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# Recent problems solved by 'nerdybill'

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 Quadratic-relations-and-conic-sections/495972: I know that the following equation will result in a circle graph (the teacher's key says so). But I would like to know how to get there. I need to isolate y: x^2 + y^2 - 4y = 21 (that is, x squared plus y squared minus 4y equals 21) Thank you 1 solutions Answer 336276 by nerdybill(6959)   on 2011-09-12 08:46:25 (Show Source): You can put this solution on YOUR website!general form of a circle: (x - h)^2 + (y - k)^2 = r^2 . your equation: x^2 + y^2 - 4y = 21 subtracting x^2 from both sides: y^2 - 4y = -x^2 + 21 "complete the square" by adding 2 to both sides: y^2 - 4y + 2 = -x^2 + 21 + 2 (y-2)(y-2) = -x^2 + 23 (y-2)^2 = -x^2 + 23 add x^2 to both sides: x^2 + (y-2)^2 = 23 (equation of the circle) . Or, you can think of it as: (x-0)^2 + (y-2)^2 = 23 Now, we can see the center is at (0,2) with a radius of square root of 23
Length-and-distance/495943: A square has a perimeter of 100 cm and its area is 9x^2 + 12x + 4 cm^2. What is x?
1 solutions

Answer 336275 by nerdybill(6959)   on 2011-09-12 08:27:38 (Show Source):
You can put this solution on YOUR website!
A square has a perimeter of 100 cm and its area is 9x^2 + 12x + 4 cm^2. What is x?
Since the perimeter is 100 cm
each side is 100/4 = 24 cm
.
area = 24^2
.
24^2 = 9x^2 + 12x + 4
576 = 9x^2 + 12x + 4
0 = 9x^2 + 12x - 572
x = {7.33, -8.67}
we can toss out the negative solution leaving:
x = 7.33
.
 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=20736 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 7.33333333333333, -8.66666666666667. Here's your graph:

 Angles/495969: A= 4x+20; B=3x If A is the supplement of the complement of B, solve for x.1 solutions Answer 336273 by nerdybill(6959)   on 2011-09-12 08:18:08 (Show Source): You can put this solution on YOUR website!A= 4x+20; B=3x If A is the supplement of the complement of B, solve for x. . "complement of B" = 90-3x "supplement of the complement of B" = 180-(90-3x) = 90+3x . 4x+20 = 90+3x 4x = 70+3x x = 70 degrees
 Mixture_Word_Problems/495967: A solution of 49% vinegar is to be mixed with a solution of 32% vinegar to form 153 liters of a 40% solution. How many liters of 49% solution must be used?1 solutions Answer 336272 by nerdybill(6959)   on 2011-09-12 08:14:41 (Show Source): You can put this solution on YOUR website!A solution of 49% vinegar is to be mixed with a solution of 32% vinegar to form 153 liters of a 40% solution. How many liters of 49% solution must be used? . Let x = amount (liters) of 49% solution then 153-x = amount (liters) of 32% solution . .49x + .32(153-x) = .40(153) .49x + 48.96-.32x = 61.2 .17x + 48.96 = 61.2 .17x = 12.24 x = 72 liters
 Age_Word_Problems/495274: A lady is 24 years older then her daughter. What will be the daughter's age when it is one-third of her mother's ? 1 solutions Answer 336047 by nerdybill(6959)   on 2011-09-11 10:20:33 (Show Source): You can put this solution on YOUR website!A lady is 24 years older then her daughter. What will be the daughter's age when it is one-third of her mother's ? . Let d = daughter's age then d+24 = mother's age . d = (1/3)(d+24) 3d = d + 24 2d = 24 d = 12 years old
 Linear-equations/494843: Find the x- and y- intercepts and graph the equation plotting the intercepts. Show all work please 3x- 6y = -211 solutions Answer 335811 by nerdybill(6959)   on 2011-09-10 08:45:54 (Show Source): You can put this solution on YOUR website!To find the y-intercept, set x = 0 and solve for y: 3x- 6y = -21 3(0)- 6y = -21 -6y = -21 y = (-21)/(-6) y = 7/2 so, y-intercept is at (0, 7/2) . To find the x-intercept, set y = 0 and solve for x: 3x- 6y = -21 3x- 6(0) = -21 3x- 0 = -21 3x = -21 x = (-21)/3 x = -7 so, x-intercept is at (-7, 0) . To graph, plot both points and draw a line through both points.
 Inverses/494830: What is the inverse of multiplying by 21 solutions Answer 335809 by nerdybill(6959)   on 2011-09-10 08:33:59 (Show Source): You can put this solution on YOUR website!It would be to divide by 2
 Linear-equations/494841: A resturant leases 15,000 square feet of space. The pie chart gives the break down of space used being: For restrooms 3%; Storage 8.6% ; kitchen 16.4% ; dinning area 52.8% ; bar 19.2%. How much leased space is taken up by storage?1 solutions Answer 335808 by nerdybill(6959)   on 2011-09-10 08:30:21 (Show Source): You can put this solution on YOUR website!Storage 8.6% .086 * 15000 = 1290 square feet
 percentage/494564: what percent of 110 is 99 ?1 solutions Answer 335696 by nerdybill(6959)   on 2011-09-09 15:24:28 (Show Source): You can put this solution on YOUR website!99/110 * 100 = .90 * 100 = 90%
 Graphs/494524: What is the y-intercept of the line? Enter your answer as an ordered pair. y = 2x + 10 1 solutions Answer 335678 by nerdybill(6959)   on 2011-09-09 13:23:39 (Show Source): You can put this solution on YOUR website!since y = 2x + 10 is already in slope-intercept form: y = ms + b where b is y-intercept at (0, b) . answer:(0,10)
 Travel_Word_Problems/494520: If I were traveling 59 miles at a rate of 83 MPH how long would it take? 1 solutions Answer 335677 by nerdybill(6959)   on 2011-09-09 13:18:42 (Show Source): You can put this solution on YOUR website!distance formula d = rt 59 = 83t 59/83 = t 0.71 hr = t or 42.7 minutes = t
 Surface-area/494508: In factored form 2c-4=1 solutions Answer 335676 by nerdybill(6959)   on 2011-09-09 13:13:45 (Show Source): You can put this solution on YOUR website!2c - 4 = 2(c - 2)
 Geometry_Word_Problems/493776: the hypotenuse of a right triangle is 13m long. if each leg were increased by 3m the hypotenuse would be increased by 4m. translate into equation.1 solutions Answer 335454 by nerdybill(6959)   on 2011-09-08 14:51:14 (Show Source): You can put this solution on YOUR website!the hypotenuse of a right triangle is 13m long. if each leg were increased by 3m the hypotenuse would be increased by 4m. translate into equation. . Let x = one leg and y = second leg . since we have two unknowns, we'll need two equations. . x^2 + y^2 = 13^2 (x+3)^2 + (y+3)^2 = (13+4)^2
 Numbers_Word_Problems/493787: If 3 times a certain number increased by 4 is equal to 28, what is the number1 solutions Answer 335452 by nerdybill(6959)   on 2011-09-08 14:48:50 (Show Source): You can put this solution on YOUR website!If 3 times a certain number increased by 4 is equal to 28, what is the number . Let n = the number then 3n + 4 = 28 3n = 24 n = 8 (solution)
 Graphs/493781: what is the slope of the line y=8x+1? 1 solutions Answer 335451 by nerdybill(6959)   on 2011-09-08 14:47:38 (Show Source): You can put this solution on YOUR website!"Slope-intercept" form of a line: y = mx + b where m is the slope b is the y-intercept at (0,b) . Since: y=8x+1 is already in "slope-intercept" form From inspection, we see that the slope is 8
 Travel_Word_Problems/493783: A truck enters a highway driving 60 mph. A car enters the highway at the same place 9 minutes later and drives 69 mph in the same direction. From the time the car enters the highway, how long will it take the car to pass the truck? 1 solutions Answer 335450 by nerdybill(6959)   on 2011-09-08 14:45:09 (Show Source): You can put this solution on YOUR website!A truck enters a highway driving 60 mph. A car enters the highway at the same place 9 minutes later and drives 69 mph in the same direction. From the time the car enters the highway, how long will it take the car to pass the truck? . Apply the distance formula of d=rt . Since speed is given in terms of "hours" we must convert 9 minutes to hours: 9 minutes = 9/60 hours = 3/20 hours . Let x = time (hours) it takes car to pass the truck then 60(x + 3/20) = 69x multiplying both sides by 20: 60(20x + 3) = 1380x 1200x + 180 = 1380x 180 = 180x 1 hour = x
 Travel_Word_Problems/493741: If a stone is tossed from the top of a 250 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 250, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer.1 solutions Answer 335444 by nerdybill(6959)   on 2011-09-08 14:08:08 (Show Source): You can put this solution on YOUR website!h(t) = -9.8t2 – 10t + 250 set h(t) to zero (ground level) and solve for t: 0 = -9.8t2 – 10t + 250 0 = 9.8t2 + 10t - 250 0 = 4.9t2 + 5t - 125 applying the "quadratic formula" we get: t = {-5.59, 4.57} we can throw away the negative solution leaving: t = 4.57 seconds
 Quadratic_Equations/493725: Really need some help please. Given the quadratic function f(x) = x2 – 18x + 81, find a value of x such that f(x) = 16.1 solutions Answer 335433 by nerdybill(6959)   on 2011-09-08 12:44:32 (Show Source): You can put this solution on YOUR website!Given the quadratic function f(x) = x2 – 18x + 81, find a value of x such that f(x) = 16 . substitute in the value of f(x): f(x) = x^2 – 18x + 81 16 = x^2 – 18x + 81 0 = x^2 – 18x + 65 factoring: 0 = (x-5)(x-13) x = {5, 13} (two possible solutions)
 logarithm/493072: Alright, the question is log base 3 2x+log base 3 7= log base 3 28. I know that the answer is 2, but i have no clue how to get to it. I tried canceling out the log base 3 part since they are all the same, and then it came out to 2x+7=28 and solved that, but then x would equal 10.5z please help!1 solutions Answer 335274 by nerdybill(6959)   on 2011-09-07 16:53:35 (Show Source): You can put this solution on YOUR website!apply "log rules":
 Average/492945: A math quiz is worth 100 points.There are 13 problems on the quiz.Some of the problems are worth 5 points, and the rest are worth 12 points.How many of each kind of problem are on the quiz? 1 solutions Answer 335222 by nerdybill(6959)   on 2011-09-07 14:30:19 (Show Source): You can put this solution on YOUR website!A math quiz is worth 100 points.There are 13 problems on the quiz.Some of the problems are worth 5 points, and the rest are worth 12 points.How many of each kind of problem are on the quiz? . Let x = number of problems worth 12 points then 13-x = number of problems worth 5 points . 12x + 5(13-x) = 100 12x + 65-5x = 100 7x + 65 = 100 7x = 35 x = 5 (number of problems worth 12 points) . number of problems worth 5 points: 13-x = 13-5 = 8
 Signed-numbers/492947: square root of 1321 solutions Answer 335221 by nerdybill(6959)   on 2011-09-07 14:27:18 (Show Source): You can put this solution on YOUR website! factor using prime numbers: pull out "pairs"
 Percentage-and-ratio-word-problems/492942: how to solve: the profit for a company in february was 5% higher than it was in january. the total profit for the two months was \$129,000. Find the profit for each month.1 solutions Answer 335220 by nerdybill(6959)   on 2011-09-07 14:21:46 (Show Source): You can put this solution on YOUR website!how to solve: the profit for a company in february was 5% higher than it was in january. the total profit for the two months was \$129,000. Find the profit for each month. . Let x = profit in Jan then 1.05x = profit in Feb . x + 1.05x = 129000 2.05x = 129000 x = \$62926.83 (profit in Jan) . profit in Feb: 1.05x = 1.05(62926.83) = 66073.17
 Travel_Word_Problems/492923: Two planes, which are 4425 miles apart, fly toward each other. their speeds differ by 35 mph. If they pass each other in 5 hours, what is the speed of each?1 solutions Answer 335219 by nerdybill(6959)   on 2011-09-07 14:18:56 (Show Source): You can put this solution on YOUR website!Two planes, which are 4425 miles apart, fly toward each other. their speeds differ by 35 mph. If they pass each other in 5 hours, what is the speed of each? . Let x = speed of slower plane then x+35 = speed of faster plane . applying the distance formula: 5x + 5(x+35) = 4425 5x + 5x+175 = 4425 10x+175 = 4425 10x = 4250 x = 425 mph (slower plane) . faster plane: x+35 = 425+35 = 460 mph
 Rectangles/492937: the area of a square is 64cm2. what is the length of one side of the square? 1 solutions Answer 335218 by nerdybill(6959)   on 2011-09-07 14:14:52 (Show Source): You can put this solution on YOUR website!the area of a square is 64cm2. what is the length of one side of the square? Let x = length of one side of square then x*x = 64 x^2 = 64 x = sqrt(64) x = 8 cm
 Angles/492843: Angles A and B are complementary angles. Determine the measures of angles A and B if angle A is four times the size of angle B.1 solutions Answer 335197 by nerdybill(6959)   on 2011-09-07 11:47:26 (Show Source): You can put this solution on YOUR website!Angles A and B are complementary angles. Determine the measures of angles A and B if angle A is four times the size of angle B. . Let x = measure of angle B then 4x = measure of angle A . x + 4x = 90 5x = 90 x = 90/5 x = 18 degrees (angle B) . Angle A: 4x = 4(18) = 72 degrees
 Angles/492299: if the measure of an angle is represented by 4x, the measure of its supplement is represented by what1 solutions Answer 334998 by nerdybill(6959)   on 2011-09-06 17:34:37 (Show Source): You can put this solution on YOUR website!Two angles are supplementary if the sum is 180 degrees... therefore: 180 - 4x
 Square-cubic-other-roots/492145: 8). Use Radical notation to rewrite the expression, then simplify if possible.. 36to the 1/2 power1 solutions Answer 334943 by nerdybill(6959)   on 2011-09-06 15:14:13 (Show Source): You can put this solution on YOUR website!36to the 1/2 power
 Finance/492085: solve by factoring 4x^2 - 8x + 4 = 0 1 solutions Answer 334935 by nerdybill(6959)   on 2011-09-06 14:14:01 (Show Source): You can put this solution on YOUR website!4x^2 - 8x + 4 = 0 4(x^2 - 2x + 1) = 0 x^2 - 2x + 1 = 0 (x-1)(x-1) = 0 (x-1)^2 = 0 x = 1
 Polynomials-and-rational-expressions/492056: How do I completely factor the following expression 81y^2 - 4z^2 1 solutions Answer 334908 by nerdybill(6959)   on 2011-09-06 12:06:37 (Show Source): You can put this solution on YOUR website!Since: 81y^2 - 4z^2 can be rewritten as: (9y)^2 - (2z)^2 This is a "difference of squares" (special case): (9y - 2z)(9y + 2z)
 percentage/492028: The selling price of a calculator is \$115. If the mark-up is 25% of the dealer's cost, what is the dealer's cost?1 solutions Answer 334895 by nerdybill(6959)   on 2011-09-06 10:38:17 (Show Source): You can put this solution on YOUR website!The selling price of a calculator is \$115. If the mark-up is 25% of the dealer's cost, what is the dealer's cost? Let d = dealer's cost then d + .25d = 115 d(1+.15) = 115 d(1.15) = 115 d = \$100
 test/492005: How do I solve for x in this equation? x + 12/x = 71 solutions Answer 334884 by nerdybill(6959)   on 2011-09-06 09:39:54 (Show Source): You can put this solution on YOUR website!x + 12/x = 7 multiply both sides by x: x^2 + 12 = 7x x^2 - 7x + 12 = 0 factoring left: (x-3)(x-4) = 0 x = {3,4}