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Quadratic_Equations/392412: Find the x intercepts of f(x) = 3x^2 -15x -13 1 solutions Answer 278514 by nerdybill(7003)   on 2011-01-09 19:22:22 (Show Source): You can put this solution on YOUR website! f(x) = 3x^2 -15x -13 set f(x) to zero and solve for x: 0 = 3x^2 -15x -13 applying the "quadratic formula" we get: x = {5.753, -0.753} . 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=381 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 5.75320354932386, -0.753203549323856. Here's your graph:

Angles/392410: the supplement of an angle measures 25 degrees more than twice it's complements. find the measure of the angle 1 solutions Answer 278513 by nerdybill(7003)   on 2011-01-09 19:19:53 (Show Source): You can put this solution on YOUR website! the supplement of an angle measures 25 degrees more than twice it's complements. find the measure of the angle . Let x = measure of the angle then 90-x = complement 180-x = supplement . 180-x = 2(90-x) + 25 180-x = 180-2x + 25 -x = -2x + 25 x = 25 degrees

Quadratic_Equations/392420: Solve for y, where y is a real number. If there is more than one solution, separate them with commas 1 solutions Answer 278509 by nerdybill(7003)   on 2011-01-09 19:15:15 (Show Source): You can put this solution on YOUR website! I think you mean: square both sides to give you: y = {-4, 5}

Quadratic_Equations/392424: Solve for x. 3x^2 - 11x = - 6 (If there is more than one solution, separate them with commas.) 1 solutions Answer 278508 by nerdybill(7003)   on 2011-01-09 19:12:48 (Show Source): You can put this solution on YOUR website! 3x^2 - 11x = - 6 3x^2 - 11x + 6 = 0 factor the left: (3x-2)(x-3) = 0 x = {2/3, 3}

Word_Problems_With_Coins/392428: A bag contains nickels and quarters. There are 6 more nickels than quarters. The total value of the coins is $4.50. How mamy of each coin are there? 1 solutions Answer 278506 by nerdybill(7003)   on 2011-01-09 19:10:44 (Show Source): You can put this solution on YOUR website! A bag contains nickels and quarters. There are 6 more nickels than quarters. The total value of the coins is $4.50. How many of each coin are there? . Let q = number of quarters then q+6 = number of nickels . .25q + .05(q+6) = 4.50 .25q + .05q+.30 = 4.50 .30q + .30 = 4.50 .30q = 4.20 q = 14 (number of quarters) . number of nickels: q+6 = 14+6 = 20

Polynomials-and-rational-expressions/392426: please help me reduce this fraction to lowest terms: 1 solutions Answer 278504 by nerdybill(7003)   on 2011-01-09 19:08:02 (Show Source): You can put this solution on YOUR website! Notice, I can factor the numerator: And, I can factor the denominator: Now, I can cancel the x^2:

Radicals/391877: Simplify Be sure to write your answer in lowest terms 1 solutions Answer 278099 by nerdybill(7003)   on 2011-01-08 03:37:34 (Show Source): You can put this solution on YOUR website!

Radicals/391882: Rewrite the following in simplified radical form Assume that all variables represent positive real numbers. 1 solutions Answer 278098 by nerdybill(7003)   on 2011-01-08 03:33:36 (Show Source): You can put this solution on YOUR website!

Miscellaneous_Word_Problems/391797: Barak bought an 18oz box of cookies for $2.50. What is the unit price in cents per ounce? Round to the nearest tenth of a cent. 1 solutions Answer 277965 by nerdybill(7003)   on 2011-01-07 16:11:19 (Show Source): You can put this solution on YOUR website! 2.50/18 = 0.139 or 13.9 cents

Travel_Word_Problems/391732: A bicyclist travels at a rate of 13 miles an hour. If the bicyclist continues at this rate, how many miles can the bicyclist travel in 0.5 hour? 1 solutions Answer 277924 by nerdybill(7003)   on 2011-01-07 11:20:42 (Show Source): You can put this solution on YOUR website! A bicyclist travels at a rate of 13 miles an hour. If the bicyclist continues at this rate, how many miles can the bicyclist travel in 0.5 hour? . Apply the "distance formula": d=rt where d is distance r is rate or speed t is time . d = 13*0.5 d = 6.5 miles

Miscellaneous_Word_Problems/391714: If a line falls on the points (15, 15) and (6, 11), what is its slope? Enter your answer as a fraction in lowest terms. Use a slash mark ( / ) as the fraction bar. 1 solutions Answer 277894 by nerdybill(7003)   on 2011-01-07 09:02:29 (Show Source): You can put this solution on YOUR website! Given two points: (15, 15) and (6, 11) . slope = (y2 - y1)/(x2- x1) slope = (11 - 15)/(6 - 15) slope = (-4)/(-9) slope = 4/9

Angles/391187: Angle A and angle b are complementary angles. If the measurement of angle A= 9x-14 and the measurement of angle B= 8x+2, then what is the measurement of each angle? 1 solutions Answer 277652 by nerdybill(7003)   on 2011-01-06 09:39:58 (Show Source): You can put this solution on YOUR website! Angle A and angle b are complementary angles. If the measurement of angle A= 9x-14 and the measurement of angle B= 8x+2, then what is the measurement of each angle? . Because they are "complementary": A + B = 90 . (9x-14) + (8x+2) = 90 17x-12 = 90 17x = 102 x = 6 . A = 9x-14 = 9(6)-14 = 54-14 = 40 degrees B = 8x+2 = 8(6)+2 = 48+2 = 50 degrees

Miscellaneous_Word_Problems/391310: the math club goes to an amusement park.student tickets cost $15 each.Non-tudent tickets cost $25 each.The club paid $315 for the tickets. write in standard form an equation that relates the number of student tickets x with the number of non-student tickets y. 1 solutions Answer 277650 by nerdybill(7003)   on 2011-01-06 09:35:43 (Show Source): You can put this solution on YOUR website! the math club goes to an amusement park.student tickets cost $15 each.Non-tudent tickets cost $25 each.The club paid $315 for the tickets. write in standard form an equation that relates the number of student tickets x with the number of non-student tickets y. . 15x + 25y = 315

Polynomials-and-rational-expressions/391247: factor completely b^3-3b^2-10b 1 solutions Answer 277564 by nerdybill(7003)   on 2011-01-05 22:52:20 (Show Source): You can put this solution on YOUR website! b^3-3b^2-10b first, pull out the common factor of b: b(b^2-3b-10) then, factor the expression inside the parenthesis: b(b-5)(b+2)

Exponential-and-logarithmic-functions/391277: solve log(x+2)+log x= 3 log 2 as algebraically and solve for any extraneous solutions. 1 solutions Answer 277563 by nerdybill(7003)   on 2011-01-05 22:49:17 (Show Source): You can put this solution on YOUR website! x = {-4, 2} Checking for extraneous solutions, we have to throw out the negative solution leaving: x = 2

Exponential-and-logarithmic-functions/391267: Use the exponential growth function P(t) = P0^e^kt where P0 is the initial population and P(t) is the population at time t, to determine the growth factor K of caribou in Canada that grew from 4700 in 1954 to about 472,000 in 1984 1 solutions Answer 277562 by nerdybill(7003)   on 2011-01-05 22:40:15 (Show Source): You can put this solution on YOUR website! Use the exponential growth function P(t) = P0^e^kt where P0 is the initial population and P(t) is the population at time t, to determine the growth factor K of caribou in Canada that grew from 4700 in 1954 to about 472,000 in 1984 . Given: P(t) = P0^e^kt Po is 4700 P(t) is 472000 t = 1984-1954=30 . 47200 = 4700e^(30k) 47200/4700 = e^(30k) ln(47200/4700) = 30k ln(47200/4700)/30 = k ln(472/47)/30 = k 0.07689 = k

Linear_Equations_And_Systems_Word_Problems/391107: A roof rises 2.7 feet vertically and 8.1 feet horizontally. What is the grade of the roof? 1 solutions Answer 277400 by nerdybill(7003)   on 2011-01-05 17:51:32 (Show Source): You can put this solution on YOUR website! A roof rises 2.7 feet vertically and 8.1 feet horizontally. What is the grade of the roof? . "Grade" is the slope, which is rise/run: 2.7/8.1 = 27/81 = 1/3

Graphs/391109: how to solve for y 3x+y>o 1 solutions Answer 277398 by nerdybill(7003)   on 2011-01-05 17:50:27 (Show Source): You can put this solution on YOUR website! start with: 3x+y>0 subtract 3x from both sides: 3x+y-3x > 0-3x y > -3x

Expressions-with-variables/391101: Stephanie had a pile of dimes and quarters that had a value of $6.75. If there were twice as many dimes as quarters, how y quarters did Stephanie have? 1 solutions Answer 277393 by nerdybill(7003)   on 2011-01-05 17:43:59 (Show Source): You can put this solution on YOUR website! Stephanie had a pile of dimes and quarters that had a value of $6.75. If there were twice as many dimes as quarters, how y quarters did Stephanie have? . Let q = number of quarters then 2q = number of dimes . .25q + .10(2q) = 6.75 25q + 10(2q) = 675 25q + 20q = 675 45q = 675 q = 15 (number of quarters)

Equations/390421: d=1/2atē rearrange the formula to isolate for a. ^ thats squared like : d equals one half at squared ^ that one half 1 solutions Answer 276825 by nerdybill(7003)   on 2011-01-03 20:24:10 (Show Source): You can put this solution on YOUR website! multiplying both sides by 2: divide both sides by t^2

Equations/390438: Find the zeros of the equation. x^2-2x-15=y. I can't find anything in my book about finding zeros. 1 solutions Answer 276821 by nerdybill(7003)   on 2011-01-03 20:17:53 (Show Source): You can put this solution on YOUR website! When they talk about finding "zeros", they are generally referring to x-intercepts. So, set y to zero and solve for x: x^2-2x-15=y x^2-2x-15=0 (x-5)(x+3) = 0 x = {-3, 5} . So, your zeros are at: (-3,0) and (5,0)

Quadratic_Equations/390276: Solve. 1 solutions Answer 276728 by nerdybill(7003)   on 2011-01-03 16:43:52 (Show Source): You can put this solution on YOUR website! . Let x = now, we can rewrite our equation as: . applying the quadratic formula, we get: x = {18.1104, -0.1104} . since w^2 = x w = x = {4.256} . 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=332 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 18.1104335791443, -0.110433579144299. Here's your graph:

Linear-equations/390274: Write the slope-intercept form of the equation parallel to y = 7x + 2, which passes through the point (1, -3). 1 solutions Answer 276727 by nerdybill(7003)   on 2011-01-03 16:39:05 (Show Source): You can put this solution on YOUR website! Write the slope-intercept form of the equation parallel to y = 7x + 2, which passes through the point (1, -3). . Since our new line is parallel to: y = 7x + 2 it must have the same slope (7). Plug the slope (7) along with the given point (1,-3) into the "point-slope" form: y-y1 = m(x-x1) y-(-3) = 7(x-1) y+3 = 7x-7 y = 7x - 10 (this is what they're looking for)

Quadratic-relations-and-conic-sections/390072: A ball is tossed into the air at an initial velocity of 38.4ft/sec from .96 feet off of the ground. At what point does the ball hit the ground? I figured out that the equation is y=-16t^2+38.4t+.96 I also figured out that the maximum height of the ball is 24 feet and it reaches it's maximum in 1.2 seconds. 1 solutions Answer 276525 by nerdybill(7003)   on 2011-01-02 19:15:19 (Show Source): You can put this solution on YOUR website! y=-16t^2+38.4t+.96 set y to 0 and solve for t: 0=-16t^2+38.4t+.96 applying the quadratic equation: t = {-0.02, 2.42} throw out the negative solution, leaving: t = 2.42 seconds . 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=1536 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.024744871391589, 2.42474487139159. Here's your graph:

Polynomials-and-rational-expressions/390035: need to factor 64x2-y2. not sure where to start 1 solutions Answer 276503 by nerdybill(7003)   on 2011-01-02 18:50:56 (Show Source): You can put this solution on YOUR website! If I rewrite it as: we now have a "difference of squares", which is a special case:

Linear-systems/389513: Find the intercepts and then use them to graph the equation. (I always have a hard time figuring out how to find the intercepts.) y= -2-2x Thank you 1 solutions Answer 276012 by nerdybill(7003)   on 2010-12-30 20:11:25 (Show Source): You can put this solution on YOUR website! Given: y= -2-2x . To find the x-intercepts, set y equal to zero and solve for x: 0= -2-2x 2 = -2x -1 = x so, x-intercept is at (-1,0) . To find the y-intercepts, set x equal to zero and solve for y: y= -2-2(0 y= -2 so, y-intercept is at (0, -2) . To plot the line, Plot each of the two points above and then simply draw a solid line through both points -- simple...

Human-and-algebraic-language/389325: The cost to purchase a song from iTunes is $0.99 per song. To purchase a song from Napster, you must be a member. The Napster membership fee is $10. In addition, each purchased song costs $0.89. How many songs must be purchased so that the costs are the same? 1 solutions Answer 275867 by nerdybill(7003)   on 2010-12-29 21:19:33 (Show Source): You can put this solution on YOUR website! The cost to purchase a song from iTunes is $0.99 per song. To purchase a song from Napster, you must be a member. The Napster membership fee is $10. In addition, each purchased song costs $0.89. How many songs must be purchased so that the costs are the same? . Let n = number of songs purchased then 10+.89n = .99n 10 = .10n 10/.10 = n 100 songs = n

Human-and-algebraic-language/389335: Homer Simpson weighs 400 pounds. He is on a diet to lose 5 pounds each week. Barney Gumble weighs 322 pounds. He is on a diet to lose 3 pounds each week. How long will it take for them to weigh the same? 1 solutions Answer 275865 by nerdybill(7003)   on 2010-12-29 21:15:14 (Show Source): You can put this solution on YOUR website! Homer Simpson weighs 400 pounds. He is on a diet to lose 5 pounds each week. Barney Gumble weighs 322 pounds. He is on a diet to lose 3 pounds each week. How long will it take for them to weigh the same? . Let w = weeks of dieting then 400-5w = 322-3w 400 = 322+2w 78 = 2w 39 weeks = w

Geometry_Word_Problems/389141: An object is launched with initial velocity of 22.5 meters per second (m/s) from a 75-meter tall platform. The equation for the object's height h at time t seconds after launched is h(t)=-4.9t^2+22.5t+75, where h is in meters. How long will it take for the object to reach the ground? what is the maximum height reached by the object? 1 solutions Answer 275686 by nerdybill(7003)   on 2010-12-28 19:19:07 (Show Source): You can put this solution on YOUR website! An object is launched with initial velocity of 22.5 meters per second (m/s) from a 75-meter tall platform. The equation for the object's height h at time t seconds after launched is h(t)=-4.9t^2+22.5t+75, where h is in meters. How long will it take for the object to reach the ground? set h(t) to zero and solve for t: 0=-4.9t^2+22.5t+75 applying the quadratic formula, we get: t = {-2.24, 6.83} toss out the negative answer leaves: t = 6.83 seconds . what is the maximum height reached by the object? . The vertex is the max height. It reaches this at: t = -b/(2a) t = -22.5/(2*(-4.9)) t = -22.5/(-9.8) t = 2.30 seconds . h(2.30) = -4.9(2.30)^2+22.5(2.30)+75 = 100.83 meters (max height)

Quadratic_Equations/389143: write an equation in standard form with roots -4,10 1 solutions Answer 275681 by nerdybill(7003)   on 2010-12-28 19:12:33 (Show Source): You can put this solution on YOUR website! For a quadratic to have -4,10 as roots then it must have the following factors: (x+4)(x-10) FOIL the above: x^2 -10x + 4x - 40 x^2 -6x - 40 . putting it in standard form: x^2 -6x - 40=0 (x^2 -6x +9) = 40 + 9 (x-3)^2 = 49 f(x) = (x-3)^2 -49

Travel_Word_Problems/389040: Two cars leave Pima Community College traveling in opposite directions. One car travels at 80mph and the other at 54mph. How many hours will they be 938 miles apart? 1 solutions Answer 275526 by nerdybill(7003)   on 2010-12-28 09:26:59 (Show Source): You can put this solution on YOUR website! Two cars leave Pima Community College traveling in opposite directions. One car travels at 80mph and the other at 54mph. How many hours will they be 938 miles apart? . Let x = time (hours) driving then applying the distance formula of d=rt 80x + 54x = 938 134x = 938 x = 938/134 x = 7 hours