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# Recent problems solved by 'nerdybill'

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 Exponents-negative-and-fractional/711645: I have problem 4^-2 +8-6^2(2+1). I got answer of -6.25. Book has -99.9375. What did I do wrong. I thought you had to make exponent positive before you could solve it. Tks1 solutions Answer 437505 by nerdybill(6948)   on 2013-02-07 09:37:55 (Show Source): You can put this solution on YOUR website!Apply the "order of operations" -- (PEMDAS) 4^-2 +8-6^2(2+1) parentheses first: 4^-2 +8-6^2(3) exponents next: 1/4^2 +8-6^2(3) 1/16 +8-36(3) multiplication/division (left to right): .0625 +8-108 addition/subtraction (left to right): 8.0625-108 -99.9375
 Linear_Algebra/711619: if x represents the first, or smallest, of three consecutive even integers, express the sum of the three integers in terms of three integers in terms of x.1 solutions Answer 437480 by nerdybill(6948)   on 2013-02-07 07:37:13 (Show Source): You can put this solution on YOUR website! if x represents the first, or smallest, of three consecutive even integers, express the sum of the three integers in terms of three integers in terms of x. . Let x = smallest of three consecutive even integer then x+2 = next largest consecutive even integer x+5 = largest of three consecutive even integers . "the sum of the three integers in terms of three integers": x + x+2 + x+5 3x+7
 logarithm/711563: Log base 0.4 of 24 - log base 4 of 121 solutions Answer 437479 by nerdybill(6948)   on 2013-02-07 07:34:40 (Show Source): You can put this solution on YOUR website!Log base 0.4 of 24 - log base 4 of 12 applying "change of base" we have: log(24)/log(0.4) - log(12)/log(4) -3.4683902388138800504298507119335 - 1.7924812503605780907268694719739 -5.2608714891744581411567201839074 or approximately: -5.26
 Percentage-and-ratio-word-problems/711586: Michael gained 109 total yards. This is about 62.4% less than Jacob. how many total yards did Jacob gain?1 solutions Answer 437478 by nerdybill(6948)   on 2013-02-07 07:29:59 (Show Source): You can put this solution on YOUR website!Michael gained 109 total yards. This is about 62.4% less than Jacob. how many total yards did Jacob gain? . Let j = total yards gained by Jacob then 109 = j - .624j factoring out a j: 109 = j(1 - .624) 109 = j(.376) 109/.376 = j 289.9 = j Or, approximately: 290 yards = j
 Geometry_Word_Problems/711609: three square were put side to form a rectangle.If the perimeter of the rectange is 48 inches.What is the side of the square1 solutions Answer 437477 by nerdybill(6948)   on 2013-02-07 07:24:10 (Show Source): You can put this solution on YOUR website!three square were put side to form a rectangle.If the perimeter of the rectange is 48 inches.What is the side of the square . Let x = measure of one side of the square then since 2(width + length) = perimeter 2(x + 3x) = 48 dividing both sides by 2: (x + 3x) = 24 4x = 24 x = 6 inches
 Travel_Word_Problems/711617: fresno is 150 miles from bakersfield. A driver leaves fresno and averages 62 miles per hour, and is traveling to bakersfield. Find the distance d from fresno, given the time t, in hours since the driver left.1 solutions Answer 437476 by nerdybill(6948)   on 2013-02-07 07:21:39 (Show Source): You can put this solution on YOUR website! fresno is 150 miles from bakersfield. A driver leaves fresno and averages 62 miles per hour, and is traveling to bakersfield. Find the distance d from fresno, given the time t, in hours since the driver left. Applying the "distance formula": d = 150 - 62t
 test/711616: You should tip your taxi driver 15% and an extra \$2 if they helped you with your bags. Your taxi ride cost \$24.20 and the driver helped you with your bags. How much should you tip the driver? What is the total cost?1 solutions Answer 437475 by nerdybill(6948)   on 2013-02-07 07:20:03 (Show Source): You can put this solution on YOUR website! You should tip your taxi driver 15% and an extra \$2 if they helped you with your bags. Your taxi ride cost \$24.20 and the driver helped you with your bags. . . How much should you tip the driver? .15*24.20 = \$3.63 . What is the total cost? 24.20 + 3.63 + 2 = \$29.83
 Quadratic_Equations/711590: A ball thrown vertically into the air has its height above ground given by h=-16t^2+112t, where t is in seconds and s is in feet. When will the ball hit the ground?1 solutions Answer 437474 by nerdybill(6948)   on 2013-02-07 07:17:56 (Show Source): You can put this solution on YOUR website! A ball thrown vertically into the air has its height above ground given by h=-16t^2+112t, where t is in seconds and s is in feet. When will the ball hit the ground? When the ball is on the ground, the height (h) is zero. So, set h to zero and solve for t: h=-16t^2+112t 0=-16t^2+112t 0=16t^2-112t 0=t^2-7t 0=t(t-7) . t = {0, 7} Throw out the 0 (start) leaving: t = 7 seconds
 Finance/711080: A man investes R90000 at 16% compound annually.calculate the amount of money he receives if he invests it for seven years1 solutions Answer 437292 by nerdybill(6948)   on 2013-02-06 08:05:50 (Show Source): You can put this solution on YOUR website!A man investes R90000 at 16% compound annually.calculate the amount of money he receives if he invests it for seven years . A = P(1+r)^t where A is amount after time t (what we're looking for) P is principal (9000) r is rate (.16) t is time (7) . A = 9000(1+.16)^7 A = 9000(1.16)^7 A = 9000(2.82621973446656) A = RS25435.98
 Quadratic_Equations/711121: How can find max/min value1 solutions Answer 437291 by nerdybill(6948)   on 2013-02-06 08:01:26 (Show Source): You can put this solution on YOUR website!Max/min values are typically associated with "quadratic equations" -- that is, polynomials of degree 2. The "vertex" of the quadratic gives max or min. General form of a quadratic: Ax^2 + Bx + C To determine whether the vertex gives the max or min you look at the "A" coefficient. If A is POSITIVE;parabola opens upwards; vertex gives the MIN. If A is NEGATIVE;parabola opens downwards; vertex gives the MAX.
 �t�e�s�t/710638: Consider the parabola to the right to determine each of the following: a. Explain whether the function has a maximum value or minimum value. b. Determine the minimum or maximum value and where it occurs. c. Identify the vertex. d. Identify the axis of symmetry. Its shows a graph. I'm sorry if I can't show the graph it is talking about. Hopefully you can be able to go from here.1 solutions Answer 437124 by nerdybill(6948)   on 2013-02-05 09:39:34 (Show Source): You can put this solution on YOUR website!Sorry. To answer the questions, the graph is necessary.
 test/710645: What is the value of f^-1 (3/4) if f(x)= (2x-3)/(2x+4) Show work 1 solutions Answer 437122 by nerdybill(6948)   on 2013-02-05 09:38:06 (Show Source): You can put this solution on YOUR website!What is the value of f^-1 (3/4) if f(x)= (2x-3)/(2x+4) . Begin by finding f^(-1): f(x)= (2x-3)/(2x+4) y = (2x-3)/(2x+4) flip variables and solve for y: x = (2y-3)/(2y+4) x(2y+4) = (2y-3) 2xy+4x = 2y-3 2xy = 2y-3-4x 2xy-2y = -3-4x y(2x-2) = -3-4x y = (-3-4x)/(2x-2) y = (3+4x)/(2-2x) f^(-1)(x) = (3+4x)/(2-2x) . f^-1 (3/4) = (3+4(3/4))/(2-2(3/4)) f^-1 (3/4) = (3+3)/(2-(3/2)) f^-1 (3/4) = (6)/((2/2)-(3/2)) f^-1 (3/4) = (6)/(-(1/2)) f^-1 (3/4) = -12
 �t�e�s�t/710637: A company producing steel construction bars uses the function R(x) = -0.06x^2+10.2x -50 to model the unit revenue in dollars for producing x bars. For what number of bars is the revenue at a maximum? What is the unit revenue at that level of production? Having a hard time understanding this problem.1 solutions Answer 437116 by nerdybill(6948)   on 2013-02-05 09:31:22 (Show Source): You can put this solution on YOUR website!A company producing steel construction bars uses the function R(x) = -0.06x^2+10.2x -50 to model the unit revenue in dollars for producing x bars. For what number of bars is the revenue at a maximum? Because the leading coefficient is negative, we KNOW the parabola opens downwards. This means the vertex is the MAXIMUM. the x-value of the vertex is: x = -b/(2a) x = -10.2/(2*(-0.06)) x = -10.2/(-0.12) x = 85 bars . What is the unit revenue at that level of production? find the revenue by plugging it back into the original equation: R(x) = -0.06x^2+10.2x -50 R(85) = -0.06(85)^2+10.2(85) -50 R(85) = -433.5 + 867 - 50 R(85) = \$383.50
 Linear-systems/710587: Find three consecutive integers such that twice the second subtracted from the sum of the other three integers is sixteen. 1 solutions Answer 437067 by nerdybill(6948)   on 2013-02-05 05:29:11 (Show Source): You can put this solution on YOUR website!Find three consecutive integers such that twice the second subtracted from the sum of the other three integers is sixteen. . Let x = first integer then x+1 = second x+2 = third . (x + x+1 + x+2)-2(x+1) = 16 (3x+3)-(2x+2) = 16 3x+3-2x-2 = 16 x+3-2 = 16 x+1 = 16 x = 15 . Solution: 15, 16, and 17
 Average/710581: If 3^x=10 then what is 81^x1 solutions Answer 437065 by nerdybill(6948)   on 2013-02-05 05:25:50 (Show Source): You can put this solution on YOUR website! If 3^x=10 then what is 81^x . solving for x: . So: 81^x 81^{log(10)/log(3)) 10000
 Equations/710554: Find A when P=3000, r=7%, n=12, and t=5 1 solutions Answer 437028 by nerdybill(6948)   on 2013-02-05 00:17:05 (Show Source): You can put this solution on YOUR website!Find A when P=3000, r=7%, n=12, and t=5 . A = P(1 + r/n)^(nt) A = 3000(1 + .07/12)^(12*5) A = 3000(1 + .005833333)^60 A = 3000(1.005833333)^60 A = 3000(1.41762526) A = \$4252.88
 Functions/710227: A function f(x)=-8x^2 what is f(-3)1 solutions Answer 436921 by nerdybill(6948)   on 2013-02-04 15:40:05 (Show Source): You can put this solution on YOUR website! A function f(x)=-8x^2 what is f(-3) . f(x)=-8x^2 f(-3)=-8(-3)^2 f(-3)=-8((-3)*(-3)) f(-3)=-8(9) f(-3)= -72
 Quadratic_Equations/709926: To solve by completing the square, what value should you add to each side of the equation? x^2+14x=-21 solutions Answer 436814 by nerdybill(6948)   on 2013-02-03 19:49:28 (Show Source): You can put this solution on YOUR website!the value you should add is (b/2)^2 = (14/2)^2 = 7^2 = 49 . answer: add 49 to both sides
 Travel_Word_Problems/709690: Two cyclist start 10 kilometers apart. They are traveling towards each other, cyclist A traveling at an average of 3.0m/s and cyclist B at a speed of 5.0 m/s. Where will the cyclists meet?1 solutions Answer 436742 by nerdybill(6948)   on 2013-02-03 09:35:22 (Show Source): You can put this solution on YOUR website!Two cyclist start 10 kilometers apart. They are traveling towards each other, cyclist A traveling at an average of 3.0m/s and cyclist B at a speed of 5.0 m/s. Where will the cyclists meet? . Convert kilometers to meters: 10 kilometers = 10*1000 = 10000 . Determine the time (t) when they will meet (applying the distance formula): d = rt 3t + 5t = 10000 8t = 10000 t = 1250 secs (this is "When" the cyclist will meet) . this is "Where" the cyclist will meet: 3*1250 = 3750 m or 3.75 kilometers (distance traveled by 3m/s cyclist) 5*1250 = 6250 m or 6.25 kilometers (distance traveled by 5m/s cyclist)
Quadratic_Equations/709684: the base and height of a triangle are (x+3)cm and (2x+5)cm respectively if the area of a triangle is 20 cm square , find x
1 solutions

Answer 436739 by nerdybill(6948)   on 2013-02-03 09:26:54 (Show Source):
You can put this solution on YOUR website!
the base and height of a triangle are (x+3)cm and (2x+5)cm respectively if the area of a triangle is 20 cm square , find x
.
Since area of a triangle is:
(1/2)bh = area
plugging in the given data:
(1/2)(x+3)(2x+5) = 20
multiplying both sides by 2:
(x+3)(2x+5) = 40
FOIL the left:
2x^2+5x+6x+15 = 40
2x^2+11x+15 = 40
2x^2+11x-25 = 0
applying the "quadratic equation" we get:
x = {1.73, -7.23}
.
 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=321 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.72911821679223, -7.22911821679223. Here's your graph:

 Exponential-and-logarithmic-functions/709672: how can i change this exponential to logarithmic form? (x + 1 )4 = 2561 solutions Answer 436722 by nerdybill(6948)   on 2013-02-03 04:30:30 (Show Source): You can put this solution on YOUR website!(x+1)^4 = 256 take log of both sides: log (x+1)^4 = log 256 or 4log(x+1) = log 256
 Coordinate-system/709668: Make y the subject of the formula in 2x+3y=5.1 solutions Answer 436721 by nerdybill(6948)   on 2013-02-03 04:25:28 (Show Source): You can put this solution on YOUR website!2x+3y=5 subtracting 2x from both sides: 3y = -3x+5 dividing both sides by 3: y = -x + 5/3
 Graphs/709327: can anyone help/explain?! Given f(x) = 2x^2 - x + 4 find f(1/b) leave all exponents positive1 solutions Answer 436518 by nerdybill(6948)   on 2013-02-01 18:40:16 (Show Source): You can put this solution on YOUR website!Given f(x) = 2x^2 - x + 4 find f(1/b) substitute 1/b in: f(1/b) = 2(1/b)^2 - (1/b) + 4 f(1/b) = 2(1/b^2) - (1/b) + 4 f(1/b) = 2/b^2 - (1/b) + 4 f(1/b) = 2/b^2 - b/b^2 + 4b^2/b^2 f(1/b) = (2 - b + 4)/b^2 f(1/b) = (6-b)/b^2 or f(1/b) = 6/b^2 - 1/b
 Age_Word_Problems/709318: Plz here is my question: The sum of the ages of a mother and her daughter are 44,3 years ago the product of their age was 192. How old is d daughter now?1 solutions Answer 436514 by nerdybill(6948)   on 2013-02-01 17:54:40 (Show Source): You can put this solution on YOUR website! The sum of the ages of a mother and her daughter are 44,3 years ago the product of their age was 192. How old is d daughter now? Let d = daughter's age and m = mom's age . from:"The sum of the ages of a mother and her daughter are 44" d+m = 44 so, m = 44-d . from:"3 years ago the product of their age was 192. How old is d daughter now?" (d-3)(m-3) = 192 (d-3)(44-d-3) = 192 (d-3)(-d+41) = 192 -d^2+41d+3d-123 = 192 -d^2+44d-123 = 192 -d^2+44d-315 = 0 d^2-44d+315 = 0 d^2-9d-35d+315 = 0 (d^2-9d)-(35d-315) = 0 d(d-9)-35(d-9) = 0 (d-9)(d-35) = 0 d = {9,35} The daughter is 9 years old
Polynomials-and-rational-expressions/709122: Solve 14x=x^2+36 . Thanks!
1 solutions

Answer 436406 by nerdybill(6948)   on 2013-02-01 01:23:11 (Show Source):
You can put this solution on YOUR website!
Solve
14x=x^2+36
0=x^2-14x+36
since you can't factor, you can apply the quadratic formula to get:
x = {10.61, 3.39}
.