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# Recent problems solved by 'nerdybill'

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 Travel_Word_Problems/380620: A car travels at an average speed of 56 miles per hour. How many miles does it travel in 4 hours and 15 minutes? 1 solutions Answer 270200 by nerdybill(6959)   on 2010-12-04 14:34:31 (Show Source): You can put this solution on YOUR website!A car travels at an average speed of 56 miles per hour. How many miles does it travel in 4 hours and 15 minutes? . apply the "distance formula": d = rt where d is distance r is rate or speed t is time . convert "4 hours and 15 minutes" to "hours": 15mins * 1hr/60mins = 15/60 = .25 hour therefore: "4 hours and 15 minutes" = 4.25 hours . d = 56 * 4.25 d = 238 miles
 Exponential-and-logarithmic-functions/380611: what is the solution to the equation logbase16^(32)=x+51 solutions Answer 270198 by nerdybill(6959)   on 2010-12-04 14:30:04 (Show Source): You can put this solution on YOUR website! applying the "change of base":
 Pythagorean-theorem/380615: Use the Pythagorean Theorem to find the length of the diagonal of a piece of paper that measures 16 inches by 24 inches. 1 solutions Answer 270194 by nerdybill(6959)   on 2010-12-04 14:24:28 (Show Source): You can put this solution on YOUR website!Use the Pythagorean Theorem to find the length of the diagonal of a piece of paper that measures 16 inches by 24 inches. . Pythagorean: a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the other two sides of the right triangle . 16^2 + 24^2 = c^2 256 + 576 = c^2 832 = c^2 sqrt(832) = c sqrt(4*4*2*2*13) = c 4*2*sqrt(13) = c 8*sqrt(13) inches = c (exact answer) or approximately: 28.84 inches = c
 Functions/380619: ***I need the steps to solve this problem by Sunday*** Please HELP!!! POPULATION DENSITY The population density D (in people/mi^2)in a large city is related to the distance x from the center of the city by D=5000x/(x^2+36). In what areas of the city does the population density exceed 400people/mi^2? Thanks!!1 solutions Answer 270191 by nerdybill(6959)   on 2010-12-04 14:19:46 (Show Source): You can put this solution on YOUR website!D=5000x/(x^2+36) Set D to 400 and solve for x: 400=5000x/(x^2+36) 400(x^2+36) = 5000x 400x^2+14400 = 5000x 400x^2-5000x+14400 = 0 4x^2-50x+144 = 0 2x^2-25x+72 = 0 (2x-9)(x-8) = 0 x = {9/2, 8} . Solution: At a distance of 4.5 and 8 miles from the center
 Complex_Numbers/380561: how do you write (-1+i)-(7-5i) as a complex number in standard form1 solutions Answer 270154 by nerdybill(6959)   on 2010-12-04 11:04:45 (Show Source): You can put this solution on YOUR website! (-1+i)-(7-5i) distribute the negative sign to terms inside parenthesis: -1+i-7+5i combining like-terms: -8+5i
 Linear-equations/379718: What is the slope of the line parallel to y=8x-101 solutions Answer 269588 by nerdybill(6959)   on 2010-12-02 12:53:19 (Show Source): You can put this solution on YOUR website!Remember the "slope-intercept" form of a line is: y = mx + b where m is the slope b is the y-intecept . Given that you have: y=8x-10 which is in the "slope-intercept" form. By inspection then, we see that the slope is: 8
 Polynomials-and-rational-expressions/379715: i was wondering if someone would be so kind to tell me if i got this correct a/sqrt a my answer sqrt a thank you so much1 solutions Answer 269587 by nerdybill(6959)   on 2010-12-02 12:51:49 (Show Source): You can put this solution on YOUR website!Yes, you are correct.
 Complex_Numbers/379680: Simplify this complex fraction. Reduce to lowest terms. 1/9 + 1/3x ------------------------- x/9 - 1/x1 solutions Answer 269579 by nerdybill(6959)   on 2010-12-02 12:15:53 (Show Source): You can put this solution on YOUR website!If you started with: 1/9 + 1/3x ------------ x/9 - 1/x . to rid ourselves of the denominator, multiply by 9x/9x to get: . x + 3 ------------ x^2 - 9 . Next, because the denominator is a "difference of squares" we can factor: . x + 3 ------------ (x+3)(x-3) . Canceling like-terms we finally get: 1 ---- x-3
 Graphs/379654: Find the equation of the line that has a slope of 3/4 and passes through a point (-2,5). 1 solutions Answer 269577 by nerdybill(6959)   on 2010-12-02 11:37:36 (Show Source): You can put this solution on YOUR website!Find the equation of the line that has a slope of 3/4 and passes through a point (-2,5). . Plug given information into the "point-slope" form": y - y1 = m(x -x1) y - 5 = (3/4)(x -(-2)) y - 5 = (3/4)(x+2) y - 5 = (3/4)x + 3/2 y = (3/4)x + 3/2 + 5 y = (3/4)x + 3/2 + 10/2 y = (3/4)x + 13/2 (slope-intercept form)
 Miscellaneous_Word_Problems/379651: Joan can shovel a certain driveway in 50 minutes. If mary can shovel the same driveway in 20 minutes, how long will it take them, to the nearest minute, to shove the driveway if they work together?1 solutions Answer 269576 by nerdybill(6959)   on 2010-12-02 11:35:02 (Show Source): You can put this solution on YOUR website!Joan can shovel a certain driveway in 50 minutes. If mary can shovel the same driveway in 20 minutes, how long will it take them, to the nearest minute, to shove the driveway if they work together? . Let x = time (minutes) it takes for both then x(1/50 + 1/20) = 1 multiplying both sides by 1000: x(20 + 50) = 1000 x(70) = 1000 x = 14.29 rounded: x = 14 minutes
 Equations/379626: What is the slope of the line that goes through the given points of (9,1), (3,9)1 solutions Answer 269557 by nerdybill(6959)   on 2010-12-02 10:22:09 (Show Source): You can put this solution on YOUR website!What is the slope of the line that goes through the given points of (9,1), (3,9) . Given two points: (x1,y1) and (x2,y2) the slope is: (y2 - y1)/(x2 - x1) . Plug in the given values: (9 - 1)/(3 - 9) 8/(-6) -4/3
 Square-cubic-other-roots/379614: An inlet pipe can fill a tank in 8 minutes. A drain can empty the tank in 12 mintes. If the tank is empty and both the pipe and drain are open, how long will it take before the tank overflows? Thanks! 1 solutions Answer 269547 by nerdybill(6959)   on 2010-12-02 09:55:58 (Show Source): You can put this solution on YOUR website!An inlet pipe can fill a tank in 8 minutes. A drain can empty the tank in 12 mintes. If the tank is empty and both the pipe and drain are open, how long will it take before the tank overflows? . Let x = time (minutes) it takes to fill tank then x(1/8 - 1/12) > 1 multiplying both sides by 96: x(12 - 8) > 96 x(4) > 96 x > 24 minutes That is, tank begins to overflow after 24 minutes
 test/376937: For 1980 through 1995, the annual sales, S (in thousands of dollars) of a photography studio can be modeled by S = -1/8t^2 + 3t +42, where t=0 represents 1980. During which year did the studio sell \$59,500?1 solutions Answer 268035 by nerdybill(6959)   on 2010-11-28 11:49:54 (Show Source): You can put this solution on YOUR website!For 1980 through 1995, the annual sales, S (in thousands of dollars) of a photography studio can be modeled by S = -1/8t^2 + 3t +42, where t=0 represents 1980. During which year did the studio sell \$59,500? . Set S to 59.5 and solve for t: 59.5 = -1/8t^2 + 3t +42 476 = -t^2 + 24t + 336 0 = -t^2 + 24t - 140 0 = t^2 - 24t + 140 0 = (t-14)(t-10) t = {10, 14} . 1980+10 = 1990 and 1980+14 = 1994 . Ans: 1990 and 1994
 Linear-equations/376898: Use Point-slope form to Complete: slope=-2/3 and passes through (-3, -5)1 solutions Answer 268029 by nerdybill(6959)   on 2010-11-28 10:21:36 (Show Source): You can put this solution on YOUR website!The "point-slope" form is: y - y1 = m(x - x1) . So, given: slope=-2/3 and passes through (-3, -5) we plug it in to: y - y1 = m(x - x1) y - (-5) = (-2/3)(x - (-3)) y + 5 = (-2/3)(x + 3) y + 5 = (-2/3)x + (-2/3)3 y + 5 = (-2/3)x - 2 y = (-2/3)x - 7 (this is what they're looking for) The above is the "slope-intercept" form of the line
 Rate-of-work-word-problems/376475: It takes Joe 12 hours to paint a fence, but Bob can do the job in 9 hours. How long does Joe work by himself before being joined by Sam if they finish the job working 3 hours together? I've tried setting up a system of equations, but am not having much luck. I think that the first equation is x/12 + y/9 = 1, with x being the number of hours Joe works and y the number of hours Bob works, but I can't figure out the second equation.1 solutions Answer 267839 by nerdybill(6959)   on 2010-11-27 11:03:05 (Show Source): You can put this solution on YOUR website!It takes Joe 12 hours to paint a fence, but Bob can do the job in 9 hours. How long does Joe work by himself before being joined by Sam if they finish the job working 3 hours together? Let x = number of hours Joe works by himself then "portion of work by Joe" + "work together" = "total job" x/12 + 3(1/12 + 1/9) = 1 x/12 + (1/4 + 1/3) = 1 multiplying both sides by 12: x + (3 + 4) = 12 x + 7 = 12 x = 5 hours
 Rational-functions/376362: the graph of the function f(x)=x^2-kx+k+8 touches the x-axis at one point. what are the possible values of k? Thanks in advance! 1 solutions Answer 267805 by nerdybill(6959)   on 2010-11-27 01:12:26 (Show Source): You can put this solution on YOUR website!Since f(x)=x^2-kx+k+8 touches the x-axis at only one point, it must be the vertex. . this must mean the "determinant" is zero: b^2-4ac = 0 (-k)^2 - 4(1)(k+8) = 0 (-k)^2 - 4(k+8) = 0 k^2 - 4k-32 = 0 (k-8)(k+4) = 0 . k = {-4, 8}
 Miscellaneous_Word_Problems/376275: If a pro basketball player has a vertical leap of about 20 inches, what is his hang time? Use the hang-time function v=48T^2 His hang-time is __________seconds. (simplify. type an integer or a decimal. round to the nearest tenth.)1 solutions Answer 267667 by nerdybill(6959)   on 2010-11-26 16:17:54 (Show Source): You can put this solution on YOUR website!v=48T^2 Set v to 20 and solve for t: 20=48T^2 20/48 = T^2 sqrt(20/48) = T 0.6 secs = T
 Polynomials-and-rational-expressions/376268: I was hoping to get some help with the following problem: Use the FOIL method to find the product (4x^2-8)(x^5-9)1 solutions Answer 267661 by nerdybill(6959)   on 2010-11-26 15:28:39 (Show Source): You can put this solution on YOUR website!(4x^2-8)(x^5-9) (4x^2)(x^5)+(x^5)(-9)+(-8)(x^5)+(-8)(-9) 4x^7-9x^5-8x^5+72 4x^7-17x^5+72
 Mixture_Word_Problems/376251: One pipe takes 30 minutes to fill a tank. After it has been running for 10 minutes, it is shut off. A second pipe is then opened and it finishes the tank in 15 minutes. How long would it take the second pipe alont to fill the tank?1 solutions Answer 267653 by nerdybill(6959)   on 2010-11-26 14:32:53 (Show Source): You can put this solution on YOUR website!One pipe takes 30 minutes to fill a tank. After it has been running for 10 minutes, it is shut off. A second pipe is then opened and it finishes the tank in 15 minutes. How long would it take the second pipe alont to fill the tank? . Let x = time (mins) it takes second pipe to fill the tank alone then 10(1/30) + 15(1/x) = 1 multiplying both sides by 30x: 10(x) + 15(30) = 30x 10x + 450 = 30x 450 = 20x 22.5 mins = x
 logarithm/376205: change from logarithmic form to exponential form log[x]=31 solutions Answer 267633 by nerdybill(6959)   on 2010-11-26 10:47:51 (Show Source): You can put this solution on YOUR website!log[x]=3 x = 10^3
 Equations/376100: I need help to solve the equation 26+8y-18=01 solutions Answer 267505 by nerdybill(6959)   on 2010-11-25 15:38:52 (Show Source): You can put this solution on YOUR website!26+8y-18=0 8+8y=0 8y=-8 y= -8/8 y= -1
 Linear-systems/376106: Find the x-and y- intercepts algebraically, showing all work. y=-(2/3)x+301 solutions Answer 267504 by nerdybill(6959)   on 2010-11-25 15:37:29 (Show Source): You can put this solution on YOUR website!y=-(2/3)x+30 . To find the y-intercepts, set x=0 and solve for y: y=-(2/3)(0)+30 y=0+30 y=30 So, the y-intercept is at (0,30) . To find the x-intercepts, set y=0 and solve for x: 0=-(2/3)x+30 -30=-(2/3)x 30=(2/3)x 90=2x 45=x so, the x-intercept is at (45,0)
 Miscellaneous_Word_Problems/375974: MACHINE A TAKES 36 HOURS TO DO A JOB THAT MACHINE B DOES IN 24 HOURS.IF MACHINE RUNS FOR 12 HRS. BEFORE MACHINE B IS TURNED ON, HOW LONG WILL IT TAKE BOTH MACHINES RUNNING TOGETHER TO FINISH THE JOB IF THEY WORK TOGETHER?1 solutions Answer 267463 by nerdybill(6959)   on 2010-11-25 09:17:20 (Show Source): You can put this solution on YOUR website!MACHINE A TAKES 36 HOURS TO DO A JOB THAT MACHINE B DOES IN 24 HOURS.IF MACHINE RUNS FOR 12 HRS. BEFORE MACHINE B IS TURNED ON, HOW LONG WILL IT TAKE BOTH MACHINES RUNNING TOGETHER TO FINISH THE JOB IF THEY WORK TOGETHER? . Since mach A ran for 12 hours, the portion of the job done is: 12(1/36) = 12/36 = 1/3 of the job completed before mach B starts . Let x = time (hrs) for mach A/B to complete job then x(1/36 + 1/24) = 1 - 1/3 x(1/36 + 1/24) = 3/3 - 1/3 x(1/36 + 1/24) = 2/3 multiplying both sides by 3: x(1/12 + 1/8) = 2 multiplying both sides by 24: x(2 + 3) = 48 x(5) = 48 x = 48/5 x = 9.6 hours or x = 9 hours and 36 minutes
 Miscellaneous_Word_Problems/375972: A swimming pool can be filled by a large pipe in 4 hrs. and by a small pipe in 6 hrs. A third pipe can empty the pool in 3 hrs. How long would it take to fill the pool if all three pipes were open at the same time?1 solutions Answer 267434 by nerdybill(6959)   on 2010-11-25 03:27:36 (Show Source): You can put this solution on YOUR website!A swimming pool can be filled by a large pipe in 4 hrs. and by a small pipe in 6 hrs. A third pipe can empty the pool in 3 hrs. How long would it take to fill the pool if all three pipes were open at the same time? . Let x = time (hours) for all three pipe to fill pool then x(1/4 + 1/6 + 1/3) = 1 Multiply both sides by 12: x(3 + 2 + 4) = 12 x(9) = 12 x = 12/9 x = 4/3 x = 1 and 1/3 hours or x = 1 hour and 20 minutes
 Mixture_Word_Problems/376010: The perimeter of a standard high school basketball court is 268 ft. The length is 34 ft greater than the width. Find the length and the width of the court.1 solutions Answer 267431 by nerdybill(6959)   on 2010-11-25 03:06:02 (Show Source): You can put this solution on YOUR website!The perimeter of a standard high school basketball court is 268 ft. The length is 34 ft greater than the width. Find the length and the width of the court. . Let w = width then w+34 = length . 2(w + w+34) = 268 dividing both sides by 2: (w + w+34) = 134 2w+34 = 134 2w = 100 w = 100 ft. (width . Length: w+34 = 100+34 = 134 ft
 Quadratic_Equations/376027: solve x^2 + (x+7)^2 = 1691 solutions Answer 267429 by nerdybill(6959)   on 2010-11-25 03:02:17 (Show Source): You can put this solution on YOUR website!x^2 + (x+7)^2 = 169 x^2 + (x+7)(x+7) = 169 x^2 + x^2+14x+49 = 169 2x^2+14x+49 = 169 2x^2+14x-120 = 0 x^2+7x-60 = 0 (x+12)(x-5) = 0 x = {-12, 5}
 Evaluation_Word_Problems/375992: How man L of a 10% saline solution must be added to 40 L of a 20% saline solution to obtain a 14% saline solution?1 solutions Answer 267427 by nerdybill(6959)   on 2010-11-25 02:58:26 (Show Source): You can put this solution on YOUR website!How many L of a 10% saline solution must be added to 40 L of a 20% saline solution to obtain a 14% saline solution? . Let x = amount (L) of 10% saline solution then .10x + .20(40) = .14(x+40) .10x + 8 = .14x + 5.6 8 = .04x + 5.6 2.4 = .04x 60 liters = x
 Polynomials-and-rational-expressions/375997: I am trying to find the answer to this, and I'm having a lot of problems. ((3x+1)/(9x^2-1)) - ((2)/3x-1))1 solutions Answer 267426 by nerdybill(6959)   on 2010-11-25 02:55:05 (Show Source): You can put this solution on YOUR website!((3x+1)/(9x^2-1)) - ((2)/3x-1)) . Notice that (9x^2-1) can be written as a "difference of squares": ((3x)^2-1^2) which can be factored as: (3x-1)(3x+1) . So,we can rewrite: ((3x+1)/(9x^2-1)) - ((2)/3x-1)) as ((3x+1)/((3x-1)(3x+1))) - ((2)/3x-1)) canceling like-terms: (1/(3x-1)) - ((2)/3x-1)) Now we can combine as: (1-2)/(3x-1) -1/(3x-1) or 1/(1-3x)
 Mixture_Word_Problems/376011: Solve by rearranging the equations first. Then use the multiplication principle and then use the elimination method: 3x=8y+11 x+6y-8=0 1 solutions Answer 267425 by nerdybill(6959)   on 2010-11-25 02:50:19 (Show Source): You can put this solution on YOUR website!Solve by rearranging the equations first. Then use the multiplication principle and then use the elimination method: 3x=8y+11 x+6y-8=0 . Rearranging equations: 3x-8y = 11 x+6y = 8 . Multiply both sides of bottom equation by -3: 3x-8y = 11 -3x-18y = -24 . Add both equations together: 3x-8y = 11 -3x-18y = -24 --------------- -26y = -13 y = -13/(-26) y = 1/2 . Substitute above into bottom equation: x+6y = 8 x+6(1/2) = 8 x+3 = 8 x = 5 . Solution: ordered pair (5,1/2)
 Mixture_Word_Problems/376012: A vending machine contains nickels and dimes worth \$14.50. There are 95 more nickels than dimes. How many nickels and how many dimes are there?1 solutions Answer 267423 by nerdybill(6959)   on 2010-11-25 02:46:03 (Show Source): You can put this solution on YOUR website!A vending machine contains nickels and dimes worth \$14.50. There are 95 more nickels than dimes. How many nickels and how many dimes are there? . Let x = number of dimes then x+95 = number of nickels . .10x + .05(x+95) = 14.50 .10x + .05x+4.75 = 14.50 .15x+4.75 = 14.50 .15x = 9.75 x = 65 (number of dimes) . number of nickels: x+95 = 65+95 = 160
 Money_Word_Problems/376024: Kim's hourly rate is based on a 40 hour work week. For overtime, she is paid 1.5 times as much. If she earned \$312 for 48 hours, what is her regular rate?1 solutions Answer 267422 by nerdybill(6959)   on 2010-11-25 02:41:59 (Show Source): You can put this solution on YOUR website!Kim's hourly rate is based on a 40 hour work week. For overtime, she is paid 1.5 times as much. If she earned \$312 for 48 hours, what is her regular rate? . Let x = regular rate then 40x + 1.5x(8) =312 40x + 12x =312 52x = 312 x = \$6 per hour