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nerdybill answered: 6957 problems
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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 apply quadratic formula to get: x = {7.33, -8.67} we can toss out the negative solution leaving: x = 7.33 . 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=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 = -21 1 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 2 1 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 number 1 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 132 1 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 what 1 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 power 1 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 = 7 1 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}