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# Recent problems solved by 'nerdybill'

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 Volume/481594: If there is a pipe that has a diameter of 12 inches and is ten ft. long with each square inch weighing 4.75lbs how much does the pipe weigh all together?1 solutions Answer 329731 by nerdybill(6958)   on 2011-08-14 18:07:22 (Show Source): You can put this solution on YOUR website!If there is a pipe that has a diameter of 12 inches and is ten ft. long with each square inch weighing 4.75lbs how much does the pipe weigh all together? . area = length * circumference circumference = (pi)d . area = length * circumference weight = area * 4.75 weight = 120 * (pi) * 12 * 4.75 weight = 120 * 3.14 * 12 * 4.75 weight = 21477.6 lbs
 expressions/481586: Can someone help me with this? Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. (3x^10y^9)^31 solutions Answer 329728 by nerdybill(6958)   on 2011-08-14 18:01:21 (Show Source): You can put this solution on YOUR website!(3x^10y^9)^3 (3)^3(x^10)^3(y^9)^3 27x^30y^27
 Linear_Equations_And_Systems_Word_Problems/481593: A chemist is mixing a 40% salt solution with a 20% salt solution to make 50 L of a new solution that will contain 25% salt. How much of each of the original solutions should the chemist use? I know the answer from a answer key but can you show me how its doen. 1 solutions Answer 329727 by nerdybill(6958)   on 2011-08-14 17:57:40 (Show Source): You can put this solution on YOUR website!A chemist is mixing a 40% salt solution with a 20% salt solution to make 50 L of a new solution that will contain 25% salt. How much of each of the original solutions should the chemist use? . Let x = amount (L) of 40% then 50-x = amount(L) of 20% . .40x + .20(50-x) = .25(50) .40x + 10 - .20x = 12.5 .20x + 10 = 12.5 .20x = 2.5 x = 12.5 L of 40% solution . 20% solution: 50-x = 50-12.5 = 37.5 L of 20% solution
 Points-lines-and-rays/481462: If I have a problem that says find an equation of the perpendicular bisector of line AB... Could someone please tell me how I would figure that out.1 solutions Answer 329675 by nerdybill(6958)   on 2011-08-14 11:14:08 (Show Source): You can put this solution on YOUR website!The way you would approach the problem depends on what was given to you. Perhaps, it is best if you have a particular problem in mind. If I have a problem that says find an equation of the perpendicular bisector of line AB.. . First, determine the slope of line AB. The slope of the perpendicular bisector is the reciprocal. . Next, apply the "mid-point" formula to get the (x,y) coordinates. . Now, you have the "slope" and one "point" plug it in to the "point-slope" formula: y - y1 = m(x - x1) . Finally, you can manipulate the above until you get the form you're looking for -- either "slope-intercept form" or "standard form". .
 Finance/481434: Pleas I really need help 3. You recently started the paperwork to purchase your new home, and you were just notified that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifters and Quick Move, to discuss their rates. Heavy Lifting charges a \$130 fee plus \$25 per hour. Quick Move charges a \$55 fee plus \$50 per hour. For what values h (hours) does Quick Move offer the better deal? Express your answer as an inequality. Explain how you reached your answer. 1 solutions Answer 329672 by nerdybill(6958)   on 2011-08-14 11:06:43 (Show Source): You can put this solution on YOUR website!You recently started the paperwork to purchase your new home, and you were just notified that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifters and Quick Move, to discuss their rates. Heavy Lifting charges a \$130 fee plus \$25 per hour. Quick Move charges a \$55 fee plus \$50 per hour. . Let h = hours needed for move then . Cost of Heavy Lifters: 25h + 130 Cost of Quick Move: 50h + 55 . For what values h (hours) does Quick Move offer the better deal? "cost of Quick Move" < "cost of Heavy Lifters" 50h + 55 < 25h + 130 25h + 55 < 130 25h < 75 h < 3 hours (this is what they're looking for)
 Points-lines-and-rays/481454: Please help I have never had geometry before. Perform each of the following operations. Leave in the simplest form. 15 degrees 29 minutes - 3 degrees 45 minutes1 solutions Answer 329671 by nerdybill(6958)   on 2011-08-14 11:00:22 (Show Source): You can put this solution on YOUR website!15 degrees 29 minutes - 3 degrees 45 minutes . First, you should know that 1 degree is equivalent to 60 minutes. . subtract minutes from minutes and subtract degrees from degrees . Since we are trying to subtract 45 minutes from 29 minutes, we need to borrow 1 degree: 14 degrees 89 minutes - 3 degrees 45 minutes so, now we have: (49-3) degrees (89-45) minutes 46 degrees 44 minutes
 Rectangles/481406: Hello, I am having a problem with the question "the length of a rectangle exceeds the width by 2 cm. If the diagonal is 10 cm long, find the width of the rectangle. I keep getting different answers. Thanks in advance!1 solutions Answer 329662 by nerdybill(6958)   on 2011-08-14 10:19:28 (Show Source): You can put this solution on YOUR website!the length of a rectangle exceeds the width by 2 cm. If the diagonal is 10 cm long, find the width of the rectangle. . Let w = width then w+2 = length . applying Pythagorean theorem we have: w^2 + (w+2)^2 = 10^2 w^2 + (w+2)(w+2) = 100 w^2 + (w^2+4w+4) = 100 2w^2+4w+4 = 100 w^2+2w+2 = 50 w^2+2w-48 = 0 (w+8)(w-6) = 0 w = {-8, 6} throw out the negative solution leaving: w = 6 cm
 logarithm/481456: Hello! I need help please. log (10,000)=? Can somebody help me? thanks1 solutions Answer 329661 by nerdybill(6958)   on 2011-08-14 10:14:03 (Show Source): You can put this solution on YOUR website!Since we are dealing with "base 10", if we rewrite: log (10,000) as log (10^4) this is equal to 4 (answer)
 Travel_Word_Problems/481315: If a ball is traveling 74 MPH how long does it take it to travel forty feet. 1 solutions Answer 329590 by nerdybill(6958)   on 2011-08-13 21:12:13 (Show Source): You can put this solution on YOUR website!If a ball is traveling 74 MPH how long does it take it to travel forty feet. . First, convert 40 ft to miles: 40 ft * 1/5280 = 0.007576 miles . Then, apply distance formula: d = rt 0.007576 = 74t 0.007576/74 = t 0.0001024 hours = t converting to seconds: 0.0001024 * 60 * 60 = 0.369 seconds
 Equations/481248: Solve 7^-x+3=501 solutions Answer 329539 by nerdybill(6958)   on 2011-08-13 16:36:58 (Show Source): You can put this solution on YOUR website!I think your equation is: if so: . . OR, if your equation was: if so:
 Square-cubic-other-roots/481249: x cubed-5x=0 i tried to factor it out- x(x squared -5) but i dont know how I could get that to equal 0.1 solutions Answer 329535 by nerdybill(6958)   on 2011-08-13 16:29:22 (Show Source): You can put this solution on YOUR website!You were correct in your approach... set each term (the "x" and the "x^2-5" to zero to get: x^2-5 = 0 x^2 = 5 x = +-sqrt(5) . and, of course x = 0 . so, the solution set is: x = {-sqrt(5), 0, sqrt(5)}
 Miscellaneous_Word_Problems/481250: Hi thank you for your time! Here is the problem I am working on. WIll you show me how you come up with your solutions? Thank you again so much for your time! The world consumption of oil in millions of barrels per day is given by f(x)=-0.1x^2 + 2x + 58, where x is the number of years since 1985 (x=0 for 1985) a. According to this equation, what was the oil consumption in 1990? b. Using this equation, the maximum oil consumption will occur in what year? c. What is the maximum oil consumption? d. Does this equation realistically describe oil in 2030? why or why not? 1 solutions Answer 329534 by nerdybill(6958)   on 2011-08-13 16:23:40 (Show Source): You can put this solution on YOUR website!f(x)=-0.1x^2 + 2x + 58, where x is the number of years since 1985 (x=0 for 1985) a. According to this equation, what was the oil consumption in 1990? 1990 - 1985 = 5 set x = 5 and solve f(5) f(x)=-0.1x^2 + 2x + 58 f(5)=-0.1(5)^2 + 2(5) + 58 f(5)=-0.1(25) + 10 + 58 f(5)= 65.5 million barrels . b. Using this equation, the maximum oil consumption will occur in what year? It would be the vertex. x = -b/(2a) x = -2/(2(-0.1)) x = -2/(-0.2) x = 10 year: 1985 + 10 = 1995 . c. What is the maximum oil consumption? set x = 10 solve for f(x) f(x)=-0.1x^2 + 2x + 58 f(5)=-0.1(10)^2 + 2(10) + 58 f(5)=-0.1(100) + 20 + 58 f(5)= 68 million barrels . d. Does this equation realistically describe oil in 2030? why or why not? 2030-1985 = 45 set x = 45 solve for f(x) f(x)=-0.1x^2 + 2x + 58 f(5)=-0.1(45)^2 + 2(45) + 58 f(5)=-0.1(2025) + 90 + 58 f(5)=-54.5 million barrels answer: NO, because the result is negative .
 Pythagorean-theorem/481228: The base of a 17-ft ladder is 7 feet away from the wall. How far above the floor is the top of the ladder? Give your answer to the nearest thousandth.1 solutions Answer 329532 by nerdybill(6958)   on 2011-08-13 16:03:04 (Show Source): You can put this solution on YOUR website!The base of a 17-ft ladder is 7 feet away from the wall. How far above the floor is the top of the ladder? Give your answer to the nearest thousandth. . Applying the Pythagorean theorem: Let x = length above the floor then x^2 + 7^2 = 17^2 x^2 + 49 = 289 x^2 = 240 x = 15.492 feet
 Linear-equations/481206: x^2-2/3x=0 I have to complete the square.1 solutions Answer 329529 by nerdybill(6958)   on 2011-08-13 14:58:48 (Show Source): You can put this solution on YOUR website!x^2-2/3x=0 take half of b, square it, and add to both sides (2/6)^2 = (1/3)^2 = 1/9: x^2-2/3x+1/9 = 1/9 (x-1/3)^2 = 1/9 x-1/3 = sqrt(1/9) x = sqrt(1/9) + 1/3 x = +-1/3 + 1/3 x = {0, 2/3}
 Quadratic_Equations/481144: A triangular garden has an area of 90 sq feet. It's height is 8 feet more than its base. Find the measure of the base.1 solutions Answer 329513 by nerdybill(6958)   on 2011-08-13 11:04:19 (Show Source): You can put this solution on YOUR website!A triangular garden has an area of 90 sq feet. It's height is 8 feet more than its base. Find the measure of the base. . Since: A = (1/2)bh where A is area b is base h is height . 90 = (1/2)b(b+8) 180 = b(b+8) 180 = b^2+8b 0 = b^2+8b-180 0 = (b+18)(b-10) b = {-18, 10} throw out the negative solution leaving: b = 10 feet (length of base)
 Equations/481165: Find the area of the triangle. Width is 13 ft the width is 40 feet1 solutions Answer 329512 by nerdybill(6958)   on 2011-08-13 11:00:12 (Show Source): You can put this solution on YOUR website!To find the area of a triangle you need the "base" and the "height": Area = (1/2)bh
 Percentage-and-ratio-word-problems/481166: if you were charged \$762 in taxes on a 2,540 purchase, what percent tax were you charged?1 solutions Answer 329507 by nerdybill(6958)   on 2011-08-13 10:47:45 (Show Source): You can put this solution on YOUR website! if you were charged \$762 in taxes on a 2,540 purchase, what percent tax were you charged? . Let x = tax rate then 2540x = 762 x = 762/2540 x = 0.30 or x = 30% (that is an awfully high tax rate!)
 Length-and-distance/481173: Hi, I would like to see if an 18ft ladder will fit in an 10ft cubic van? Thanks1 solutions Answer 329505 by nerdybill(6958)   on 2011-08-13 10:44:01 (Show Source): You can put this solution on YOUR website!Giving just the volume is not enough information. You need to provide the width, length and height of the storage area. . 9'11" (L) x 6'4" (W) x 6'2" (H) But, these dimensions does NOT equate to a 10 cubic foot volume (as stated earlier). . The longest part would be the diagonal: Let d = length of diagonal then d^2 = 9.917^2 + 6.333^2 d^2 = 138.454 d = 11.76 feet . No, the ladder will NOT fit.
 Travel_Word_Problems/481116: A cyclist travel 27 km in 2 hours.How far would he travel in 7 hours? 1 solutions Answer 329478 by nerdybill(6958)   on 2011-08-13 07:54:24 (Show Source): You can put this solution on YOUR website!A cyclist travel 27 km in 2 hours.How far would he travel in 7 hours? . distance formula: d = rt d = (27/2)(7) d = (189/2) d = 94.5 km
 Quadratic_Equations/481104: solving quadratic equations by completing the square HELP PLEASE x^2+4+1=0 or like x^2+x-1=0 thank you!!1 solutions Answer 329477 by nerdybill(6958)   on 2011-08-13 07:52:25 (Show Source): You can put this solution on YOUR website!You forgot the x-term: I'm assuming instead of: x^2+4+1=0 you meant: x^2+4x+1=0 x^2+4x=-1 half b then double -- add to both sides: x^2+4x+4=-1+4 (x+2)^2 = 3 x+2 = sqrt(3) x = +-sqrt(3) - 2 x = {-3.732, -0.268} . . x^2+x-1=0 x^2+x = 1 x^2+x+ 1/4 = 1 + 1/4 (x+ 1/2)^2 = 1.25 (x+.5)^2 = 1.25 x+.5 = sqrt(1.25) x = +-sqrt(1.25) - .5 x = {-1.618, 0.618}
 Expressions-with-variables/481056: Hi could you please solve- 16+ 12x- x^3 when x=3 1 solutions Answer 329435 by nerdybill(6958)   on 2011-08-12 22:49:32 (Show Source): You can put this solution on YOUR website!16+ 12x- x^3 when x=3 . just substitute the x with a 3 and solve: 16+ 12(3)- 3^3 16+ 36 - 27 16+ 36 - 27 52 - 27 25
 Polynomials-and-rational-expressions/480902: Factor. r^2 + 10r+251 solutions Answer 329292 by nerdybill(6958)   on 2011-08-12 12:26:33 (Show Source): You can put this solution on YOUR website!r^2 + 10r+25 (r+5)(r+5) or (r+5)^2
 Miscellaneous_Word_Problems/480874: Angela takes 40 minutes to dust and clean her home while her sister rani takes an hour (6o min) to do same work. One day their mother joins the two sisters and together the three of them dust and clean their house in just 15 min. How long would their mother take if she did the job alone.1 solutions Answer 329275 by nerdybill(6958)   on 2011-08-12 10:18:00 (Show Source): You can put this solution on YOUR website! Angela takes 40 minutes to dust and clean her home while her sister rani takes an hour (6o min) to do same work. One day their mother joins the two sisters and together the three of them dust and clean their house in just 15 min. How long would their mother take if she did the job alone. . Let x = time (min) for mother to do it alone then 15(1/40 + 1/60 + 1/x) = 1 multiplying both sides by 2400x: 15(60x + 40x + 2400) = 2400x 15(100x + 2400) = 2400x 1500x + 36000 = 2400x 36000 = 900x 40 mins = x
 Quadratic_Equations/480854: Each cycle of a screen saver program generates and then erases numbers of little animated figures called froobies. The formula P=-2x^2+106x-674 models the population, P, of froobies after x minutes within a cycle. How many minutes into a cycle will the froobie population reach 118?1 solutions Answer 329274 by nerdybill(6958)   on 2011-08-12 10:08:15 (Show Source): You can put this solution on YOUR website! Each cycle of a screen saver program generates and then erases numbers of little animated figures called froobies. The formula P=-2x^2+106x-674 models the population, P, of froobies after x minutes within a cycle. How many minutes into a cycle will the froobie population reach 118? . Given: P=-2x^2+106x-674 Set P to 118 and solve for x: 118=-2x^2+106x-674 0 = -2x^2+106x-792 0 = 2x^2-106x+792 0 = x^2-53x+396 factoring we have: 0 = (x-9)(x-44) x = {9, 44} minutes
 Rectangles/480862: The length of the longest rod which can be kept inside a rectangular box is 17 cm. If the inner length and breadth of the box are 12 cm and 8 cm respectively, find its inner height.1 solutions Answer 329272 by nerdybill(6958)   on 2011-08-12 10:01:52 (Show Source): You can put this solution on YOUR website!The length of the longest rod which can be kept inside a rectangular box is 17 cm. If the inner length and breadth of the box are 12 cm and 8 cm respectively, find its inner height. . Draw a diagram, it'll help you see the solution. . Begin by find the length of the diagonal on the bottom: Let d = diagonal then d^2 = 8^2 + 12^2 d^2 = 64 + 144 d^2 = 208 d = sqrt(208) d = 14.222 cm . Now, we can find the inner height: Let h = inner height then h^2 + 14.222^2 = 17^2 h^2 + 208 = 289 h^2 = 81 h = 9 cm
 Quadratic_Equations/480732: What is the solution to the equation x(x-1)=0?1 solutions Answer 329218 by nerdybill(6958)   on 2011-08-12 00:58:16 (Show Source): You can put this solution on YOUR website!What is the solution to the equation x(x-1)=0? . Set each term on the left to zero and solve: (x)(x-1)=0 . So: x = 0 or x-1 = 0 x = 1 . solution: x = {0,1}
 Functions/480762: f(x)=x^2+1 find for f(x+2) f(x+2)=(x+2)^2 +1 =x^2+4+1 =x^2 +5 But book answer is: f(x+2)=x^2+4x=5 I can not figure out where you get the 4x- what step am I missing?1 solutions Answer 329216 by nerdybill(6958)   on 2011-08-12 00:55:36 (Show Source): You can put this solution on YOUR website!You have to apply FOIL . f(x)=x^2+1 find for f(x+2) . f(x+2)=(x+2)^2+1 f(x+2)=(x+2)(x+2)+1 f(x+2)=(x^2+2x+2x+4)+1 f(x+2)=(x^2+4x+4)+1 f(x+2)= x^2+4x+5
 Equations/480495: A manufacturing company makes ladies purses receiving \$120 for each purse sold. If x represents the number of purses made, the income received is determined by the revenue function R(x) = 120x. The company has a fixed cost of \$12,000 per month and variable costs of \$57.50 for each purse made. The cost function is C(x) = 57.5x + 12000. How many purses must the company sell for revenue to equal cost?1 solutions Answer 329051 by nerdybill(6958)   on 2011-08-11 09:10:55 (Show Source): You can put this solution on YOUR website!A manufacturing company makes ladies purses receiving \$120 for each purse sold. If x represents the number of purses made, the income received is determined by the revenue function R(x) = 120x. The company has a fixed cost of \$12,000 per month and variable costs of \$57.50 for each purse made. The cost function is C(x) = 57.5x + 12000. How many purses must the company sell for revenue to equal cost? 120x = 57.5x + 12000 62.5x = 12000 x = 192 purses
 Equations/480496: Assume that a company has total annual fixed costs of \$480,000 and that variable costs is \$6 per unit. If each unit sells for \$10, then each unit exceeds the specific variable costs by \$4. a. What is the cost function? b. What is the revenue function? c. How many units must be sold in order for the company to break-even? 1 solutions Answer 329050 by nerdybill(6958)   on 2011-08-11 09:08:53 (Show Source): You can put this solution on YOUR website!Assume that a company has total annual fixed costs of \$480,000 and that variable costs is \$6 per unit. If each unit sells for \$10, then each unit exceeds the specific variable costs by \$4. a. What is the cost function? C(x) = 6x + 480000 b. What is the revenue function? R(x) = 10x c. How many units must be sold in order for the company to break-even? set R(x) = C(x) 10x = 6x + 480000 4x = 480000 x = 120,000 units
 Equations/480499: In business, the break-even point means?1 solutions Answer 329048 by nerdybill(6958)   on 2011-08-11 09:06:04 (Show Source): You can put this solution on YOUR website!Break-even means: "Revenue" = "Costs"
 Angles/480491: two complementary angles are (a+20*) and (a+30*).what is the value of a? 1 solutions Answer 329046 by nerdybill(6958)   on 2011-08-11 09:02:02 (Show Source): You can put this solution on YOUR website!two complementary angles are (a+20*) and (a+30*).what is the value of a? . I'm assuming the * indicates degrees. . When two angles ar complementary, the sum is 90 degrees giving us our equation: (a+20) + (a+30) = 90 2a + 50 = 90 2a = 40 a = 20 degrees