jun-agruda
jun-agruda
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w—width: 2(w + 2w - 3) = 42 3w - 3 = 21 3w = 24 w = 8 Length: = 2(8) - 3 = 16 - 3 = 13 Answer: width, 8 meters; length, 13 meters
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2x² - 7x - 15 = 0 x² - 7/4x = 15/2 + (- 7/4)² x² - 7/4x = (120 + 49)/16 (x - 7/4)² = 169/16 x - 7/4 = ± 13/4 = x - 7/4 - 13/4, = x - 20/4, = x - 5 = x - 7/4 + 13/4, = x + 6/4, = x + 3/2, = 2x + 3 Answer: (x - 5)(2x + 3)
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2x² - 7x - 15 = 0 x² - 7/4x = 15/2 + (- 7/4)² x² - 7/4x = (120 + 49)/16 (x - 7/4)² = 169/16 x - 7/4 = ± 13/4 = x - 7/4 - 13/4, = x - 20/4, = x - 5 = x - 7/4 + 13/4, = x + 6/4, = x + 3/2, = 2x + 3 Answer: (x - 5)(2x + 3)
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2/3g + 1/2g = 14 4g + 3g = 84 7g = 84 g = 12 Answer: g = 12 Proof: 2/3(12) + 1/2(12) = 14 8 + 6 = 14
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2/3g + 1/2g = 14 4g + 3g = 84 7g = 84 g = 12 Answer: g = 12 Proof: 2/3(12) + 1/2(12) = 14 8 + 6 = 14
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= 4(2x + 5) + 2(3x - 2) = 8x + 20 + 6x - 4 = 14x + 16 Answer: 14x + 16 OR 2(7x + 8)
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Distance jogged—d: d/8 + (6 - d)/12 = 2/3 3d + 2(6 - d) = 16 3d + 12 - 2d = 16 d = 4 No. of minutes jogging: = 60(4 mi/8 mph) = 60(1/2 hour) = 60/2 or 30 minutes No. of minutes running: = 60([6 - 4 mi]/12 mph) = 60(2 mi/12 mph) = 60(…
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Distance jogged—d: d/8 + (6 - d)/12 = 2/3 3d + 2(6 - d) = 16 3d + 12 - 2d = 16 d = 4 No. of minutes jogging: = 60(4 mi/8 mph) = 60(1/2 hour) = 60/2 or 30 minutes No. of minutes running: = 60([6 - 4 mi]/12 mph) = 60(2 mi/12 mph) = 60(…
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1st integer—x: x + x + 2 + x + 4 + x + 6 = 64 4x = 52 x = 13 2nd integer: = 13 + 2 = 15 3rd integer: = 13 + 4 = 17 4th integer: = 13 + 6 = 19 Answer: 13, 15, 17 & 19 are the integers. Their sum is 64.
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1st integer—x: x + x + 2 + x + 4 + x + 6 = 64 4x = 52 x = 13 2nd integer: = 13 + 2 = 15 3rd integer: = 13 + 4 = 17 4th integer: = 13 + 6 = 19 Answer: 13, 15, 17 & 19 are the integers. Their sum is 64.
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Let x = no. of years for Sharon to be 4 times as old as Sam. 48 + x = 4(3 + x) 48 + x = 12 + 4x 48 - 12 = 4x - x 36 = 3x x = 36 / 3 x = 12 Answer: 12 years must pass for Sharon's age to be 4 times the age of Sam. Proof: 48 + 12 = 4(3 …
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1st factor is 5: = (5x² - 15x + 10)/5 = x² - 3x + 2 2nd factor is x - 1: = (x² - 3x + 2)/(x - 1) = x - 2 At this point, x - 2 cannot be further factored. Therefore the factors are: 5, x - 1 and x - 2 and they can be expressed in the fol…
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Total to be accounted for is $30.00 Accounted for as follows: = the checker + the trio + the bellhop = ($30.00 - $5.00) + ($1.00 * 3) + ($5.00 - $3.00) = $25.00 + $3.00 + $2.00 = $30.00 The premises in your accounting is a departure. It sh…
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x² + 4x - 14 = 0 x² + 2x = 14 + 2² x² + 2x = 14 + 4 (x + 2)² = 18 x + 2 = ± √18 Answer: (x + 2 + √18)(x + 2 - √18) are the factors.
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x² + 4x - 14 = 0 x² + 2x = 14 + 2² x² + 2x = 14 + 4 (x + 2)² = 18 x + 2 = ± √18 Answer: (x + 2 + √18)(x + 2 - √18) are the factors.
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1st interpretation: 14/(3x) + 2/5 = 8/(3x) 70 + 6x = 40 6x = - 30 x = - 5 Answer: x = - 5 ----------- Another interpretation: (14/3)x + 2/5 = (8/3)x 70x + 6 = 40x 30x = - 6 x = - 6/30 or - 1/5
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Paddling rate—r: 2/(r + 3) = (1/2)/(r - 3) 2r - 6 = 1/2r + 3/2 4r - 12 = r + 3 3r = 15 r = 5 Answer: 5 mph is the paddling rate of a person. Proof: 2mi/(5 + 3 mph) = (1/2mi)/(5 - 3 mph) 2mi/8mph = (1/2mi)/2mph 1/4 hr = 1/4 hr
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Paddling rate—r: 2/(r + 3) = (1/2)/(r - 3) 2r - 6 = 1/2r + 3/2 4r - 12 = r + 3 3r = 15 r = 5 Answer: 5 mph is the paddling rate of a person. Proof: 2mi/(5 + 3 mph) = (1/2mi)/(5 - 3 mph) 2mi/8mph = (1/2mi)/2mph 1/4 hr = 1/4 hr
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= 6($6.00/[60{60}]) = 6($6.00/3,600) = 6($1.00/36) = $1/36 Answer: $1/36 OR 2 7/9 cents per washing
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4% CD—c: 0.04c + 0.05($5,000 - c) = $228 0.04c + $250 - 0.05c = $228 0.01c = $22 c = $2,200 5% CD: = $5,000 - $2,200 = $2,800 Answer: 4% CD, $2,200; 5% CD, $2,800
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4% CD—c: 0.04c + 0.05($5,000 - c) = $228 0.04c + $250 - 0.05c = $228 0.01c = $22 c = $2,200 5% CD: = $5,000 - $2,200 = $2,800 Answer: 4% CD, $2,200; 5% CD, $2,800
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= 3/4(100%) = (3/[4/4])(100%/4) = 3(25%) = 75% Answer: c. 75%
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4x = 3(25 - x) 4x = 75 - 3x 7x = 75 x = 75/7 OR 10 5/7 Answer 1: 75/7 OR 10 5/7 is the number. -------------- 1st equation—smaller number (y) in terms of larger number (x): x + y = 15 y = 15 - x 2nd equation—larger number (x): x = 3(15…
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1/4x +3/2x = 7 1/4x 6/4x = 7 7/4x = 7 x = 7 / (7/4) x = 7 * 4/7 x = 28/7 x = 4 Proof: 1/4(4) + 3/2(4) = 7 1 + 6 = 7
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1/4x +3/2x = 7 1/4x 6/4x = 7 7/4x = 7 x = 7 / (7/4) x = 7 * 4/7 x = 28/7 x = 4 Proof: 1/4(4) + 3/2(4) = 7 1 + 6 = 7
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(2 * N)^(1/2) 2N^2 4N N = 4/2 or 2 (3 * N) ^ (1/3) 3N^3 27N N = 27/3 N = 9 (5 * N) ^ (1/5) 5N^5 3125N N = 3125/5 N = 625
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= (m + 5)³ - (m - 2)² = m³ + 15m² + 75m + 125 - (m³ - 6m² + 12m - 8) = m³ + 15m² + 75m + 125 - m³ + 6m² - 12m + 8 = 21m² + 63m + 133 = 7(3m² + 9m + 19) Answer: 7(3m² + 9m + 19)
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Distance (x): 60x = 45(21 - x) 60x = 945 - 45x 105x = 945 x = 9 Answer: 9 miles
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Distance (x): 60x = 45(21 - x) 60x = 945 - 45x 105x = 945 x = 9 Answer: 9 miles
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Q1: 2nd no. (y) in terms of 1st no. (x): x + y = 58 y = 58 - x x - y = 16 y = x - 16 1st number (x): 58 - x = x - 16 2x = 74 x = 37 2nd number (1st equation): = 58 - 37 = 21 Answer: 37 & 21 and the numbers. Proof (differe…