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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. Tks 1 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 12 1 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 square 1 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 years 1 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 value 1 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^x 1 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=-2 1 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} . details of quadratic follows: 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 = 256 1 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 positive 1 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} . details of quadratic formula follows: 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=52 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 10.605551275464, 3.39444872453601. Here's your graph:

logarithm/709144: what is 2^-3=.125 in log form 1 solutions Answer 436404 by nerdybill(6948)   on 2013-02-01 01:18:52 (Show Source): You can put this solution on YOUR website! -3 = (that is, log base 2 of .125)

logarithm/709145: what is 10^-3=.001 in log form 1 solutions Answer 436402 by nerdybill(6948)   on 2013-02-01 01:16:44 (Show Source): You can put this solution on YOUR website! what is 10^-3=.001 in log form . -3 = log(.001)

Equations/709161: how would i solve for m the equation 2m^3=54, i am guessing it should start off with 2m^3-54=0 then, 2(m^3)=2(-27)=0, but then i get totaly lost and confused any help please 1 solutions Answer 436401 by nerdybill(6948)   on 2013-02-01 01:15:15 (Show Source): You can put this solution on YOUR website! 2m^3=54 divide both sides by 2: m^3=27 take the "cube root" of both sides: m = cubeRt(27) factor to prime numbers: m = cubeRt(3*3*3) m = 3

�t�e�s�t/709093: vertex form, identify vertex. g(x)=X^2-12x+39 1 solutions Answer 436388 by nerdybill(6948)   on 2013-01-31 22:05:56 (Show Source): You can put this solution on YOUR website! We solve this by "completing the square": g(x)=x^2-12x+39 g(x)=(x^2-12x)+39 g(x)=(x^2-12x+36)+39-36 g(x)=(x-6)^2+3 (vertex form) Vertex: (6,3)

logarithm/708952: logb6=1/3 1 solutions Answer 436334 by nerdybill(6948)   on 2013-01-31 17:51:40 (Show Source): You can put this solution on YOUR website! logb6=1/3 6=b^(1/3) (6)^3=(b^(1/3))^3 (6)^3= b^(3/3) (6)^3= b^1 (6)^3= b 216 = b

logarithm/708949: logb1/2=-1 1 solutions Answer 436324 by nerdybill(6948)   on 2013-01-31 17:32:56 (Show Source): You can put this solution on YOUR website! logb1/2=-1 1/2= b^(-1) 1/2= 1/b^(1) 1/2= 1/b cross-multiply to get: b = 2