# See tutors' answers!

Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'nerdybill'

nerdybill answered: 6961 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989, >>Next

 Geometry_proofs/201493: This question is from textbook two angles are complementary. one angle is 12 degree larger than the other. using two variables x and y, find the size of each angle by solving a system of equations.1 solutions Answer 151698 by nerdybill(6963)   on 2009-06-29 02:42:10 (Show Source): You can put this solution on YOUR website!two angles are complementary. one angle is 12 degree larger than the other. using two variables x and y, find the size of each angle by solving a system of equations. . Two angles are complementary if the sum of the two angles equals 90 deg. . Let x = one angle and y = second angle . equation 1: x + y = 90 equation 2: y = x+12 . Substitute the value of y from equation 2 into equation 1 and solve for x: x + y = 90 x + x+12 = 90 2x + 12 = 90 2x = 78 x = 39 degrees . Substitute the above into equation 2 and solve for y: y = x+12 y = 39+12 y = 51 degrees . Angles are 39 and 51 degrees.
 Travel_Word_Problems/201453: If a parade 2mi long is proceeding at 3 mph, how long will it take a runner, jogging at 6 mph, to travel from the front of the parade to the end of the parade? 1 solutions Answer 151662 by nerdybill(6963)   on 2009-06-28 17:15:12 (Show Source): You can put this solution on YOUR website!If a parade 2mi long is proceeding at 3 mph, how long will it take a runner, jogging at 6 mph, to travel from the front of the parade to the end of the parade? . Apply the distance formula: d = rt where d is distance r is rate or speed t is time . Let x = time it takes jogger to get to end of parade then 3x + 6x = 2 9x = 2 x = 2/9 = 1/3 hours or x = 20 minutes
 Equations/201411: Find an equation of the the line satisfying the given conditions. Through (2, 8); perpendicular to 9x + 7y = 74 1 solutions Answer 151639 by nerdybill(6963)   on 2009-06-28 12:09:25 (Show Source): You can put this solution on YOUR website!Find an equation of the the line satisfying the given conditions. Through (2, 8); perpendicular to 9x + 7y = 74 . First, find the slope of: 9x + 7y = 74 Do this by putting it into the "slope-intercept" form: 7y = -9x + 74 y = (-9/7)x + 74/7 Therefore, slope = -9/7 . If a line is perpendicular, we need the negative reciprocal of the slope above: Our new slope is then 7/9 Use the slope (7/9) and the given point (2,8) and plug it into the "point-slope" form: y-y1 = m(x-x1) y-8 = 7/9(x-2) y-8 = 7/9(x) - 14/9 y = 7/9(x) - 14/9 + 8 y = 7/9(x) - 14/9 + 72/9 y = 7/9(x) + 58/9 (slope-intercept form of new line)
 Equations/201417: Determine whether the given ordered pair is a solution of the given equation. (x - 4)^2 + (y + 7)^2 = 45; (1, -1) 1 solutions Answer 151638 by nerdybill(6963)   on 2009-06-28 12:02:58 (Show Source): You can put this solution on YOUR website!Determine whether the given ordered pair is a solution of the given equation. (x - 4)^2 + (y + 7)^2 = 45; (1, -1) . Plug in the given ordered pair: (x,y) = (1,-1) into (x - 4)^2 + (y + 7)^2 = 45 (1 - 4)^2 + (-1 + 7)^2 = 45 (-3)^2 + (6)^2 = 45 9 + 36 = 45 45 = 45 (checks) . So, yes, (1,-1) is a solution
 Equations/201415: Write an equation in standard form for a line passing through the pair of points. (2, -2) and (0, 3) 1 solutions Answer 151635 by nerdybill(6963)   on 2009-06-28 11:49:37 (Show Source): You can put this solution on YOUR website!Write an equation in standard form for a line passing through the pair of points. (2, -2) and (0, 3) . First, find the slope between the two points: m (slope) = (y2-y1)/(x2-x1) m (slope) = (3-(-2))/(0-2) m (slope) = (3+2)/(0-2) m (slope) = (5)/(-2) m (slope) = -5/2 . Using the slope above and one point (0,3) plug it into the point slope form: y-y1 = m(x-x1) y-3 = -5/2(x-0) y-3 = -5/2(x) 5/2(x) + y - 3 = 0 (this is what they're looking for)
 Equations/201419: Find the slope of the line, if it is defined. Through (-3, -9) and (5, 4) 1 solutions Answer 151633 by nerdybill(6963)   on 2009-06-28 11:44:51 (Show Source): You can put this solution on YOUR website!Find the slope of the line, if it is defined. Through (-3, -9) and (5, 4) . m (slope) = (y2-y1)/(x2-x1) m (slope) = (4-(-9))/(5-(-3)) m (slope) = (4+9)/(5+3) m (slope) = (13)/(8) m (slope) = 13/8
 Equations/201418: Find the slope of the line, if it is defined. Through (7, -4) and (3, 8) 1 solutions Answer 151632 by nerdybill(6963)   on 2009-06-28 11:42:34 (Show Source): You can put this solution on YOUR website!Find the slope of the line, if it is defined. Through (7, -4) and (3, 8) m (slope) = (y2-y1)/(x2-x1) m (slope) = (8-(-4))/(3-7) m (slope) = (8+4)/(3-7) m (slope) = (12)/(-3) m (slope) = -4
 Word_Problems_With_Coins/201395: Maria has \$169 in ones,fives, and tens. She has twice as many one-dollar bills as she has five dollar bills, and five more ten-dollar bills than five-dollar bills. How many of each type bill does she have?1 solutions Answer 151621 by nerdybill(6963)   on 2009-06-28 09:08:48 (Show Source): You can put this solution on YOUR website! Maria has \$169 in ones,fives, and tens. She has twice as many one-dollar bills as she has five dollar bills, and five more ten-dollar bills than five-dollar bills. How many of each type bill does she have? . Let x = number of five dollar bills then 2x = number of one dollar bills x+5 = number of ten dollar bills . 2x + 5x + 10(x+5) = 169 2x + 5x + 10x+50 = 169 17x+50 = 169 17x = 119 x = 7 (number of five dollar bills) . One dollar bills: 2x = 2(7) = 14 . Ten dollar bills: x+5 = 7+5 = 12
 Graphs/201381: Hello! I need a help with ASAP!!! Problem 1. In 1920, the record for a certain race was 45.4 sec. In 1990, it was 44.0 sec. Let R(t)= the record in the race and t= the number of the year since 1920. a) Find a linear function that the date b) Use the function in (a) to predict the record in 2003 and in 2006. c) Find the year when the record will be 43.56 sec Find a linear function that fits the data. R(t)= ?? -002-45.4??? What is the predicted record for 2003? 43.74?? What is the predicted record for 2006? 43.68?? In what year will the predicted record be 43.56 sec?? I appreciate this. Thank you! 1 solutions Answer 151614 by nerdybill(6963)   on 2009-06-28 03:49:11 (Show Source): You can put this solution on YOUR website!In 1920, the record for a certain race was 45.4 sec. In 1990, it was 44.0 sec. Let R(t)= the record in the race and t= the number of the year since 1920. . a) Find a linear function that the date Think of the x-axis representing the year and the y-axis representing the "record-time" in seconds. The problem, then, really gives you two data points: (remember, since 1920) 1920 we get: (0,45.4) 1990 we get: (70,44) Slope then is (y2-y1)/(x2-x1) = (44-45.4)/(70-0) = -1.4/70 = -0.02 . Using the slope and one (70,44) of the two points substitute it into the "point-slope" form: y-y1 = m(x-x1) y-44 = -0.02(x-70) y = -0.02(x-70) + 44 y = -0.02x + 1.4+44 y = -0.02x + 45.4 Replacing y with R(t) and x with t we get: R(t) = -0.02t + 45.4 . b) Use the function in (a) to predict the record in 2003 and in 2006. For 2003: t = 2003-1920 = 83 R(t) = -0.02t + 45.4 R(t) = -0.02(83) + 45.4 R(t) = -1.66 + 45.4 R(t) = -1.66 + 45.4 R(t) = 43.74 seconds . For 2006: t = 2006-1920 = 86 R(t) = -0.02t + 45.4 R(t) = -0.02(86) + 45.4 R(t) = -1.66 + 45.4 R(t) = -1.72 + 45.4 R(t) = 43.68 seconds . c) Find the year when the record will be 43.56 sec R(t) = -0.02t + 45.4 43.56 = -0.02t + 45.4 43.56-45.4 = -0.02t -1.84 = -0.02t 92 = t Year then = 1920+92 = 2012
 Geometry_Word_Problems/201345: A rectangle is 4 times as long as it is wide. A second rectangle is 5 centimeters longer and 2 centimeters wider than the first. The area of the second rectangle is 270 square centimeters greater than the first. What are the demensions of the original rectangle?1 solutions Answer 151601 by nerdybill(6963)   on 2009-06-27 19:59:08 (Show Source): You can put this solution on YOUR website! A rectangle is 4 times as long as it is wide. A second rectangle is 5 centimeters longer and 2 centimeters wider than the first. The area of the second rectangle is 270 square centimeters greater than the first. What are the demensions of the original rectangle? . Let w = width of original rectangle then 4w = length of original rectangle . (w+2)(4w+5) = w(4w) + 270 (if you don't see this, write back) 4w^2+5w+8w+10 = 4w^2 + 270 4w^2+13w+10 = 4w^2 + 270 13w+10 = 270 13w = 260 w = 20 cm (width of original rectangle) . Length: 4w = 4(20) = 80 cm (length of original rectangle)
 Equations/201324: Find an equation of the line satisfying the given conditions. Throung (0,5); m=-(2/3)1 solutions Answer 151546 by nerdybill(6963)   on 2009-06-27 08:52:49 (Show Source): You can put this solution on YOUR website!Find an equation of the line satisfying the given conditions. Through (0,5); m=-(2/3) . Plug into the "point-slope" form: y-y1 = m(x-x1) . y-5 = -(2/3)(x-0) y-5 = -(2/3)x y = -(2/3)x + 5 (this is what they're looking for) The above is the "slope-intercept" form. Where slope (m) is -(2/3) and y-intercept is at (0,5)
 Equations/201328: Determine wheather the given ordered pair is a solution of the given equation. 2x-5y=18;(4,2)1 solutions Answer 151544 by nerdybill(6963)   on 2009-06-27 08:30:38 (Show Source): You can put this solution on YOUR website! 2x-5y=18;(4,2) . An "ordered pair" is denoted as (x,y) So, in this problem, they are asking if x were equal to 4 and y were equal to 2 is that a solution for: 2x-5y=18 . To check, Plug the given values back into the equation and check: 2x-5y=18 2(4)-5(2)=18 8-10=18 -2 = 18 (NOT true) . Therefore (4,2) is NOT a solution.
 Linear-systems/201332: Do lines always intersect? 1 solutions Answer 151543 by nerdybill(6963)   on 2009-06-27 08:26:42 (Show Source): You can put this solution on YOUR website!No. Two lines will not intersect if they are parallel.
 Age_Word_Problems/201310: The sum of Richard's age and Ruel's age is 60. Nine years ago, Richard was twice as old as Ruel, then how old is Ruel? (pls. include o how you solved the problem) 1 solutions Answer 151531 by nerdybill(6963)   on 2009-06-27 02:37:26 (Show Source): You can put this solution on YOUR website!The sum of Richard's age and Ruel's age is 60. Nine years ago, Richard was twice as old as Ruel, then how old is Ruel? . Let x = Ruel's age and y = Richard's age . From:"The sum of Richard's age and Ruel's age is 60." we get: x + y = 60 (equation 1) . From:"Nine years ago, Richard was twice as old as Ruel" we get: y-9 = 2(x-9) (equation 2) . Solve equation 1 for y: x + y = 60 y = 60 - x . Substitute the above back into equation 2 and solve for x: y-9 = 2(x-9) 60-x -9 = 2(x-9) 51-x = 2x-18 51 = 3x-18 69 = 3x 23 years = x (Ruel's age)
 Quadratic_Equations/201306: Could someone help me solve for x: 2x/x+4-1/x-3=01 solutions Answer 151530 by nerdybill(6963)   on 2009-06-27 02:30:15 (Show Source): You can put this solution on YOUR website! . Multiplying both sides by a common denominator: (x+4)(x-3) we get: . x = {-1/2, 4}
 Complex_Numbers/201309: 6 _____________ a^-3a-54 + 10 ______________ a^+5a-6 Hi we are talking about complex fractions. For some reason I cannot figure it out can you please help me!!! Above is a problem that was given to solve. Will you explain it please? Thanks1 solutions Answer 151526 by nerdybill(6963)   on 2009-06-27 00:41:33 (Show Source): You can put this solution on YOUR website!I believe you mean: (correct me if I'm wrong) . . Factoring the denominators we get: . Now, find common denominator: (a-9)(a+6)(a-1) and convert each term to have the same denominator: . Combining the two terms: . . Factoring the numerator:
 Graphs/201147: write a system of two equations in two unknowns for each problem. Solve each system by substitution. Question: Investing her bonus. Donna invested her 33,000 bonus and recieved a total of \$970 in interest after one year. If part of the money returned 4% and the remainder 2.25% then how much did she invest at each rate?1 solutions Answer 151359 by nerdybill(6963)   on 2009-06-25 10:27:43 (Show Source): You can put this solution on YOUR website!Investing her bonus. Donna invested her 33,000 bonus and recieved a total of \$970 in interest after one year. If part of the money returned 4% and the remainder 2.25% then how much did she invest at each rate? . Let x = amount invested at 4% and y = amount invested at 2.25% . From:"Donna invested her 33,000 bonus" x + y = 33000 (equation 1) . From:"a total of \$970 in interest after one year" .04x + .0225y = 970 . Solving equation 1 for y: x + y = 33000 y = 33000 -x . Substitute the above into equation 2 and solve for x: .04x + .0225y = 970 .04x + .0225(33000-x) = 970 .04x + 742.5 -.0225x = 970 .04x -.0225x = 227.5 0.0175x = 227.5 x = \$13000 (amount invested at 4%) . Amount invested at 2.25% y = 33000 -x = 33000 -13000 = \$20000
 Geometric_formulas/201138: This question is from textbook geometry can you please help me solve ((( A rectangular solid with length 8 and width3 has bolume 48. Find its height. )))1 solutions Answer 151353 by nerdybill(6963)   on 2009-06-25 09:06:08 (Show Source): You can put this solution on YOUR website! can you please help me solve ((( A rectangular solid with length 8 and width3 has bolume 48. Find its height. ))) . Since the volume on any rectangular solid is length*width*height we have: . Let h = height then 8*3*h = 48 24h = 48 h = 2 (height)
 Rectangles/201130: A rectangular swimming pool is 2 m longer than it is wide. If the width is decreased by 3 m, and the length is increased by 4 m, the area remains the same as the original area, Find the original dimensions of the pool. 1 solutions Answer 151352 by nerdybill(6963)   on 2009-06-25 09:03:57 (Show Source): You can put this solution on YOUR website! A rectangular swimming pool is 2 m longer than it is wide. If the width is decreased by 3 m, and the length is increased by 4 m, the area remains the same as the original area, Find the original dimensions of the pool. . Let w = width of pool then w+2 = length of pool . (w-3)(w+2 +4) = w(w+2) (w-3)(w+6) = w(w+2) w^2+6w-3w-19 = w^2+2w w^2+3w-19 = w^2+2w 3w-19 = 2w w-19 = 0 w = 19 m (width of pool) . Length: w+2 = 19+2 = 21 m (length of pool) . Dimensions: 19m x 21m
 Miscellaneous_Word_Problems/201094: The area fo a rectangle is 66ft squared and the diagonal of the rectangle is square root of 157 ft. What are the dimensions of the rectangle.1 solutions Answer 151350 by nerdybill(6963)   on 2009-06-25 07:06:21 (Show Source): You can put this solution on YOUR website! The area fo a rectangle is 66ft squared and the diagonal of the rectangle is square root of 157 ft. What are the dimensions of the rectangle. . Let x = width and y = length . Since we have two unknowns, we'll need two equations: Equation 1: xy = 66 Equation 2: x^2 + y^2 = 157 . Solving equation 1 for y: y = 66/x Substituting the above into equation 2 we can solve for x: x^2 + y^2 = 157 x^2 + (66/x)^2 = 157 x^2 + 4356/x^2 = 157 x^4 + 4356 = 157x^2 x^4 - 157x^2 + 4356 = 0 Factoring we get: (x^2-121)(x^2-36) = 0 x = {11,6} . Dimensions of rectangle are 11 feet by 6 feet
 expressions/201017: Rewrite the formula V=1/3BH to solve for h1 solutions Answer 151265 by nerdybill(6963)   on 2009-06-24 13:51:19 (Show Source): You can put this solution on YOUR website!V=1/3BH Multiplying both sides by 3: 3V=BH Dividing both sides by B: 3V/B = H
 Geometric_formulas/200998: This question is from textbook geometry can you please help me solve (((Find the volume of a sphere with radius 3cm. Leave answer in terms of pie)))1 solutions Answer 151229 by nerdybill(6963)   on 2009-06-24 09:45:27 (Show Source): You can put this solution on YOUR website!Volume of any sphere: So, if r = 3 cm then . . . . cubic cm
 Geometric_formulas/201000: This question is from textbook geometry can you please help me solve (((What is the volume of a cube with edge 2? )))1 solutions Answer 151227 by nerdybill(6963)   on 2009-06-24 09:38:54 (Show Source): You can put this solution on YOUR website!By definition, all sides of a cube are the same. Therefore, the volume is: 2*2*2 = 8
 Linear_Equations_And_Systems_Word_Problems/200947: please help me solve this problem: a farmer and his son leave a barn at the same time and walk in opposite driections checking a fence line. the son walks at the speed of 3.5km/h and the farmer at 4.0km/h. how much time will have elapsed when the farmer and his son are 2.5km apart1 solutions Answer 151187 by nerdybill(6963)   on 2009-06-23 18:15:04 (Show Source): You can put this solution on YOUR website!a farmer and his son leave a barn at the same time and walk in opposite driections checking a fence line. the son walks at the speed of 3.5km/h and the farmer at 4.0km/h. how much time will have elapsed when the farmer and his son are 2.5km apart . Apply the distance formula: d = rt where d is distance r is rate or speed t is time . Let t = elapsed time then 3.5t + 4t = 2.5 7.5t = 2.5 t = 2.5/7.5 t = 25/75 t = 1/3 of an hour (or 20 minutes)
 Length-and-distance/200920: This question is from textbook Geometry Given points A (-5,8) and B (3,4)sketch vector AB on the graph provided1 solutions Answer 151185 by nerdybill(6963)   on 2009-06-23 18:11:52 (Show Source): You can put this solution on YOUR website! Plot point (-5,8) on the graph Plot point (3,4) on the graph Connect the two points with a solid line The vector starts at A and ends at B, so draw the arrow head at B.
 Square-cubic-other-roots/200950: Simplify sqrt 5 / sqrt 111 solutions Answer 151182 by nerdybill(6963)   on 2009-06-23 18:08:57 (Show Source): You can put this solution on YOUR website! . You have to "rationalize" the fraction -- remove all radicals from the denominator. . .
 Equations/200843: 5.8 + [-log(10^-6)-log(1)-2](2.9)= x1 solutions Answer 151097 by nerdybill(6963)   on 2009-06-22 16:07:23 (Show Source): You can put this solution on YOUR website!5.8 + [-log(10^-6)-log(1)-2](2.9)= x 5.8 + [-(-6)-0-2](2.9)= x 5.8 + [6-0-2](2.9)= x 5.8 + [4](2.9)= x 5.8 + 11.6= x 5.8 + 11.6= x 17.4=x
 Geometry_Word_Problems/200841: A circle is tangent to the x-axis and to the y-axis. The coordinates of its center are both positive. The area of the circle is 64pie. What are the coordinates of the point of tangency on the y-axis?1 solutions Answer 151065 by nerdybill(6963)   on 2009-06-22 10:26:18 (Show Source): You can put this solution on YOUR website! A circle is tangent to the x-axis and to the y-axis. The coordinates of its center are both positive. The area of the circle is 64pie. What are the coordinates of the point of tangency on the y-axis? . Area of a circle = (pi)r^2 . They gave us the area as 64(pi) . 64(pi) = (pi)r^2 64 = r^2 8 = r (radius) . Since the coordinates of the center are both positive, we know it is in the 1st quadrant. . point tangent on the y-axis is then (0,8)
 Miscellaneous_Word_Problems/200817: It takes Steve 3 hrs longer to paint a floor than it takes Paul. When working together, it takes them 2 hours. How long would each take to do the job alone?1 solutions Answer 151057 by nerdybill(6963)   on 2009-06-22 08:51:19 (Show Source): You can put this solution on YOUR website! It takes Steve 3 hrs longer to paint a floor than it takes Paul. When working together, it takes them 2 hours. How long would each take to do the job alone? . Let p = time it takes for Paul to paint the floor alone then p+3 = time it takes for Steve to paint the floor alone . 2(1/p + 1/(p+3)) = 1 2/p + 2/(p+3) = 1 2(p+3) + 2p = p(p+3) 2p+ 6 + 2p = p^2+3p 8p+ 6 = p^2+3p 6 = p^2-5p 0 = p^2-5p-6 0 = (p-6)(p+1) p = {6, -1} We throw out the negative solution leaving us with: p = 6 hours (time it takes Paul) . Steve: p+3 = 6+3 = 9 hours (time it takes Steve)
 Linear-systems/200813: get the value of x and y x-y=5 3x+y=31 solutions Answer 151054 by nerdybill(6963)   on 2009-06-22 07:23:41 (Show Source): You can put this solution on YOUR website!Applying the substitution method: x-y=5 (equation 1) 3x+y=3 (equation 2) . Solve equation 1 for x: x-y=5 x = y+5 Substitute the above into equation 2 and solve for y: 3x+y=3 3(y+5)+y=3 3y+15+y=3 4y+15=3 4y = -12 y = -3 . Substitute the above into equation 1 and solve for x: x-y=5 x-(-3)=5 x+3 = 5 x = 2 . Solution: x=2 and y=-3