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# Recent problems solved by 'nerdybill'

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 Linear-equations/254282: I am trying to help my daughter. she was learning ax(squared) + bx + c = y, which she understands. However she was given vertex (2, -3) contains points (-1,-12) y-k=a(x-h)squared she has to find "a" then plug in to the vertix form to find the ax form1 solutions Answer 186632 by nerdybill(6948)   on 2010-01-06 17:55:10 (Show Source): You can put this solution on YOUR website!given vertex (2, -3) contains points (-1,-12) y-k=a(x-h)squared she has to find "a" then plug in to the vertex form to find the ax form . The "vertex form" of a parabola is: y= a(x-h)^2+k http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php . y-k = a(x-h)^2 where (h,k) is the vertex . Plug in what the problem gave: vertex (2, -3) contains points (-1,-12) y-k = a(x-h)^2 Plugging in (2, -3) we get: y-(-3) = a(x-2)^2 Plugging in our point (-1,-12) -12-(-3) = a(-1-2)^2 -12+3 = a(-3)^2 -9 = a(9) -1 = a
 Polynomials-and-rational-expressions/254283: Writing this function in factored form: y=4x^3-49x1 solutions Answer 186627 by nerdybill(6948)   on 2010-01-06 17:47:24 (Show Source): You can put this solution on YOUR website!y=4x^3-49x y=x(4x^2-49) y=x(2x-7)(2x+7)
 Pythagorean-theorem/254189: The foot of a ladder is placed 6 feet from a wall. If the top of the ladder rests 8 feet up on the wall, how long is the ladder? 1 solutions Answer 186496 by nerdybill(6948)   on 2010-01-06 12:01:16 (Show Source): You can put this solution on YOUR website! The foot of a ladder is placed 6 feet from a wall. If the top of the ladder rests 8 feet up on the wall, how long is the ladder? . Applying Pythagorean theorem we have: Let x = length of the ladder then x^2 = 6^2 + 8^2 x^2 = 36 + 64 x^2 = 100 x = 10 feet
 Surface-area/254125: A farmer wishes to put a diagonal brace on his gate. How long should the brace be if the gate is rectangular 12 by 5 ft1 solutions Answer 186459 by nerdybill(6948)   on 2010-01-06 09:49:32 (Show Source): You can put this solution on YOUR website!Apply Pythagorean theorem: Let x = length of diagonal then x^2 = 12^2 + 5^2 x^2 = 144 + 25 x^2 = 169 x = 13 feet
 Miscellaneous_Word_Problems/254152: A number is increased by 32. The new number is one-third of 60% of the original number. What was the original number?1 solutions Answer 186455 by nerdybill(6948)   on 2010-01-06 09:46:16 (Show Source): You can put this solution on YOUR website! A number is increased by 32. The new number is one-third of 60% of the original number. What was the original number? . Let x = original number then x+32 = (1/3)(.60x) 3(x+32) = .60x 3x+96 = .60x 2.4x+96 = 0 2.4x = -96 x = -40
 Finance/253302: The population of a local high school has grown over the past three years from 7,054 to 7,741 students. What has been the rate of increase over that time period? Use the equation A = P(1 + r)t to model the growth where A is the population at the end of a specific length of time, P is the initial population, r is the rate of growth expressed as a decimal, and t is the time in years. Round to the nearest hundredth of a percent1 solutions Answer 185751 by nerdybill(6948)   on 2010-01-04 07:06:51 (Show Source): You can put this solution on YOUR website!The population of a local high school has grown over the past three years from 7,054 to 7,741 students. What has been the rate of increase over that time period? Use the equation A = P(1 + r)t to model the growth where A is the population at the end of a specific length of time, P is the initial population, r is the rate of growth expressed as a decimal, and t is the time in years. Round to the nearest hundredth of a percent. . The problem gives the equation: A = P(1 + r)^t . And it also gives: A = 7,741 P = 7,054 t = 3 . Plug everything in and solve for r: A = P(1 + r)^t 7741 = 7054(1 + r)^3 7741/7054 = (1 + r)^3 1.0974 = (1 + r)^3 1.0315 = 1 + r .0315 = r or 3.15% = r
 Miscellaneous_Word_Problems/253458: A fence 320 feet long has wooden posts each 40 feet apart How many posts are there? (A) 8 (B) 7 (C) 10 (D) 11 (E) 9 1 solutions Answer 185750 by nerdybill(6948)   on 2010-01-04 06:56:30 (Show Source): You can put this solution on YOUR website!A fence 320 feet long has wooden posts each 40 feet apart How many posts are there? . 320/40 + 1 = 8 + 1 = 9
 logarithm/253368: All logs are base 12 Logx=.5log9+1/3log27 I got 49.5, I'm just wondering if it's right. THANKS!1 solutions Answer 185711 by nerdybill(6948)   on 2010-01-04 00:03:14 (Show Source): You can put this solution on YOUR website! . . . . . .
 Linear-equations/253392: in a graph with the points (-5,10) (3,y) and the slope=-(3/8) I need to solve for y 1 solutions Answer 185708 by nerdybill(6948)   on 2010-01-03 23:54:48 (Show Source): You can put this solution on YOUR website!in a graph with the points (-5,10) (3,y) and the slope=-(3/8) I need to solve for y . slope, given two points: m = (y2 - y1)/(x2 - x1) . The problem gives us: m = -3/8 (x1,y1) as (-5,10) (x2,y2) as (3,y) . Plug the given info into: m = (y2 - y1)/(x2 - x1) we get -3/8 = (y - 10)/(3 - (-5)) -3/8 = (y - 10)/(3 + 5) -3/8 = (y - 10)/8 Multiplying both sides by 8: -3 = y - 10 7 = y
 Problems-with-consecutive-odd-even-integers/253165: find two consecutive even integers if one-third of the smaller one is equal to one-fourth of the larger one1 solutions Answer 185426 by nerdybill(6948)   on 2010-01-03 09:23:28 (Show Source): You can put this solution on YOUR website! find two consecutive even integers if one-third of the smaller one is equal to one-fourth of the larger one . Let x = smaller consecutive even integer then x+2 = larger consecutive even integer . 1/3(x) = 1/4(x+2) Multiply both sides by 12: 4x = 3(x+2) 4x = 3x+6 x = 6 (smaller integer) . Larger integer: x+2 = 6+2 = 8 . Solution: 6 and 8
 Percentage-and-ratio-word-problems/253170: One-tenth is what part of three-fourths ? (A) 3/40 (B) 1/8 (C) 2/15 (D) 15/2 (E) 40/3 1 solutions Answer 185425 by nerdybill(6948)   on 2010-01-03 09:19:49 (Show Source): You can put this solution on YOUR website! One-tenth is what part of three-fourths ? (A) 3/40 (B) 1/8 (C) 2/15 (D) 15/2 (E) 40/3 . Let x = the fractional part then 1/10 = 3/4(x) . Solving for x: multiply both sides by 40: 4 = 30x 4/30 = x 2/15 = x (Answer:C)
 Miscellaneous_Word_Problems/253191: If p pencils cost c cents, how many pencils can be bought for d dollars? A) dp/c B) 100c/dp C) 100cp/d D) 100cd/p E) 100dp/c 1 solutions Answer 185420 by nerdybill(6948)   on 2010-01-03 09:14:58 (Show Source): You can put this solution on YOUR website!If p pencils cost c cents, how many pencils can be bought for d dollars? A) dp/c B) 100c/dp C) 100cp/d D) 100cd/p E) 100dp/c . Cost for one pencil is: c/p "d dollars" is equal to: 100d cents Therefore, number of pencils you can buy is: 100d/(c/p) 100dp/c (Answer E)
 Expressions-with-variables/253040: A 400g solution made up of 40% sugar must be added to a 2oog solution. What should be the percentage of sugar in 200g of solution in order to produce a 38% sugar solution?1 solutions Answer 185246 by nerdybill(6948)   on 2010-01-02 11:58:10 (Show Source): You can put this solution on YOUR website! A 400g solution made up of 40% sugar must be added to a 2oog solution. What should be the percentage of sugar in 200g of solution in order to produce a 38% sugar solution? . Let x = percentage of sugar in 200g solution then 200x + .40(400) = .38(400+200) 200x + .40(400) = .38(600) 200x + 160 = 228 200x = 228-160 200x = 68 x = .34 or x = 34%
 Equations/252966: 17. You are lying 120 ft away from a tree that is 50 feet tall. You look up at the top of the tree. Approximately how far is your hear from the top of the tree in a straight line1 solutions Answer 185157 by nerdybill(6948)   on 2010-01-01 20:23:37 (Show Source): You can put this solution on YOUR website!17. You are lying 120 ft away from a tree that is 50 feet tall. You look up at the top of the tree. Approximately how far is your hear from the top of the tree in a straight line . Apply Pythagorean theorem: Let x = distance from ear to top of tree then x^2 = 50^2 + 120^2 x^2 = 2500 + 14400 x^2 = 16900 x = sqrt(16900) x = 130 feet
 Polynomials-and-rational-expressions/252895: Factor: a^6+b^61 solutions Answer 185003 by nerdybill(6948)   on 2010-01-01 10:07:47 (Show Source): You can put this solution on YOUR website!A special case of factoring is "sum of cubes": . Your problem: can be rewritten as: which is "sum of cubes" which we now factor as:
 Human-and-algebraic-language/252873: the sum of two numbers is 39. When the smaller number is doubled and the larger is increased by 3, the resulting numbers are equal. What are the numbers?1 solutions Answer 184972 by nerdybill(6948)   on 2009-12-31 20:59:02 (Show Source): You can put this solution on YOUR website! the sum of two numbers is 39. When the smaller number is doubled and the larger is increased by 3, the resulting numbers are equal. What are the numbers? . Let x = smaller number and y = larger number . x + y = 39 2x = y+3 . Reordering the pair of equations above: x + y = 39 2x - y = 3 . Adding the two equations together: x + y = 39 2x - y = 3 ----------- 3x = 42 x = 14 (smaller number) . Larger number: x + y = 39 14 + y = 39 y = 39-14 y = 25 (larger number)
 Travel_Word_Problems/252842: A missile is fired vertically into the air. The distance s (in feet) above the ground as a function of time t (in seconds) is given by the equation below. (a) When will the missile hit the ground? (b) When will the missile be 1000 feet above the ground? h=300+500t-16t^2 I have tried several attempts at this one and nothing! Anyone willing to help, I would really appreciate it.1 solutions Answer 184939 by nerdybill(6948)   on 2009-12-31 15:03:54 (Show Source): You can put this solution on YOUR website!A missile is fired vertically into the air. The distance s (in feet) above the ground as a function of time t (in seconds) is given by the equation below. (a) When will the missile hit the ground? (b) When will the missile be 1000 feet above the ground? h=300+500t-16t^2 . Reordering: h=300+500t-16t^2 h=-16t^2+500t+300 (a) When will the missile hit the ground? Set h to 0 and solve for t: h=-16t^2+500t+300 0=-16t^2+500t+300 0=-4t^2+125t+75 Applying the quadratic equation we get: t = {-0.59, 31.84} The negative solution doesn't make sense -- so, throw it out leaving us with: t = 31.98 seconds . (b) When will the missile be 1000 feet above the ground? set h = 1000 and solve for t: h=-16t^2+500t+300 1000=-16t^2+500t+300 0=-16t^2+500t-700 0=-4t^2+125t-175 Applying the quadratic equation we get: t = {1.47 secs, 29.78 secs} The first time is on the way up and the second time is on the way down.
 logarithm/252821: Can you please write this as a single logarithm log(b,x) - log(b,y)1 solutions Answer 184912 by nerdybill(6948)   on 2009-12-31 11:11:27 (Show Source):
 Miscellaneous_Word_Problems/252812: Instead of multiplying a number by 7, the number is divided by 7. What is the percentage of error obtained ?1 solutions Answer 184885 by nerdybill(6948)   on 2009-12-31 09:43:05 (Show Source): You can put this solution on YOUR website! Instead of multiplying a number by 7, the number is divided by 7. What is the percentage of error obtained ? . Say, "the number" is x. . The correct answer was: 7x The actual answer: x/7 The error: 7x-x/7 = 49x/7 - x/7 = 48x/7 . Percentage of error: (48x/7)/7x *100 = (48x/49)/x *100 = (48/49) *100 = 97.96%
 Linear_Algebra/252783: Write a linear function f such that it has the indicated function values: f(-1)=4, f(-3)=81 solutions Answer 184854 by nerdybill(6948)   on 2009-12-31 03:15:51 (Show Source): You can put this solution on YOUR website!Write a linear function f such that it has the indicated function values: f(-1)=4, f(-3)=8 . The problem gives you two points: (-1, 4) and (-3, 8) . Slope of the line: m = (8-4)/(-3- -1) m = (8-4)/(-3+1) m = 4/(-2) m = -2 . Plug one point (-1, 4) and slope -2 into "point-slope" form: y - y1 = m(x - x1) y - 4 = -2(x - -1) y - 4 = -2(x + 1) y - 4 = -2x - 2 y = -2x + 2 (this is the "slope-intercept" of the line)
 Percentage-and-ratio-word-problems/252375: An item for sale is marked down 20%. By what percent must it then be marked up in order to return to the original selling price?1 solutions Answer 184222 by nerdybill(6948)   on 2009-12-27 09:47:00 (Show Source): You can put this solution on YOUR website!An item for sale is marked down 20%. By what percent must it then be marked up in order to return to the original selling price? . Let x=original price then the sale price is x - .20x x(1-.20) x(.80) .80x . Let y = mark up to get back to the original price then .80x * y = x y = x/(.80x) y = 1/.80 y = 1.25 or y = 125%
 Miscellaneous_Word_Problems/252379: If xy = 2 and x^2 + y^2 = 5 , then x/y + y/x = ?1 solutions Answer 184221 by nerdybill(6948)   on 2009-12-27 09:36:17 (Show Source): You can put this solution on YOUR website!If xy = 2 and x^2 + y^2 = 5 , then x/y + y/x = ? . Start with: x^2 + y^2 = 5 Divide both sides by xy: (x^2 + y^2)/(xy) = 5/(xy) x^2/(xy) + y^2/(xy) = 5/(xy) x/y + y/x = 5/(xy) . Finally, substitute xy with 2: x/y + y/x = 5/(xy) x/y + y/x = 5/2
 Rate-of-work-word-problems/252292: Working alone, pump A can fill a pool in 8 hours, while pump B can fill it in 10 hours. The two pumps are turned on at the same time and run until the pool is 75% full. Pump A then stops working, but pump B continues until the pool is filled. How long does it take to fill the empty pool? a 10/3 hours b 16/3 hours c 23/6 hours d 29/6 hours e 35/6 hours1 solutions Answer 184124 by nerdybill(6948)   on 2009-12-26 08:26:31 (Show Source): You can put this solution on YOUR website!Working alone, pump A can fill a pool in 8 hours, while pump B can fill it in 10 hours. The two pumps are turned on at the same time and run until the pool is 75% full. Pump A then stops working, but pump B continues until the pool is filled. How long does it take to fill the empty pool? . Let x = time pumps ran when filling to 75% and y = time pump B ran to complete filling the pool then x(1/8 + 1/10) = .75 y(1/10) = .25 . Solving x: x(1/8 + 1/10) = .75 Multiply both sides by 80: x(10 + 8) = 60 18x = 60 x = 60/18 = 10/3 . Solving y: y(1/10) = .25 y = 2.5 = 5/2 . Adding the two together: 10/3 + 5/2 = 20/6 + 15/6 = 35/6 hours
 Functions/252274: solve: 1 solutions Answer 184116 by nerdybill(6948)   on 2009-12-25 23:59:50 (Show Source): You can put this solution on YOUR website!solve: . Let y = then instead of: solve: solve: . Or,
 Travel_Word_Problems/252246: Susan left her home, on foot, at 9:00 am at 1.5 mph. At 10:00 am her friend, following the same route, ran at 5.25 mph to meet her. How many minutes, after 10:00 am, did the two friends meet?1 solutions Answer 184061 by nerdybill(6948)   on 2009-12-25 09:55:57 (Show Source): You can put this solution on YOUR website!Susan left her home, on foot, at 9:00 am at 1.5 mph. At 10:00 am her friend, following the same route, ran at 5.25 mph to meet her. How many minutes, after 10:00 am, did the two friends meet? . Apply the distance formula: d = rt d is distance r is rate or speed t is time . Let x = minutes after 10 am when the two friends meet then 1.5(x/60 + 1) = 5.25(x/60) Multiplying both sides by 60: 1.5(x + 60) = 5.25x 1.5x + 90 = 5.25x 90 = 3.75x 24 minutes = x
 Miscellaneous_Word_Problems/252241: If Mr. Wersted equally distributed the money in his pocket among the students in his class, each would receive \$ 1.26 . If there had been four more students, then each would have received \$ 1.05 . How much money was in his pocket?1 solutions Answer 184060 by nerdybill(6948)   on 2009-12-25 09:50:53 (Show Source): You can put this solution on YOUR website! If Mr. Wersted equally distributed the money in his pocket among the students in his class, each would receive \$ 1.26 . If there had been four more students, then each would have received \$ 1.05 . How much money was in his pocket? . Let x = number of students in class then total = 1.26x (before adding 4 students) after adding 4 students: total = 1.05(x+4) . 1.26x = 1.05(x+4) 1.26x = 1.05x + 4.20 0.21x = 4.20 x = 20 (students in his class) . Amount in his pocket: total = 1.26x = 1.26(20) = \$25.20
 Miscellaneous_Word_Problems/252243: If (x,y) = (4.8, B) gives the coordinates of a point on the graph of y = 5/8 x + 5 then what is the value of B?1 solutions Answer 184057 by nerdybill(6948)   on 2009-12-25 09:45:32 (Show Source): You can put this solution on YOUR website!If (x,y) = (4.8, B) gives the coordinates of a point on the graph of y = 5/8 x + 5 then what is the value of B? . The problem gives x=4.8 -- plug this into: y = 5/8 x + 5 y = 5/8(4.8) + 5 y = 5(0.6) + 5 y = 3 + 5 y = 8 . Therefore, B = 8
 Percentage-and-ratio-word-problems/252237: If x is 250 percent of y, then what percent of x is 2y? A. 25% B. 40% C. 60% D. 75% E. 80%1 solutions Answer 184055 by nerdybill(6948)   on 2009-12-25 09:41:45 (Show Source): You can put this solution on YOUR website!If x is 250 percent of y, then what percent of x is 2y? A. 25% B. 40% C. 60% D. 75% E. 80% . Since: x is 250 percent of y we have x = 2.50y Solving for y: y = x/2.50 . 2y then would be: 2y = 2x/2.50 2y = x/1.25 2y = 0.8x answer: E. 80%
 Word_Problems_With_Coins/252168: Suppose I have \$2.00 in nickels, dimes, and quarters. If I have the same number of each type of coin, how many coins do I have? A. 6 B. 9 C. 12 D. 15 E. 181 solutions Answer 183972 by nerdybill(6948)   on 2009-12-24 11:07:32 (Show Source): You can put this solution on YOUR website!Suppose I have \$2.00 in nickels, dimes, and quarters. If I have the same number of each type of coin, how many coins do I have? A. 6 B. 9 C. 12 D. 15 E. 18 . Let x = number of coins of each type: then .05x + .10x + .25x = 2 .05x + .35x = 2 .40x = 2 x = 2/.40 x = 5 (of each type) . Since we have three different types (nickel, dime, and quarter): 3x = 3(5) = 15 . Answer: D
 Linear-equations/252192: In an (x, y) coordinate system, write the equation of the vertical line passing through the point of intersection of 3x + 4y = 1 and x + 3y = 7 .1 solutions Answer 183958 by nerdybill(6948)   on 2009-12-24 09:45:23 (Show Source): You can put this solution on YOUR website!In an (x, y) coordinate system, write the equation of the vertical line passing through the point of intersection of 3x + 4y = 1 and x + 3y = 7 . . First, find out where the two lines intersect: 3x + 4y = 1 x + 3y = 7 . Multiply second equation by -3: 3x + 4y = 1 -3x - 9y = -21 . Add the two equations together: 3x + 4y = 1 -3x - 9y = -21 ---------------- -5y = -20 y = 4 . Use the second equation to find x: x + 3y = 7 x + 3(4) = 7 x + 12 = 7 x = -5 (which is also the vertical line they are looking for)
 Rectangles/252176: A square piece of paper is folded in half vertically. If the resulting figure has a perimeter of 18 cm, what was the area of the original square? A. 9 cm2 B. 18 cm2 C. 24 cm2 D. 36 cm2 E. 81 cm21 solutions Answer 183957 by nerdybill(6948)   on 2009-12-24 09:31:39 (Show Source): You can put this solution on YOUR website!A square piece of paper is folded in half vertically. If the resulting figure has a perimeter of 18 cm, what was the area of the original square? A. 9 cm2 B. 18 cm2 C. 24 cm2 D. 36 cm2 E. 81 cm2 . Draw a diagram of the problem. It'll help you see the solution. . Let x = measure of one side of square then x/2 = width of rectangle x = length . 2(x/2 + x) = 18 x/2 + x = 9 3x/2 = 9 3x = 18 x = 6 cm . Therefore the area of the square is: 6*6 = 36 cm^2