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# Recent problems solved by 'nerdybill'

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 Length-and-distance/393646: A ship leave port and steams 100km due North. It then turns and steams 120km due East. How far is it from port now?1 solutions Answer 279372 by nerdybill(6950)   on 2011-01-12 10:21:03 (Show Source): You can put this solution on YOUR website!A ship leave port and steams 100km due North. It then turns and steams 120km due East. How far is it from port now? . Since it forms a "right triangle" we can apply Pythagorean theorem: Let d = distance then d^2 = 100^2 + 120^2 d^2 = 10000 + 14400 d^2 = 24400 d = 156.20 km
 Pythagorean-theorem/393676: how far up the wall is a 13ft ladder if the base of the ladder is 8ft away from the wall?1 solutions Answer 279371 by nerdybill(6950)   on 2011-01-12 10:18:14 (Show Source): You can put this solution on YOUR website!how far up the wall is a 13ft ladder if the base of the ladder is 8ft away from the wall? . Applying Pythagorean theorem: Let h= height up wall then h^2 + 8^2 = 13^2 h^2 + 64 = 169 h^2 = 105 h = 10.25 feet
 Linear-systems/392664: carlos and maria drove a total of 280 miles in 5.5 hours. carlos drove the forst part of the trip and averaged 49 miles per hour. maria drove the remainder of the trip and avereged 54 miles per hour. for approximately how many hours did maria drive? round your answer to the nearset tenth if necessary.1 solutions Answer 278705 by nerdybill(6950)   on 2011-01-10 10:47:13 (Show Source): You can put this solution on YOUR website!carlos and maria drove a total of 280 miles in 5.5 hours. carlos drove the forst part of the trip and averaged 49 miles per hour. maria drove the remainder of the trip and avereged 54 miles per hour. for approximately how many hours did maria drive? round your answer to the nearset tenth if necessary. . Apply the "distance formula" of d=rt . Let h = number of hours Maria drove then 5.5-h = number of hours Carlos drove . 49(5.5-h) + 54h = 280 269.5-49h + 54h = 280 269.5 + 5h = 280 5h = 10.5 h = 2.1 hours
 Travel_Word_Problems/392660: How long would it take a train traveling 45 miles per hour to get 15 miles?1 solutions Answer 278704 by nerdybill(6950)   on 2011-01-10 10:43:10 (Show Source): You can put this solution on YOUR website!How long would it take a train traveling 45 miles per hour to get 15 miles? 1/45 * 15 = 15/45 = 1/3 hour or 20 minutes
 Linear-systems/392668: a ine passes through (3,4)and(4,7) write an equation for the line in point slope form rewrite the equation in standard form using integers1 solutions Answer 278701 by nerdybill(6950)   on 2011-01-10 10:41:54 (Show Source): You can put this solution on YOUR website!First, determine slope of: (3,4)and(4,7) m = (y2-y1)/(x2-x1) m = (7-4)/(4-3) m = (3)/(1) m = 1 . Using the slope above and one of the two points (3,4) and plug it into the "point-slope" form: y - y1 = m(x - x1) y - 4 = 1(x - 3) y - 4 = x - 3 y = x + 1 (equation of line in "slope-intercept" form) . standard form: y = x + 1 -x + y = 1 x - y = 1
 Equations/392621: x²+71=-81x-91 solutions Answer 278693 by nerdybill(6950)   on 2011-01-10 09:27:22 (Show Source): You can put this solution on YOUR website! factoring: x = {-80, -1}
 Evaluation_Word_Problems/392645: An old stamp machine at the post office is very cantankerous and will only take nickels and quarters. If there are 45 coins totaling \$10.25 when it is emptied st noon, how many nickels are there?1 solutions Answer 278692 by nerdybill(6950)   on 2011-01-10 09:25:13 (Show Source): You can put this solution on YOUR website!An old stamp machine at the post office is very cantankerous and will only take nickels and quarters. If there are 45 coins totaling \$10.25 when it is emptied st noon, how many nickels are there? . Let n = number of nickels then 45-n = number of quarters . .05n + .25(45-n) = 10.25 .05n + 11.25 - .25n = 10.25 11.25 - .20n = 10.25 -.20n = -1 n = (-1)/(-.20) n = 5 (number of nickels)
Quadratic_Equations/392412: Find the x intercepts of
f(x) = 3x^2 -15x -13
1 solutions

Answer 278514 by nerdybill(6950)   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}
.
 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 angle1 solutions Answer 278513 by nerdybill(6950)   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 commas1 solutions Answer 278509 by nerdybill(6950)   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(6950)   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(6950)   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(6950)   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/391882: Rewrite the following in simplified radical form Assume that all variables represent positive real numbers.1 solutions Answer 278098 by nerdybill(6950)   on 2011-01-08 03:33:36 (Show Source):
 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(6950)   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(6950)   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(6950)   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(6950)   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(6950)   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^2-10b1 solutions Answer 277564 by nerdybill(6950)   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(6950)   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 19841 solutions Answer 277562 by nerdybill(6950)   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(6950)   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>o1 solutions Answer 277398 by nerdybill(6950)   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(6950)   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=1/2at² rearrange the formula to isolate for a. ^ thats squared like : d equals one half at squared ^ that one half1 solutions Answer 276825 by nerdybill(6950)   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(6950)   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)

1 solutions

Answer 276728 by nerdybill(6950)   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}
.
 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(6950)   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(6950)   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