 − 400 = 5.29 p + 400 − 400 850 = 5.29 p 850 5.29 p = 5.29 5.29 160.68 ≈ p If you have $700 and gamble half of it, you can stay in Las Vegas for only two days 30 Let C be the total cost (in dollars) for a trip to The photographer can edit and print 160 proofs with a Orlando, Florida, for a family of four, and let d be the budget of $1250 number of days you stay 32 Let R be the total amount a photographer charges her a C = 1000 + 400d clients for editing and printing p proofs b a R = 7.50 p + 250 C = 1000 + 400 ( ) b C = 1000 + 2000 C = 3000 R = 7.50 (100 ) + 250 R = 750 + 250 A five day trip to Orlando, Florida, will cost a family of R = 1000 four $3000 The photographer will charge her client $1000 to edit and print 100 proofs c Let P be the profit (in dollars) from editing and printing p proofs Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ 1.1 Exercises b R = 2.50 ( 3000 ) = 7500 The total monthly revenue P = R −C P = ( 7.50 p + 250 ) − ( 5.29 p + 400 ) from selling 3000 snow cones is $7500 P = 7.50 p + 250 − 5.29 p − 400 c Let P be the profit (in dollars) from selling s snow P = 2.21 p − 150 cones d P = R −C P = 2.21(100 ) − 150 P = 2.50 s − ( 7000 + 0.45s ) P = 221 − 150 P = 2.50 s − 7000 − 0.45s P = 71 P = 2.05s − 7000 The photographer makes a $71 profit from editing and d printing 100 proofs from the wedding shoot P = 2.05 ( 4500 ) − 7000 e P = 9225 − 7000 Let P = P = 2225 2.21 p − 150 = The vendor makes a $2225 profit from selling 4500 snow 2.21 p = 150 cones 2.21 p 150 = 2.21 2.21 p ≈ 67.9 e = 2.05s − 7000 7000 = 2.05s − 7000 + 7000 The photographer must edit and print 68 proofs to break 7000 = 2.05s even a Let C be the total cost (in dollars) for selling s snow cones 7000 2.05s = 2.05 2.05 s ≈ 3414.63 for a month The vendor must sell 3415 snow cones to break even Fixed costs are: 5500 + 1500 = 7000 35 C = 7000 + 0.45s a Let C be the total cost (in dollars) for the Squeaky b Clean Window Company to clean windows for a day C = 7000 + 0.45 ( 3000 ) when w windows are cleaned C = 1.50w + 230 C = 8350 b 33 The monthly cost for selling 3000 snow cones is $8350 C = 1.50 ( 60 ) + 230 c C = 90 + 230 10, 600 = 7000 + 0.45s C = 320 10, 600 − 7000 = 7000 − 7000 + 0.45s If the Squeaky Clean Window Company cleans 60 3600 = 0.45s windows in a day, it will cost the company $320 3600 0.45s = 0.45 0.45 8000 = s c For a $10,600 budget, the vendor can sell up to 8000 450 − 230 = 1.50 w + 230 − 230 450 = 1.50w + 230 220 = 1.50w snow cones a Let R be the monthly revenue (in dollars) for selling s snow 220 1.50 w = 1.50 1.50 146.7 ≈ w cones for a month R = 2.50 s To stay within a budget of $450, the Squeaky Clean 34 Window Company can clean up to 146 windows Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions 36 a Let R be the monthly revenue (in dollars) for the C = 150 + 38 (18 ) Squeaky Clean Window Company to clean windows for a C = 150 + 684 day when w windows are cleaned R = w + 50 C = 834 b If the house has an initial treatment, and then is treated for R = ( 20 ) + 50 an additional 1.5 years, it will cost $834 R = 140 + 50 40 R = 190 a The Squeaky Clean Window Company will charge a P = 2.57 ( 3) + 249.78 business $190 to clean 20 windows P = 7.71 + 249.78 c Let P be the profit for the Squeaky Clean Window P = 257.49 Company to clean windows when w windows are cleaned The population of the United States was approximately P = R −C 257.49 million in 1993 P = ( w + 50 ) − (1.50 w + 230 ) b P = w + 50 − 1.50w − 230 P = 5.50w − 180 270 = 2.57t + 249.78 270 − 249.78 = 2.57t + 249.78 − 249.78 20.22 = 2.57t d 20.22 2.57t = 2.57 2.57 7.87 ≈ t P = 5.50 ( 40 ) − 180 P = 220 − 180 P = 40 In about 1998, the population of the United States was The Squeaky Clean Window Company makes a $40 profit approximately 270 million by washing 40 windows c e 300 = 2.57t + 249.78 = 5.50w − 180 300 − 249.78 = 2.57t + 249.78 − 249.78 + 180 = 5.50 w − 180 + 180 50.22 = 2.57t 180 = 5.50w 50.22 2.57t = 2.57 2.57 19.54 ≈ t 180 5.50 w = 5.50 5.50 32.73 ≈ w By mid 2009, the population of the United States reached They must clean at least 33 windows to break even 300 million 37 Maria’s work is correct Javier needs a decimal to 41 correctly represent 55 cents per bottle in terms of dollars a Let C be the total monthly cost (in dollars) for a per bottle manufacturer to produce g sets of golf clubs 38 Rosemary’s work is correct Will needs to use parentheses so that so that the entire cost is subtracted C = 23, 250 + 145 g 39 b a Let C be the total cost (in dollars) for pest management C = 23, 250 + 145 (100 ) from Enviro-Safe Pest Management when m monthly C = 23, 250 + 14,500 C = 37, 750 treatments are done C = 150 + 38m b There are 18 months in 1.5 years It costs the manufacturer $37,750 to produce 100 sets of golf clubs Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ 1.1 Exercises c c 20, 000 − 23, 250 = 23, 250 − 23, 250 + 145 g This is model breakdown Their costs can never be lower 2000 = 1500 + 1.50n 2000 − 1500 = 1500 − 1500 + 1.50n 500 = 1.50n 500 1.50n = 1.50 1.50 333.3 ≈ n than their fixed costs of $23,250 With a budget of $2000, Rockon can order 333 CDs d d −3250 = 145 g −3250 145 g = 145 145 −22.41 ≈ g 42 a C = 150 + 5t for t ≥ 100 3000 = 1500 + 1.50n 3000 − 1500 = 1500 − 1500 + 1.50n 1500 = 1.50n 1500 1.50n = 1.50 1.50 1000 = n b With a budget of $3000, Rockon can order 1000 CDs C = 150 + ( 300 ) This is model breakdown They can only order up to 500 C = 150 + 1500 CDs C = 1650 44 It costs $1650 to make 300 T-shirts a c Five years in operation: t = One year in operation: t = −4 $37, 750 = $377.50 per set 100 sets To break even selling 100 sets of golf clubs per month, the manufacturer must sell each set for $377.50 1500 = 150 + 5t 1500 − 150 = 150 − 150 + 5t 1350 = 5t 1350 5t = 5 270 = t P = −3 ( −4 ) + 50 P = 12 + 50 = 62 After one year in operation, 62% of companies are still in business b The camp can have 270 T-shirts made for $1500 d Five years in operation: t = 25 years in operation: t = 20 $1650 = $5.50 per T-shirt 300 T-shirts P = −3 ( 20 ) + 50 P = −60 + 50 = −10 To break even selling 300 T-shirts, the camp should sell This is model break down each for $5.50 c 43 35 = −3t + 50 35 − 50 = −3t + 50 − 50 −15 = −3t −15 −3t = −3 −3 5=t a C = 1500 + 1.50n for n ≤ 500 b C = 1500 + 1.50 ( 250 ) C = 1500 + 375 C = 1875 After 10 years, only 35% of companies are still in It costs Rockon $1875 to make 250 CDs business Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions 45 49 x + 60 = x + 90 x + 60 − x = x + 90 − x 3x + 60 = 90 3x + 60 − 60 = 90 − 60 3x = 30 3x 30 = 3 x = 10 m+ = 3 4⎞ ⎛1 3⎜ m + ⎟ = 3( 4) 3⎠ ⎝3 m + = 12 m + − = 12 − m=8 50 46 x+ =5 2 3⎞ ⎛1 ⎜ x + ⎟ = ( 5) 2⎠ ⎝2 x + = 10 x + − = 10 − x=7 x + 20 = x + x + 20 − x = x + − x −3x + 20 = −3x + 20 − 20 = − 20 −3x = −15 −3x −15 = −3 −3 x=5 51 −3x − = 14 + x 47 −3x − − x = 14 + x − x d + = 14 d + − = 14 − d =8 5⎛2 ⎞ ⎜ d ⎟ = (8) 2⎝5 ⎠ d = 20 −11x − = 14 −11x − + = 14 + −11x = 20 −11x 20 = −11 −11 20 x=− 11 52 5r − = 18r + 48 5r − − 18r = 18r + − 18r x − 17 = 20 x − 17 + 17 = 20 + 17 x = 37 4⎛3 ⎞ ⎜ x ⎟ = ( 37 ) 3⎝4 ⎠ 148 x= −13r − = −13r − + = + −13r = 11 −13r 11 = −13 −13 11 r=− 13 10 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ 1.1 Exercises 53 56 3.7 m − 4.6 = −1.8 ( 6m + ) d − = d +4 10 3⎞ ⎛5 ⎛4 ⎞ 70 ⎜ d − ⎟ = 70 ⎜ d + ⎟ 10 ⎠ ⎝7 ⎝7 ⎠ 50d − 21 = 40d + 280 3.7 m − 4.6 = −10.8m − 14.4 3.7 m − 4.6 + 10.8m = −10.8m − 14.4 + 10.8m 14.5m − 4.6 = −14.4 14.5m − 4.6 + 4.6 = −14.4 + 4.6 50d − 21 − 40d = 40d + 280 − 40d 14.5m = −9.8 10d − 21 = 280 14.5m −9.8 = 14.5 14.5 m ≈ −0.68 10d − 21 + 21 = 280 + 21 10d = 301 10d 301 = 10 10 301 d= 10 57 ( c + ) − 21 = 107 3c + 15 − 21 = 107 3c − = 107 54 3c − + = 107 + p− = p+7 4⎞ ⎛ ⎛5 ⎞ 72 ⎜ p − ⎟ = 72 ⎜ p + ⎟ 9⎠ ⎝8 ⎝8 ⎠ 27 p − 32 = 45 p + 504 3c = 113 3c 113 = 3 113 c= 27 p − 32 − 45 p = 45 p + 504 − 45 p 58 −18 p − 32 = 504 −18 p − 32 + 32 = 504 + 32 5k + = ( 6k − 14 ) + 56 −18 p = 536 5k + = 12k − 28 + 56 −18 p 536 = −18 −18 268 p=− 5k + = 12k + 28 55 −7k = 21 1.25d − 3.4 = −2.3 ( 5d + ) −7 k 21 = −7 −7 k = −3 5k + − 12k = 12k + 28 − 12k −7k + = 28 −7k + − = 28 − 1.25d − 3.4 = −11.5d − 9.2 1.25d − 3.4 + 11.5d = −11.5d − 9.2 + 11.5d 12.75d − 3.4 = −9.2 59 12.75d − 3.4 + 3.4 = −9.2 + 3.4 1.7 d + 5.7 = 29.7 + 5d 12.75d = −5.8 1.7d + 5.7 − 5d = 29.7 + 5d − 5d −3.3d + 5.7 = 29.7 12.75d −5.8 = 12.75 12.75 d ≈ −0.45 −3.3d + 5.7 − 5.7 = 29.7 − 5.7 −3.3d = 24 −3.3d 24 = −3.3 −3.3 d ≈ −7.27 11 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions 60 63 2.1m + 3.4 = 7.2 − 9.4m −3 ( 2v + ) − ( 3v − ) = 4v + ( 2v − ) 2.1m + 3.4 + 9.4m = 7.2 − 9.4m + 9.4m −6v − 27 − 9v + 21 = 4v + 12v − 48 11.5m + 3.4 = 7.2 −15v − = 16v − 48 11.5m + 3.4 − 3.4 = 7.2 − 3.4 −15v − − 16v = 16v − 48 − 16v −31v − = −48 11.5m = 3.8 −31v − + = −48 + 11.5m 3.8 = 11.5 11.5 m ≈ 0.33 −31v = −42 −31v −42 = −31 −31 42 v= 31 61 ( z − ) = ( −3z + ) 7 15 12 36 z− =− z+ 7 7 15 ⎞ 36 ⎞ ⎛6 ⎛ 12 7⎜ z − ⎟ = 7⎜ − z + ⎟ 7⎠ ⎠ ⎝7 ⎝ z − 15 = −12 z + 36 64 ( x + ) − ( x − ) = 12 x + ( x − ) x + 28 − 24 x + 48 = 12 x + 12 x − 27 −16 x + 76 = 24 x − 27 −16 x + 76 − 24 x = 24 x − 27 − 24 x z − 15 + 12 z = −12 z + 36 + 12 z −40 x + 76 = −27 18 z − 15 = 36 −40 x + 76 − 76 = −27 − 76 18 z − 15 + 15 = 36 + 15 −40 x = −103 18 z = 51 −40 x −103 = −40 −40 103 x= 40 18 z 51 = 18 18 51 z= 18 17 z= 65 ( 3t + ) = t − 12 24 40 − t− = t − 12 9 ⎛ 24 40 ⎞ ⎛2 ⎞ ⎜ − t − ⎟ = ⎜ t − 12 ⎟ ⎠ ⎝ ⎝3 ⎠ −24t − 40 = 6t − 108 − 62 ( 3r − 8) = ( −4r + ) 5 16 12 18 r− =− r+ 5 5 16 ⎞ 18 ⎞ ⎛6 ⎛ 12 5⎜ r − ⎟ = 5⎜ − r + ⎟ 5⎠ 5⎠ ⎝5 ⎝ 6r − 16 = −12r + 18 −24t − 40 − 6t = 6t − 108 − 6t −30t − 40 = −108 −30t − 40 + 40 = −108 + 40 −30t = −68 6r − 16 + 12r = −12r + 18 + 12r 18r − 16 = 18 −30t −68 = −30 −30 68 t= 30 34 t= 15 18r − 16 + 16 = 18 + 16 18r = 34 18r 34 = 18 18 34 r= 18 17 r= 12 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ 1.1 Exercises 66 71 ( x + ) = x − 15 28 − x− = x − 15 7 28 4⎞ ⎛ ⎛ ⎞ 28 ⎜ − x − ⎟ = 28 ⎜ x − 15 ⎟ 7⎠ ⎝ ⎝ 28 ⎠ −32 x − 16 = x − 420 ω = ω0 + α t ω − ω0 = ω0 + α t − ω0 ω − ω0 = α t ω − ω0 α t − t ω − ω0 α= −32 x − 16 − x = 3x − 420 − x t 72 −35 x − 16 = −420 y = mx + b y − mx = mx + b − mx y − mx = b b = y − mx −35 x − 16 + 16 = −420 + 16 −35 x = −404 −35 x −404 = −35 −35 404 x= 35 73 Iω ⎛1 ⎞ ( K ) = ⎜ Iω ⎟ ⎝2 ⎠ K= 67 F = ma F ma = m m F a= m 2K = Iω 2K = ω2 68 I= W = mg Iω ω2 2k ω2 74 W mg = g g W m= g kx ⎛1 ⎞ (U ) = ⎜ kx ⎟ ⎝2 ⎠ U= 69 2U = kx J = Ft J Ft = t t J F= t 2U kx = x2 x 2U k= x 75 70 mv ⎛1 ⎞ ( K ) = ⎜ mv ⎟ ⎝2 ⎠ K= P = 10h P 10h = 10 10 P h= 10 K = mv 2 K mv = v2 v 2K m= v 13 Full file at https://TestbankDirect.eu/ = t Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions 76 81 xz ⎛1 ⎞ ( y ) = ⎜ xz ⎟ ⎝2 ⎠ b = 2c + 3d y= y = xz b − 3d = 2c + 3d − 3d b − 3d = 2c b − 3d 2c = 2 b − 3d c= 2 y xz = z2 z 2y x= z 82 x = y + 5z 77 x − 5z = y + 5z − 5z ax + by = c ax + by − ax = c − ax by = c − ax by c − ax = b b c − ax y= b x − 5z = y x − 5z y = 3 x − 5z y= 83 5x2 + y = z 78 5x2 + y − 5x2 = z − 5x2 2x − y = z y = z − 5x2 2x − y + y = z + y y z − 5x2 = 3 z − 5x2 y= 2x = y + z 2x y + z = 2 y+z x= 84 79 4a − 5b = c ax + = y 4a − 5b + 5b = c + 5b ax + − = y − 4a = c + 5b ax = y − 4a c + 5b = 4 c + 5b a= ax y − = a a y −5 x= a 85 Rounding the outside temperature to 73D F is 80 appropriate because a difference of 0.4D F would not be 4m + n = p 4m + n − n = p − n felt 4m = p − n 86 A body temperature of 100.3D F would not be rounded 4m p − n = 4 p−n m= to the nearest whole degree A 0.3D F difference in body temperature could be critical 87 A result of $236.5725 would be rounded to $236.57 because our monetary units extend to the nearest hundredth 14 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ 1.1 Exercises 88 The correct rounding of 2200.8 pens would be 2200 pens If the budget is limited to $500, rounding up would result in going over budget 89 The company would need to wash 313 cars (312.25 rounded up) to make a profit of $400 Anything less would result in a profit of less than $400 90 Your example 15 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions Section 1.2 c When b = 200, then C = $485 The cost of producing 200 a The total prize money at Wimbledon in 2002 was 8.5 key lime bars on a stick is about $485 million British pounds d Domain: ≤ b ≤ 200 , range: 240 ≤ C ≤ 485 b In 2003, the total prize money at Wimbledon was 16 million British pounds a Dependent variable: C = Cost to produce custom printed c ( 0, ) In the year 2000, the winnings were million metal pens in dollars British pounds Independent variable: p = number of pens produced in d Domain: [ 2,11] , range: [8.5,14] hundreds p a 145.5 million The population of Russia in 2001 was C about 145.5 million 90 b The population of Russia will be about 140 million by 125 2010 10 405 c (0,146) The population of Russia in 2000 was about 146 30 1105 million 50 1805 d Domain: [1,10] , range: [140.4,145.5] b (A) and (F) (C) and (E) (C) and (E) (C) and (F) 50 25 c When p = , then C ≈ 230 The cost to produce 500 0.01 custom printed metal pens is approximately $230 10 0.0001 d Domain: 0.5 ≤ p ≤ 100 , range: 70 ≤ C ≤ 3600 11 50 12 500 17 13 10,000 a Dependent variable: G = Gross Profit for Quicksilver, 14 2,000,000 Inc in millions of dollars 15 Independent variable: t = years since 2000 a Dependent variable: C = Cost in dollars for producing b chocolate dipped key lime pie bars Independent variable: b = Number of bars produced b c When t = 10 , then G = 1850 The gross profit for Quicksilver, Inc in 2010 will be approximately $1850 million d Domain: ≤ t ≤ 10 , range: 50 ≤ G ≤ 1850 16 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ 1.2 Exercises 18 23 a Dependent variable: N = Net sales (in billions of dollars) a Dependent variable: P = Population of the United States for Home Depot in millions Independent variable: t years from 2000 Independent variable: t = Years since 1995 t N b -1 38.4 45.7 53.6 58.2 64.8 c When t = 14 then P ≈ 308 The population of the United 73.1 States in 2009 will be around 308 million people 81.5 d Domain: [ 0,14 ] , range: [ 266,308] 90.8 e ( 0, 266 ) b f In 1995, there were approximately 266 million people in the United States 24 a Dependent variable: P = Population of Florida in millions Independent variable: t = Number of years since 2000 t P 16.0 16.4 16.7 17.0 17.4 20 Incorrect The vertical intercept is ( 0, ) , which means 17.8 18.1 in 2000, there were four cases of hepatitis A per 100,000 b c When t = 9, then N ≈ 110 In 2009, the net sales for Home Depot will be about $110 billion d Domain: −2 ≤ t ≤ , range: 30 ≤ N ≤ 110 19 Maria’s model fits the data better There is a smaller variance between the data points and the line of best fit population Maria’s answer was incorrect She has the horizontal intercept at ( 8.2, ) 21 ≤ t ≤ 10 is not a reasonable domain because the model predicts a negative value of cases per 100,000 population for t-values of greater than 8.2 This is model breakdown Domain: ≤ t ≤ , range: 0.6 ≤ A ≤ 4.1 c When t = 15, then P ≈ 21.3 In 2015, the population of 22 Maria’s answer is incorrect The model shows that for Florida will be about 21.3 million 2007, there is about 0.6 cases of hepatitis A per 100,000 d Domain: [ −5,10] , range: [14,19.5] population e (0,16) f In 2000, there were about 16 million people in Florida 17 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions 25 27 a Let W be the number of deaths of women induced by a Let T be the number of years someone is expected live if illegal drugs in the United States t years since 2000 they are a years in age t W 6583 7452 9306 10,297 11,349 b When a = 45, then T = 35 According to the model, a 45-year-old person will live approximately 35 years c Domain: [ 0,80] , range: [3, 77 ] d The graphical model predicts a 90-year-old to live negative years This is model breakdown e The vertical intercept is ( 0, 77 ) b When f At birth, a person will live about 77 years t = 7, then W ≈ 15, 000 The number of drug- 28 induced deaths of females in the United States in 2007 was a Let S be the salary for teachers in thousands of dollars, around 15,000 and let E be the number of years of experience c The number of drug-induced deaths of females in the United States reached 4000 in 1998 d Domain: −1 ≤ t ≤ 7, range: 5200 ≤ W ≤ 15, 000 26 a Let D be the death rate per 100,000 people for heart disease in the United States t years since 2000 E S 49.9 52.4 62.1 67.0 10 74.3 12 79.2 b In 2006, the death rate per 100,000 will be about 200 c Domain: [ −5, 6] , range: [ 200,305] b When E = 7, then S ≈ 66 A teacher with years of d In 1995, the death rate from heart disease was about 305 experience should be making approximately $66,000 per 100,000 c Domain: [0,16] , range: [49,88.6] e ( 0, 258 ) d A teacher with about 4.5 years of experience will earn f In 2000, the death rate from heart disease was 258 per $60,000 per year 100,000 population e (0,49) f An instructor with years of experience will earn about $49,000 per year 18 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ 29 e y = −3 from the point ( 20, −3) a ( 0, ) The point that crosses the y-axis 34 b ( −3, ) The point that crosses the x-axis a (10, ) The point that crosses the x-axis c x = from the point ( 3, ) b ( 0, −50 ) The point that crosses the y-axis d y = 2.6 from the point (1, 2.6 ) c x = 110 from the point (110,500 ) 30 d x = −30 from the point ( −30, −200 ) a ( 0, −3) The point that crosses the y-axis e y = 450 from the point (100, 450 ) b ( 4, ) The point that crosses the x-axis 35 c x = 1.5 from the point (1.5, −2 ) a False, vertical intercept = ( 0, −2 ) d y = −4.5 from the point ( −2, −4.5 ) b True c False, x = −4.5 31 d False, x = −1.5 a ( 0,5 ) The point that crosses the y-axis e True b ( 4, ) The point that crosses the x-axis 36 c The input value is −10 when the output value is 18 a False, x-intercept = (100, ) That is, x = −10 when y = 18 b False, y -intercept = ( 0, 400 ) d The input value is 15 when the output value is −15 c True That is, x = 15 when y = −15 d False, x = 150 e The output value is −8 when the input value is 10 That e True is, y = −8 when x = 10 37 a ( −15, ) The point that crosses the x-axis 32 a ( 0, ) The point that crosses the y-axis b ( 0, −10 ) The point that crosses the y-axis b (12, ) The point that crosses the x-axis c x = 15 from the point (15, −20 ) c The input value is −13 when the output value is 15 d x = 7.5 from the point ( 7.5, −15 ) That is, x = −13 when y = 15 d The input value is 15 when the output value is −2 That e y = −3 from the point ( −10, −3) is, x = 15 when y = −2 38 e The output value is 13 when the input value is −10 a (13, ) The point that crosses the x-axis That is, y = 13 when x = −10 b ( 0, −10 ) The point that crosses the y-axis 33 c x = 25 from the point ( 25,10 ) a ( 0, −8 ) The point that crosses the y-axis d x = −9 from the point ( −9 − 17 ) b ( 31, ) The point that crosses the x-axis e y = from the point ( 20,5 ) c x = 11 from the point (11, −5 ) 39 d x = −9 from the point ( −9, −10 ) a ( 0,1) The point that crosses the y-axis 19 Full file at https://TestbankDirect.eu/ 1.2 Exercises Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions b ( −2, ) The point that crosses the x-axis c The input value is when the output value is 1.5 That is, x = when y = 1.5 d The input value is −4 when the output value is −1 That is, x = −4 when y = −1 e The output value is 2.5 when the input value is That is, y = 2.5 when x = 40 a ( 0, ) The point that crosses the y-axis b (1.5, ) The point that crosses the x-axis c The input value is −1.5 when the output value is That is, x = −1.5 when y = d The input value is when the output value is −2 That is, x = when y = −2 e The output value is −3.3 when the input value is That is, y = −3.3 when x = 20 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ 1.3 Exercises Section 1.3 c Vertical intercept: (0,5) d Horizontal intercept: (1, 0) a Use two points: ( 0, − 1) & ( 2, ) a − ( −1) Slope = = 2−0 Use two points: ( 0,10 ) & ( 4, ) b Increasing Slope = c Vertical intercept: (0,-1) b Decreasing d Horizontal intercept: (2,0) − 10 −10 −5 = = 4−0 c Vertical intercept: (0,10) d Horizontal intercept: (4, 0) a y = x + Use two points: ( −3, ) & ( 0, ) Slope = 2−0 = − ( −3) b Increasing x y = 2x + -3 ( −3 ) + = −3 -1 ( −1) + = (0) + = c Vertical intercept: (0, 2) d Horizontal intercept: (−3, 0) a Use two points: ( −3, − 15 ) & ( 3, ) Slope = − ( −15 ) − ( −3 ) = 15 = y = x − x y c y-intercept: (0, −7.5) ( ) − = −8 d x-intercept: (3,0) ( ) − = −2 4 3( 4) − = b Increasing a Use two points: ( −1, ) & ( 3, − ) Slope = −2 − −6 − = = − ( −1) b Decreasing c y-intercept: ( 0, 2.5 ) x = y + d x-intercept: (1.7, ) x y 5 ( −1) + = −1 -1 a (0) + = (1) + = Use two points: ( 0,5 ) & (1, ) 0−5 = −5 Slope = 1− b Decreasing 21 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions 10 x = −2 y − x y −2 ( −1) − = −5 -1 −2 ( −4 ) − = -4 13 y = x+6 −2 ( − ) − = -7 x y -6 ( −6 ) + = 2 ( 0) + = 3 ( 3) + = 14 y = x −3 11 y = x + x y -3 ( −3) -2 ( −2 ) ( 0) +2=2 x ( 2) +2=6 ( ) − = −3 ( 3) + = 11 4 ( ) − = −2 12 (12 ) − = + = 11 +2=6 12 y = x − x y -3 ( −3 ) -2 ( −2 ) ( 0) ( −2 ) ( 3) 15 x = −4 = −4 = −4 =5 22 Full file at https://TestbankDirect.eu/ y−4 y x −4 =5 − = −4 2 y ( −3) − = −6 -3 ( ) − = −2 3 ( 6) − = Solution Manual for Intermediate Algebra 1st Edition by Clark Full file at https://TestbankDirect.eu/ −1.5 ( ) + = −2 16 x = y + 1.3 Exercises y x ( −4 ) + = − -4 ( 0) + = ( 4) + = 4 20 x = −2.5 y + 10 x y −2.5 ( ) + 10 = −5 −2.5 ( ) + 10 = −2.5 ( ) + 10 = 10 17 y = 0.5 x − x y -2 0.5 ( −2 ) − = −4 0.5 ( ) − = −2 0.5 ( ) − = 21 y = −2 x + 15 18 y = −0.4 x + x y -3 −2 ( −3) + 15 = −3 -2 −2 ( −2 ) + 15 = −2 ( ) + 15 = 15 2 x y −2 ( ) + 15 = -5 −0.4 ( −5 ) + = −2 ( 3) + 15 = −3 −0.4 ( ) + = 5 −0.4 ( ) + = 19 x = −1.5 y + x y −1.5 ( ) + = −1.5 ( ) + = 23 Full file at https://TestbankDirect.eu/ 2 Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions 22 y = −1.5 x + b x y -3 −1.5 ( −3) + = −5.5 -2 −1.5 ( −2 ) + = −1.5 ( ) + = −1.5 ( ) + = 25 −1.5 ( 3) + = −5.5 a Let W be the sales clerk’s weekly salary in dollars for 2 2 selling s dollars of merchandise during the week W = 0.04s + 100 b s W 100 23 B = 0.55m + 29.95 100 104 a 500 120 m B 1000 140 29.95 1500 160 10 35.45 c 20 40.95 30 46.45 40 51.95 b 26 a Let W be the sales clerk’s weekly salary in dollars for selling s dollars of merchandise during the week 24 W = 0.03s + 200 a b e F s W 100,000 1000 203 500,000 160,000 500 215 400,000 180,000 1000 230 500,000 200,000 1500 245 600,000 220,000 2000 260 24 Full file at https://TestbankDirect.eu/ ... of $88 dollars for selling only 75 books will be 24.5 psi P = 5.5(75) − 500.50 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear... 10 C = $50 The total monthly cost for talking 200 minutes is $50 Full file at https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/... https://TestbankDirect.eu/ Solution Manual for Intermediate Algebra 1st Edition by Clark Full file1atLinear https://TestbankDirect.eu/ Chapter Functions 25 27 a Let W be the number of deaths of women induced by a