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# Recent problems solved by 'nerdybill'

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 Travel_Word_Problems/545499: MOTION PROBLEMS Can you please help me solve this problem: An airplane flew for 4 hours with a 20-km/h tail wind. The return flight against the same wind took 5 hours. Find the speed of the plane in still air.1 solutions Answer 355603 by nerdybill(7003)   on 2011-12-11 17:29:43 (Show Source): You can put this solution on YOUR website!An airplane flew for 4 hours with a 20-km/h tail wind. The return flight against the same wind took 5 hours. Find the speed of the plane in still air. . Let x = speed of plane in still air then from distance formula: 4(x+20) = 5(x-20) 4x+80 = 5x-100 80 = x-100 180 km/hr = x
Triangles/545262: The hypotenuse of a right triangle is 5 feet long. One leg is 3 feet longer then the other leg. Find the perimeter of the triangle.

1 solutions

Answer 355546 by nerdybill(7003)   on 2011-12-11 11:19:43 (Show Source):
You can put this solution on YOUR website!
The hypotenuse of a right triangle is 5 feet long. One leg is 3 feet longer then the other leg. Find the perimeter of the triangle.
.
Let x = length of "other leg"
then
x+3 = length of "one leg"
.
applying Pythagorean theorem:
x^2 + (x+3)^2 = 5^2
x^2 + (x+3)(x+3) = 25
x^2 + x^2+6x+9 = 25
2x^2+6x+9 = 25
2x^2+6x-16 = 0
x^2+3x-8 = 0
applying the "quadratic formula" results in:
x = {1.7, -4.7}
Throw out the negative solution leaving:
x = 1.7 feet (other leg)
"one leg":
x+3 = 1.7+3 = 4.7 feet
Perimeter:
4.7 + 1.7 + 5 = 11.4 feet
.
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=41 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.70156211871642, -4.70156211871642. Here's your graph:

 Angles/545267: If an angle has a measure of 45°12' 10", the measure of its complement is what?1 solutions Answer 355545 by nerdybill(7003)   on 2011-12-11 11:12:50 (Show Source): You can put this solution on YOUR website! If an angle has a measure of 45°12' 10", the measure of its complement is what? The sum of two angles that are complementary is 90 degrees: 90° - 45°12' 10" 89°60' - 45°12' 10" 89°59'60" - 45°12' 10" (89°-45°)(59'-12')(60"-10") (44°)(47')(50") 44°47'50"
 Linear-equations/545269: give the equation for a line with a slope of 5 that passes through the point (4,1)1 solutions Answer 355544 by nerdybill(7003)   on 2011-12-11 11:09:11 (Show Source): You can put this solution on YOUR website! give the equation for a line with a slope of 5 that passes through the point (4,1) . Plug the given information into the "point-slope" form: y - y1 = m(x - x1) y - 1 = 5(x - 4) y - 1 = 5x - 20 y = 5x - 21 (this is what they're looking for - in "slope-intercept" form)
 logarithm/545148: Its a chem problem. 9.00=9.25 + log(x/.0375) Solved on my calc to get aproxx .0215 but I want to know why. I am forgetting some basic rules of solving logs. -.25 = logx - log(.0375) ?1 solutions Answer 355509 by nerdybill(7003)   on 2011-12-11 00:25:24 (Show Source): You can put this solution on YOUR website!-.25 = logx - log(.0375) ? -.25 = logx/(.0375) 10^(-.25) = x/(.0375) .0375*10^(-0.25) = x 0.0211 = x
 Finance/545062: 1.43=1.05(1+g)4 trying to solve for g to give me the dividend growth rate. the answer in the book is .0803 I just forgot how to do this type of algebra. 1 solutions Answer 355396 by nerdybill(7003)   on 2011-12-10 16:37:24 (Show Source): You can put this solution on YOUR website!1.43=1.05(1+g)^4 1.43/1.05 = (1+g)^4 (1.43/1.05)^(1/4) = 1+g (1.43/1.05)^(1/4) - 1 = g 0.08 = g or 8% = g
 Equations/545045: It states Solve for x: x^2-5x-14=01 solutions Answer 355393 by nerdybill(7003)   on 2011-12-10 16:34:46 (Show Source): You can put this solution on YOUR website!x^2-5x-14=0 factoring the left side: (x-7)(x+2) = 0 x = {-2, 7}
 logarithm/544974: domain for log3(2x-7)1 solutions Answer 355376 by nerdybill(7003)   on 2011-12-10 13:15:00 (Show Source): You can put this solution on YOUR website!domain for log3(2x-7) . Since, you can't take a log of a negative number: 2x-7 >= 0 2x >= 7 x >= 7/2 x >= 3.5 (domain) 'x' must be "greater than or equal" to 3.5
 Exponential-and-logarithmic-functions/544977: log2 3x + log2 5 =log2 301 solutions Answer 355375 by nerdybill(7003)   on 2011-12-10 13:12:41 (Show Source):
 Percentage-and-ratio-word-problems/544995: Find 50% of 401 solutions Answer 355372 by nerdybill(7003)   on 2011-12-10 13:07:27 (Show Source): You can put this solution on YOUR website!50% of 40 50/100 * 40 1/2 * 40 20
 Numbers_Word_Problems/544735: i am working on my math homework and i came to this word problem and i tried it but i still couldn't figure out what the answer was nor could my boyfriend. please help me. two numbers total 57 and have a difference of 9. 1 solutions Answer 355200 by nerdybill(7003)   on 2011-12-09 15:31:43 (Show Source): You can put this solution on YOUR website!two numbers total 57 and have a difference of 9 Let x,y be the two numbers x+y = 57 x-y = 9 . Add both equations together: x+y = 57 x-y = 9 ------------ 2x = 66 x = 33 . substitute above into: x+y = 57 33+y = 57 y = 24 . solution: 24 and 33
 Functions/543806: f(x)=1/(4x+3) Domain1 solutions Answer 354932 by nerdybill(7003)   on 2011-12-07 22:29:00 (Show Source): You can put this solution on YOUR website!f(x)=1/(4x+3) Domain . Domain specifies all possible values of x: The only value you must exclude is when the denominator is zero: 4x+3 = 0 4x = -3 x = -3/4 x = -0.75 . In set-notation: (-oo, -0.75) U (-.75, +oo) where oo stands for infinity
 Polynomials-and-rational-expressions/543221: Is this correct?8^-3=1/512 this is how i arrive at the answer 8*8=64*8=512 so 8^-3=1/512 or 1/8^3? which is correct?1 solutions Answer 354789 by nerdybill(7003)   on 2011-12-07 08:34:31 (Show Source): You can put this solution on YOUR website!Yes, you are correct.
 logarithm/542514: express a single logarithm: LOGa9+LOGa701 solutions Answer 354608 by nerdybill(7003)   on 2011-12-06 10:13:01 (Show Source): You can put this solution on YOUR website!LOGa9+LOGa70 LOGa(9*70) LOGa630
 Equations/542505: √(16Tt^2)1 solutions Answer 354606 by nerdybill(7003)   on 2011-12-06 10:06:02 (Show Source): You can put this solution on YOUR website!√(16Tt^2) √(4*4Tt^2) 4*√(Tt^2) 4*√(Ttt) 4t*√(T)
 Linear-equations/542511: What is the slope and y- intercept of -3y = 4(6x - 3)?1 solutions Answer 354604 by nerdybill(7003)   on 2011-12-06 10:04:52 (Show Source): You can put this solution on YOUR website!What is the slope and y- intercept of -3y = 4(6x - 3)? Begin by rearranging given equation inot "slope-intercept" form of: y = mx + b . -3y = 4(6x - 3) -3y = 24x - 12 3y = -24x + 12 y = -8x + 4 . From inspection then: slope is -8 y-intercept is at (0,4)
 Quadratic_Equations/541931: What is the vertex of (x-3)^2?1 solutions Answer 354346 by nerdybill(7003)   on 2011-12-05 14:04:47 (Show Source): You can put this solution on YOUR website!What is the vertex of (x-3)^2? Since the "vertex form" of a parabola is: y = a(x-h)^2 + k where (h,k) is the vertex . From: (x-3)^2 we can rewriet as: (x-3)^2 + 0 So, the vertex is at (3,0)
 Quadratic_Equations/541823: THe height in feet a ball is t seconds after being throan in the air is given by H(t)=-16t^2+64t+5 A)How long did it take the ball to reach its maximum height above the ground B)What was the maximum height above the ground the ball reached1 solutions Answer 354298 by nerdybill(7003)   on 2011-12-05 10:29:04 (Show Source): You can put this solution on YOUR website!THe height in feet a ball is t seconds after being throan in the air is given by H(t)=-16t^2+64t+5 A)How long did it take the ball to reach its maximum height above the ground Vertex of parabola is the max: t = -b/(2a) t = -64/(2(-16)) t = -64/(-32) t = 2 seconds . B)What was the maximum height above the ground the ball reached plug t=2 into: H(t)=-16t^2+64t+5 H(2)=-16(2)^2+64(2)+5 H(2)=-16(4)+128+5 H(2)=-64+128+5 H(2)= 69 feet
 Miscellaneous_Word_Problems/541809: A certain radioactive isotope has a half-life of approximately 1300 milliseconds. How much time would be required for a given amount of this isotope to decay to 35% of that amount? Use the formula A=Ie^kt where A is the amount at the time, I is the initial amount and k is the decay constant unique to the substance. Thank you1 solutions Answer 354297 by nerdybill(7003)   on 2011-12-05 10:26:12 (Show Source): You can put this solution on YOUR website!A certain radioactive isotope has a half-life of approximately 1300 milliseconds. How much time would be required for a given amount of this isotope to decay to 35% of that amount? Use the formula A=Ie^kt where A is the amount at the time, I is the initial amount and k is the decay constant unique to the substance. . Given: A=Ie^kt Use: "A certain radioactive isotope has a half-life of approximately 1300 milliseconds." to find the constant 'k': Let x = initial amount x/2 = half the initial amount x/2 = xe^(k*1300) dividing both sides by x: 1/2 = e^(k*1300) ln(.5) = k*1300 ln(.5)/1300 = k . Now we can answer: How much time would be required for a given amount of this isotope to decay to 35% of that amount? Let x = initial amount then .35x = 35% of initial amount our formula: A=Ie^kt .35x = xe^(t*ln(.5)/1300) dividing both sides by x: .35 = e^(t*ln(.5)/1300) ln(.35) = t*ln(.5)/1300 1300*ln(.35) = t*ln(.5) 1300*ln(.35)/ln(.5) = t 1968.95 milliseconds = t OR, 1.96 seconds = t
 logarithm/541818: log base 10 of 0.001 how do I go about finding this I know: 10^x = 0.001 but then i am stuck1 solutions Answer 354296 by nerdybill(7003)   on 2011-12-05 10:18:12 (Show Source): You can put this solution on YOUR website!Since: 0.001 is equivalent to: 0.001 = 10^(-3) then log base 10 of 0.001 = -3 . -3 is your answer
 Travel_Word_Problems/540499: at 8 am your car's odometer reads 2475 km at noon it reads 2895 km what is the average speed1 solutions Answer 353722 by nerdybill(7003)   on 2011-12-02 08:22:02 (Show Source): You can put this solution on YOUR website!at 8 am your car's odometer reads 2475 km at noon it reads 2895 km what is the average speed . time traveled: 12-8 = 4 hours distance traveled: 2895 - 2475 = 420 km . speed = 420/4 speed = 105 km/hr
 Graphs/539842: A line has a rise of 6 and a slope of 1/20. What is the run? 1 solutions Answer 353569 by nerdybill(7003)   on 2011-12-01 09:45:04 (Show Source): You can put this solution on YOUR website!A line has a rise of 6 and a slope of 1/20. What is the run? . Since slope = rise/run . 6/run = 1/20 cross-multiplying 6*20 = run 120 = run
 Graphs/539180: what is the y-intercept of the equation, y=1.7x+40 1 solutions Answer 353351 by nerdybill(7003)   on 2011-11-30 11:36:33 (Show Source): You can put this solution on YOUR website!what is the y-intercept of the equation, y=1.7x+40 . Because the equation is already in "slope-intercept" form of y = mx + b where m is the slope b is the y-intercept at (0,b) . From inspection then, y-intercept is at (0, 40)
 logarithm/539105: find the domain of the function f(x)=log base 2 (x+1)1 solutions Answer 353333 by nerdybill(7003)   on 2011-11-30 10:10:31 (Show Source): You can put this solution on YOUR website!find the domain of the function f(x)=log base 2 (x+1) . since you can't take a log of a negative number: x+1 >= 0 x >= -1 x has to be greater than or equal to -1
 logarithm/539104: solve equation log base 2 (X2-7x+14)=1 in this eqation, 2 is the base of log and 2 is the exponent for X1 solutions Answer 353332 by nerdybill(7003)   on 2011-11-30 10:08:04 (Show Source): You can put this solution on YOUR website!log base 2 (x^2-7x+14)=1 (x^2-7x+14)=2^1 x^2-7x+14 = 2 x^2-7x+12 = 0 (x-4)(x-3) = 0 x = {3, 4}
 Linear-equations/538647: I am trying to help my son but I cant even understand, Does the system of equations have no solution, one solution, or infinitely many solutions? y = 5x – 4 y = 5x – 5 1 solutions Answer 353219 by nerdybill(7003)   on 2011-11-29 17:54:31 (Show Source): You can put this solution on YOUR website!Does the system of equations have no solution, one solution, or infinitely many solutions? y = 5x – 4 y = 5x – 5 . Since slope (5) is the same for both but the y-intercepts are diffferent we conclude that there is "no solution" . See the site below, it describes the three cases: http://www.mathwarehouse.com/algebra/linear_equation/systems-of-equation/index.php
 Linear-equations/538398: find the x and y intercepts of: y = -2x - 61 solutions Answer 353163 by nerdybill(7003)   on 2011-11-29 09:59:44 (Show Source): You can put this solution on YOUR website!find the x and y intercepts of: y = -2x - 6 . to find the x-intercepts, set y=0 solve for x: y = -2x - 6 0 = -2x - 6 6 = -2x -3 = x so, x-intercept is at (-3,0) . to find the y-intercepts, set x=0 solve for y: y = -2x - 6 y = -2(0) - 6 y = -6 so, y-intercept is at (0,-6)
 Percentage-and-ratio-word-problems/537209: From the top of the building in the illustration, a ball is thrown straight up with an initial velocity of 40 feet per second. The equation s = -16t2 + 40t + 48 gives the height s of the ball t seconds after it is thrown. Find the maximum height reached by the ball and the time it takes for the ball to hit the ground. (Round your answer to one decimal place.) Thank you in advance!1 solutions Answer 352762 by nerdybill(7003)   on 2011-11-27 14:59:05 (Show Source): You can put this solution on YOUR website!From the top of the building in the illustration, a ball is thrown straight up with an initial velocity of 40 feet per second. The equation s = -16t2 + 40t + 48 gives the height s of the ball t seconds after it is thrown. Find the maximum height reached by the ball and the time it takes for the ball to hit the ground. (Round your answer to one decimal place.) s = -16t2 + 40t + 48 The "vertex" defines the max height. It reaches this height when t = -b/(2a) t = -40/(2(-16)) t = -40/(-32) t = 1.25 seconds . Max height: s = -16(1.25)^2 + 40(1.25) + 48 s = 73.0 feet
 Percentage-and-ratio-word-problems/537211: The height (in feet) of the water level in a reservoir over a 1 year period is modeled by the function H(t) = 2.4(t - 10)2 + 15, where t = 1 represents January, t = 2 represents February, and so on. How low did the water level get that year, and when did it reach the low mark? Thank you in advance!1 solutions Answer 352761 by nerdybill(7003)   on 2011-11-27 14:54:26 (Show Source): You can put this solution on YOUR website!The height (in feet) of the water level in a reservoir over a 1 year period is modeled by the function H(t) = 2.4(t - 10)2 + 15, where t = 1 represents January, t = 2 represents February, and so on. How low did the water level get that year, and when did it reach the low mark? The vertex of H(t) = 2.4(t - 10)2 + 15 gives you the low point: equation given is in the "vertex" form: y= a(x-h)^2+k vertex is at (10,15) when did it reach the low mark? t = 10 (October) How low did the water level get: h(t) = 15 feet
 Linear-equations/537074: How do you change 4x-2y=10 into slope-intercept form? I have no idea what to do. Thanks for your time.1 solutions Answer 352718 by nerdybill(7003)   on 2011-11-27 10:57:15 (Show Source): You can put this solution on YOUR website!How do you change 4x-2y=10 into slope-intercept form? . The "slope-intercept" form of a line is: y = mx + b all you need to do, is to rearrange the terms of the given equation to make it look like the form above... You started with: 4x-2y=10 begin by subtracting 4x from both sides: -4x+4x-2y = -4x+10 -2y = -4x+10 multiply both sides by -1: 2y = 4x-10 divide both sides by 2: y = 2x-5 (this is what they're looking for)
 Length-and-distance/537067: A 18-foot ladder leans against a wall at a 74 degree angle of elevation. Find the distance from the ladder's base to the wall.1 solutions Answer 352713 by nerdybill(7003)   on 2011-11-27 10:05:15 (Show Source): You can put this solution on YOUR website!A 18-foot ladder leans against a wall at a 74 degree angle of elevation. Find the distance from the ladder's base to the wall. . Let x = distance (base to wall) . Applying trigonometry: cos x = adjacent/hypotenuse cos(74) = x/18 18*cos(74) = x 4.96 feet = x or approximately: 5 feet = x