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Pythagorean-theorem/612626: one leg of a right triangle measures three inches less than the other leg. find the length of both legs if the hypotenuse is 4 inches long 1 solutions Answer 385632 by nerdybill(6948)   on 2012-05-19 09:46:57 (Show Source): You can put this solution on YOUR website! one leg of a right triangle measures three inches less than the other leg. find the length of both legs if the hypotenuse is 4 inches long . Let x = longer leg then x-3 = shorter leg . applying Pythagorean theorem: x^2 + (x-3)^2 = 4^2 x^2 + (x-3)(x-3) = 16 x^2 + x^2-6x+9 = 16 2x^2-6x+9 = 16 2x^2-6x-7 = 0 applying the "quadratic formula" yields: x = {3.9, -0.9} throw out the negative solution (extraneous) leaving x = 3.9 inches (longer leg) . shorter leg: x-3 = 3.9-3 = .9 inches . answer: 3.9 inches and .9 inches . . 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=92 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3.89791576165636, -0.89791576165636. Here's your graph:

Linear-systems/612625: The sum of two numbers is 9 and their difference is 6. What are the two numbers? 1 solutions Answer 385631 by nerdybill(6948)   on 2012-05-19 09:40:45 (Show Source): You can put this solution on YOUR website! The sum of two numbers is 9 antheir difference is 6. What are the two numbers? Let x,y be the two number then from "sum of two numbers is 9" we have: x+y = 9 (equation 1) . and from "their difference is 6" we have: x-y = 6 (equation 2) . applying "elimination method" we combine both equations together: x+y = 9 x-y = 6 -------- 2x = 15 x = 15/2 x = 7.5 . to find y, we substitute above into equation 1: x+y = 9 7.5+y = 9 y = 9-7.5 y = 1.5 . the two numbers are 7.5 and 1.5

Travel_Word_Problems/612616: Two cars leave the origin; one goes north at 35 mph and the other goes south at 50 mph. After how many hours will they be 500 miles apart? 1 solutions Answer 385618 by nerdybill(6948)   on 2012-05-19 03:57:24 (Show Source): You can put this solution on YOUR website! Two cars leave the origin; one goes north at 35 mph and the other goes south at 50 mph. After how many hours will they be 500 miles apart? . Let t = time (hours) traveled then distance traveled north is 35t distance traveled south is 50t . 35t + 50t = 500 85t = 500 t = 500/85 t = 5.88 hours or t = 5 hours and 53 minutes

Triangles/612610: I know the answer to this already but I don't know the proper way to solve for it so that is what i'm looking for here. The hypotenuse of a right triangle is 25m and the difference between the lengths of the two legs are 17m what are the lengths of the two sides. 1 solutions Answer 385617 by nerdybill(6948)   on 2012-05-19 01:38:06 (Show Source): You can put this solution on YOUR website! The hypotenuse of a right triangle is 25m and the difference between the lengths of the two legs are 17m what are the lengths of the two sides. . Let x = length of one leg then x+17 = length of second leg . applying Pythagorean theorem x^2 + (x+17)^2 = 25^2 x^2 + (x+17)(x+17) = 25^2 x^2 + x^2+34x+289 = 625 2x^2+34x+289 = 625 2x^2+34x-336 = 0 x^2+17x-168 = 0 (x+24)(x-7) = 0 x = {-24, 7} throw out the negative solution (extraneous) leaving: x = 7 meters (one leg) . second leg: x+17 = 7+17 = 24 meters

Rate-of-work-word-problems/612503: one painter can paint a house in 12 hours, and the second panter can paint a house in 8 hours. how long would it take them to paint the house together? 1 solutions Answer 385609 by nerdybill(6948)   on 2012-05-18 21:57:09 (Show Source): You can put this solution on YOUR website! one painter can paint a house in 12 hours, and the second panter can paint a house in 8 hours. how long would it take them to paint the house together? . Let x = time (hours) for both together then x(1/12 + 1/8) = 1 multiply both sides by 24: x(2 + 3) = 24 x(5) = 24 x = 24/5 x = 4.8 hours or x = 4 hours and 48 minutes

Triangles/612586: if the altitude of a triangle is 10 cm and its area is 120cm^2, what is its base? 1 solutions Answer 385607 by nerdybill(6948)   on 2012-05-18 21:54:11 (Show Source): You can put this solution on YOUR website! if the altitude of a triangle is 10 cm and its area is 120cm^2, what is its base? . area of any triangle: (1/2)bh where b is length of base h is height or altitude . (1/2)b(10) = 120 b(5) = 120 b = 120/5 b = 24 cm

Polynomials-and-rational-expressions/612415: x³+2x²+3x+6=0 1 solutions Answer 385448 by nerdybill(6948)   on 2012-05-18 09:46:36 (Show Source): You can put this solution on YOUR website! group terms: factor each group:

Trigonometry-basics/612314: Please help me solve this problem: There is a weather balloon going west between two stations that are 12 miles apart. The balloon is angled from each station at 18 degrees and 76 degrees. How high is the balloon? *I need to a system of equations. I need to have two equations that are set equal to each other and I must use substitution. Then I must find the final answer of how high the balloon is. 1 solutions Answer 385429 by nerdybill(6948)   on 2012-05-18 09:09:34 (Show Source): You can put this solution on YOUR website! There is a weather balloon going west between two stations that are 12 miles apart. The balloon is angled from each station at 18 degrees and 76 degrees. How high is the balloon? . Apply trig: Let h = height and x = length of base of 18 deg triangle . then tan 18 = h/x (equation 1) OR tan 76 = h/(12-x) (equation 2) . Solve equation 1 for x: tan 18 = h/x xtan 18 = h x = h/tan 18 . plug above into equation 2 and solve for h: tan 76 = h/(12-x) tan 76 = h/(12-(h/tan 18)) dividing both sides by tan 18: tan 76/tan 18 = h/(12tan 18-h) (tan 76/tan 18)(12tan 18-h) = h (tan 76/tan 18)(12tan 18) - (tan 76/tan 18)h = h (tan 76/tan 18)(12tan 18) = h+(tan 76/tan 18)h (tan 76/tan 18)(12tan 18) = h(1+(tan 76/tan 18)) (tan 76/tan 18)(12tan 18)/(1+(tan 76/tan 18)) = h 3.61 miles = h

Linear-equations/612388: graph the equation -2y = -x + 8 1 solutions Answer 385424 by nerdybill(6948)   on 2012-05-18 08:51:46 (Show Source): You can put this solution on YOUR website! graph the equation -2y = -x + 8 multiplying both sides by -1: 2y = x - 8 dividing both sides by 2: y = (1/2)x - 4 this is a line with a slope of 1/2 and the y-intercept at -4 . Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/1 = 8. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/-2 = -4. Slope is -1/-2 = 0.5. Equation in slope-intercept form: y=0.5*x+-4.

Geometry_Word_Problems/612389: the navy pier ferris wheel is 150 ft tall and has 40 spokes. a.) find the measure of the angle between any two spokes b.) two spokes form a central angle of 72 degrees. how many spokes are between the two spokes? c.) the bottom of the wheel is 10 ft from the ground. find the diameter and radius of the wheel. explain your reasoning. 1 solutions Answer 385422 by nerdybill(6948)   on 2012-05-18 08:42:47 (Show Source): You can put this solution on YOUR website! the navy pier ferris wheel is 150 ft tall and has 40 spokes. a.) find the measure of the angle between any two spokes 360/40 = 9 degrees . b.) two spokes form a central angle of 72 degrees. how many spokes are between the two spokes? 72/9 = 8 spokes . c.) the bottom of the wheel is 10 ft from the ground. find the diameter and radius of the wheel. explain your reasoning. diameter must be 150-10 = 140 feet radius is 1/2(diameter) = 70 feet

Polynomials-and-rational-expressions/612391: I need help on this please!! Completely factor the following expression: 36y^2 – z ^2 Any help would be greatly helpful!! 1 solutions Answer 385421 by nerdybill(6948)   on 2012-05-18 08:39:42 (Show Source): You can put this solution on YOUR website! think "difference of squares" 36y^2 – z^2 can be rewritten as: (6y)^2 – z^2 (now, it is a difference of squares) factoring: (6y-z)(6y+z)

Quadratic_Equations/612304: a ball thrown from the height of 3m with the speed of 4m/s. find quadretic equation.i got answer -9.8t^2+4t+3but i donot understand how -9.8 1 solutions Answer 385419 by nerdybill(6948)   on 2012-05-18 08:35:51 (Show Source): You can put this solution on YOUR website! The "acceleration of gravity" is 9.8 meters/sec^2 since, the force is downward it will be negative. . The general form of the equation of motion is: (1/2)gt^2 + vt + h where g is gravity (m/sec^2) t is time (sec) v is initial velocity h is initial height . your equation should be: -(1/2)gt^2 + vt + h -(1/2)9.8t^2+4t+3 -4.9t^2+4t+3

logarithm/612328: Which expression shows the expansion of ? A. B. C. D. 1 solutions Answer 385354 by nerdybill(6948)   on 2012-05-18 00:31:23 (Show Source): You can put this solution on YOUR website! answer: B

�t�e�s�t/612334: If ln x=A and ln y=B write in expanded from the expression ln(x^2/y^3) in terms of A & B. I will appreciate the help.. 1 solutions Answer 385353 by nerdybill(6948)   on 2012-05-18 00:29:35 (Show Source): You can put this solution on YOUR website! If ln x=A and ln y=B write in expanded from the expression ln(x^2/y^3) . ln(x^2/y^3) ln(x^2) - ln(y^3) 2ln(x) - 3ln(y) 2A-3B

Linear-equations/612063: write an equation of the line that passes through each point with the given slope. (-3, -4), m=3 1 solutions Answer 385263 by nerdybill(6948)   on 2012-05-17 14:22:58 (Show Source): You can put this solution on YOUR website! write an equation of the line that passes through each point with the given slope. (-3, -4), m=3 . Plug given info into the "point-slope" form of a line: y - y1 = m(x - x1) y - (-4) = 3(x - (-3)) y + 4 = 3(x + 3) y + 4 = 3x + 9 y = 3x + 5 (this is what they're looking for in "slope-intercept" form)

absolute-value/612013: How do I simplify this: -7[92-(-98-3)] 1 solutions Answer 385246 by nerdybill(6948)   on 2012-05-17 12:51:10 (Show Source): You can put this solution on YOUR website! -7[92-(-98-3)] -7[92-(-101)] -7[92+101] -7[193] -1351

logarithm/612025: If log2=0.30 and log3=0.48,what is the approximate value of log72 Plz help. 1 solutions Answer 385245 by nerdybill(6948)   on 2012-05-17 12:48:36 (Show Source): You can put this solution on YOUR website! If log2=0.30 and log3=0.48,what is the approximate value of log72 . since we can rewrite: log(72) as log(2*2*2*3*3) log(2)+log(2)+log(2)+log(3)+log(3) substitute in our given values 0.30+0.30+0.30+0.48+0.48 1.86

logarithm/612022: What is the value of log2 64? Plz help. 1 solutions Answer 385243 by nerdybill(6948)   on 2012-05-17 12:38:31 (Show Source): You can put this solution on YOUR website!

Mixture_Word_Problems/611975: What amount of a 35% solution must be added to 20 milliliters of a 15% solution to get a 25% solution. 1 solutions Answer 385220 by nerdybill(6948)   on 2012-05-17 09:56:09 (Show Source): You can put this solution on YOUR website! What amount of a 35% solution must be added to 20 milliliters of a 15% solution to get a 25% solution. . Let x = amount (milliliters) of 35% solution added then .35x + .15(20) = .25(x+20) .35x + 3 = .25x+5 .10x + 3 = 5 .10x = 2 x = 2/.10 x = 20 milliliters

logarithm/611973: Ln(4x+1)=ln(2x+5) 1 solutions Answer 385219 by nerdybill(6948)   on 2012-05-17 09:53:18 (Show Source): You can put this solution on YOUR website! ln(4x+1)=ln(2x+5) 4x+1 = 2x+5 2x+1 = 5 2x = 4 x = 2

Rectangles/611936: a painting measuring 12 inches by 18 inches is surrounded by a frame of uniform width. if the combined area of the painting and the frame is 432 square inches, determine the width of the frame 1 solutions Answer 385214 by nerdybill(6948)   on 2012-05-17 09:03:32 (Show Source): You can put this solution on YOUR website! a painting measuring 12 inches by 18 inches is surrounded by a frame of uniform width. if the combined area of the painting and the frame is 432 square inches, determine the width of the frame . Let w = width of frame then (12+2w)(18+2w) = 432 216+24w+36w+4w^2 = 432 216+60w+4w^2 = 432 4w^2+60w+216 = 432 4w^2+60w-216 = 0 w^2+15w-54 = 0 (w+18)(w-3) = 0 w = {-18,3} throw out the negative solution (extraneous) leaving: w = 3 inches

Triangles/611934: The altitude of an equilateral triangle is 3root3, find its area? 1 solutions Answer 385211 by nerdybill(6948)   on 2012-05-17 08:49:11 (Show Source): You can put this solution on YOUR website! The altitude of an equilateral triangle is 3root3, find its area? . First, find the length of the base: Let b = length of base then applying Pythagorean theorem: . area of triangle is (1/2)bh square units

logarithm/611956: Log2 4+ log2 9 1 solutions Answer 385210 by nerdybill(6948)   on 2012-05-17 08:41:02 (Show Source): You can put this solution on YOUR website! Log2 4+ log2 9

logarithm/611962: Please help me solve this equation: use the laws of logarithms to solve this equation. ln(3-x)=ln(3x-x^2) 1 solutions Answer 385209 by nerdybill(6948)   on 2012-05-17 08:38:33 (Show Source): You can put this solution on YOUR website! ln(3-x)=ln(3x-x^2) 3-x = 3x-x^2 -x+3 = 3x-x^2 x^2-x+3 = 3x x^2-4x+3 = 0 (x-1)(x-3) = 0 x = {1,3} since you can't take ln(0), we determine that x=3 is an extraneous solution -- throw it out leaving: x = 1

Travel_Word_Problems/611657: Two cars are 190 miles apart and travel toward each other along the same road. They meet in 2 hr. One car travels 4 mph faster than the other. what is the average speed of each car? 1 solutions Answer 385089 by nerdybill(6948)   on 2012-05-16 14:34:58 (Show Source): You can put this solution on YOUR website! Two cars are 190 miles apart and travel toward each other along the same road. They meet in 2 hr. One car travels 4 mph faster than the other. what is the average speed of each car? . Let x = speed (mph) of slower car then x+4 = speed of faster car . 2(x + x+4) = 190 (x + x+4) = 95 2x+4 = 95 2x = 91 x = 45.5 mph (speed of slower car) . speed of faster car: x+4 = 45.5+4 = 49.5 mph

Polynomials-and-rational-expressions/611659: Find all numbers for which the rational expression is not defined 7/b+6 1 solutions Answer 385086 by nerdybill(6948)   on 2012-05-16 14:31:32 (Show Source): You can put this solution on YOUR website! Find all numbers for which the rational expression is not defined 7/b+6 . Since you can't divide by zero: set the denominator to zero and solve for b: b+6=0 b = -6 . Answer: -6

logarithm/611562: -7log5 7n= -7 the 5 is the base 1 solutions Answer 385029 by nerdybill(6948)   on 2012-05-16 09:50:36 (Show Source): You can put this solution on YOUR website!

Geometry_Word_Problems/611489: 1. Wagon has a volume of 900 cu in. It is 30 in. long and 10 in. wide. How deep is the wagon? 2. A flower box is 7 feet long, 2 feet wide, and 2 feet deep. How many cubic feet of dirt will it hold? 3. If dirt is sold in bags that hold 3.5 cu ft, how many bags of dirt will it take to fill the box? 1 solutions Answer 385027 by nerdybill(6948)   on 2012-05-16 09:44:22 (Show Source): You can put this solution on YOUR website! 1. Wagon has a volume of 900 cu in. It is 30 in. long and 10 in. wide. How deep is the wagon? Let d = depth of box then d*30*10=900 d*300=900 d = 900/300 d = 3 inches . 2. A flower box is 7 feet long, 2 feet wide, and 2 feet deep. How many cubic feet of dirt will it hold? 7*2*2 = 14*2 = 24 cubic feet . 3. If dirt is sold in bags that hold 3.5 cu ft, how many bags of dirt will it take to fill the box? 24/3.5 = 6.86 so, it will take 7 bags

Sequences-and-series/611554: 87 cents/ 30 in = ?/ ft 1 solutions Answer 385023 by nerdybill(6948)   on 2012-05-16 09:33:01 (Show Source): You can put this solution on YOUR website! 87 cents/30 in . since there are 12 in per feet: 87 cents/30 in * 12 in/1 feet (87*12)/30 cents/feet 34.8 cents/feet

Square-cubic-other-roots/611556: What is the answer to this equation by using the Square Root Property: x^2-2x+1=18? 1 solutions Answer 385022 by nerdybill(6948)   on 2012-05-16 09:30:24 (Show Source): You can put this solution on YOUR website! What is the answer to this equation by using the Square Root Property: x^2-2x+1=18? . First, you must complete the square: take half 'b', square it and add to both sides: now, you can take the square root of both sides: . TWO answers: and

Miscellaneous_Word_Problems/611532: If one sheet of paper is 22.75 inches, how many feet of this paper will be printed if you print 50,000 an hour. 1 solutions Answer 384994 by nerdybill(6948)   on 2012-05-16 07:17:09 (Show Source): You can put this solution on YOUR website! If one sheet of paper is 22.75 inches, how many feet of this paper will be printed if you print 50,000 an hour. . In inches: 22.75 * 50000 1137500 inches . since there are 12 inches per feet: 1137500/12 94791.67 feet per hour