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Recent problems solved by 'edjones'

edjones answered: 7568 problems
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Pythagorean-theorem/146958: Diagnal brace. The width of a retangular gate is 2 meters (m) larger than its heiht. The diagonal brace measures (Square root) 6 m. Find the width and height. 1 solutions Answer 107569 by edjones(7569)   on 2008-07-04 18:30:15 (Show Source): You can put this solution on YOUR website! We have a right triangle of height h, width h+2, and hypotenuse sqrt(6). a^2+b^2=c^2 h^2+(h+2)^2=sqrt(6)^2 h^2+h^2+4h+4=6 2h^2+4h-2=0 2(h^2+2h-1)=0 h^2+2h =1 h^2+2h+1=1+1 completing the square. (h+1)^2=2 h+1=+-sqrt(2) Square root of each side. h= -1+sqrt(2) m w= 1+sqrt(2) m . Ed

test/146924: find the shortest distance between the parallel lines with equations 5x-12y+33=0 and 5x-12y-6=0 1 solutions Answer 107568 by edjones(7569)   on 2008-07-04 17:44:30 (Show Source): You can put this solution on YOUR website! 5x-12y+33=0 5x-12y-6=0 . 5x-12y+33=0 -12y=-5x-33 y=5x/12 + 33/12 . 5x-12y-6=0 -12y=-5x+6 y=5x/12 - 1/2 . The distance between the parallel lines is |33/12 + 1/2|=3.25 This is easier to see if we change the slope from 5x/12 (1st graph) to 0x/12 (2nd graph) . Ed . .

Problems-with-consecutive-odd-even-integers/146915: Hi I need your help. Three consecutive odd integers are such that the square of the third is 264 more than the square of the second. Find the three integers. I'm trying to understand how you would write this out to be able to work it. Thank you, Reuben 1 solutions Answer 107567 by edjones(7569)   on 2008-07-04 17:41:43 (Show Source): You can put this solution on YOUR website! Let the integers be x, x+2, x+4 (x+4)^2=(x+2)^2+264 x^2+8x+16=x^2+4x+4+264 4x-252=0 subtract the right side from the left. 4x=252 x=63 63, 65, 67 are the integers. . Ed

Polynomials-and-rational-expressions/147122: Subtgract5m+3n-2p from3m-3n+14p 1 solutions Answer 107566 by edjones(7569)   on 2008-07-04 17:28:43 (Show Source): You can put this solution on YOUR website! 3m-3n+14p -5m-3n+2p Change all the signs and add. ---------- -2m-6n+16p

Geometry_Word_Problems/147135: Find the verex and intercepts. Sketch the graph g(x) = x^2 + -6 1 solutions Answer 107544 by edjones(7569)   on 2008-07-04 15:17:32 (Show Source): You can put this solution on YOUR website! The y intercept is -6 . x^2-6=0 x^2=6 x=-sqrt(6), x=sqrt(6) the x intercepts. . The vertex at x=sqrt(6)-sqrt(6)=0 The vertex at y=-6 special case. . . Ed

Equations/146974: 6a^2-4a^3+8a^4 8x^3 + 1/8y^3 1 solutions Answer 107390 by edjones(7569)   on 2008-07-02 01:15:41 (Show Source): You can put this solution on YOUR website! 6a^2-4a^3+8a^4 =2a^2(3-2a+4a^2) . 8x^3 + 1/8y^3 =8x^3 + 8y^-3 =8(x^3+y^-3) . Ed

Quadratic_Equations/147018: Solve and check each of the following for X: [5/(x-2)]+[6/(x+2)]=2 1 solutions Answer 107389 by edjones(7569)   on 2008-07-02 01:07:14 (Show Source): You can put this solution on YOUR website! [5/(x-2)]+[6/(x+2)]=2 5(x+2)+6(x-2)=2(x^2-4) Multiply each side by (x+2)(x-2) to eliminate fractions. 5x+10+6x-12=2x^2-8 11x-2=2x^2-8 2x^2-11x-6=0 2x^2-12x+x-6=0 2x(x-6)+(x-6)=0 Factoring by grouping. (2x+1)(x-6)=0 2x=-1 x=-1/2 x=6 . Ed

Miscellaneous_Word_Problems/147019: Solve following word problems: A: One number is 3 times another. If the sum of their reciprocals is 1/6, find the two numbers. B: If one-third of a number is subtracted from three-fourths of that number, the difference is 15. What is the number? 1 solutions Answer 107385 by edjones(7569)   on 2008-07-02 00:47:09 (Show Source): You can put this solution on YOUR website! a=3b 1/a + 1/b = 1/6 1/3b + 1/b = 1/6 substitute 2+6=b Multiply each side by 6b to eliminate fractions. b=8 a=24 . Let x be the number. 3x/4 - x/3 = 15 9x-4x=180 Multiply each side by 12 to eliminate fractions. 5x=180 x=36 . Ed

decimal-numbers/147056: i have a question if my multiple choice answers for my question find the shortest distance between the parallel lines with equations 5x-12y+33=0 and 5x-12y-6=0 A.3 B.39 C.27/5 D.27/13 E.N/a how did u come up with the answer 3.25 1 solutions Answer 107383 by edjones(7569)   on 2008-07-02 00:31:29 (Show Source): You can put this solution on YOUR website! 5x-12y+33=0 5x-12y-6=0 . 5x-12y+33=0 -12y=-5x-33 y=5x/12 + 33/12 . 5x-12y-6=0 -12y=-5x+6 y=5x/12 - 1/2 . The distance between the parallel lines is |33/12 + 1/2|=3.25 This is easier to see if we change the slope from 5x/12 (1st graph) to 0x/12 (2nd graph) . Ed . .

Rectangles/147042: Robin is mowing a rectangular field that measures 24 yards by 32 yards , by pushing a mower around and around the outside of the plot. This creates a widening border that surrounds the unmowed grass in the center. During a brief test, Robin wonders whether the job is half done yet. How wide is the uniform mowed border when Robin is half done? 1 solutions Answer 107381 by edjones(7569)   on 2008-07-02 00:20:45 (Show Source): You can put this solution on YOUR website! 32*24=768 Area of field 768/2=384 Half done area. (32-x)(24-x)=384 x^2-56x+768=384 x^2-56x+384=0 (x-8)(x-48)=0 x=8 yards. Width of the uniform border. . Ed

Geometry_Word_Problems/147046: The perimeter of a rectangle is one more than twice it's width. If the perimeter is 74inches, find the dimensions of the rectangle. I have tried to us this: Given: p=2w+1, p=74, 2p+2l=74. Find: p=perimeter, and w=width. Equation:P=2l+2w. Work: P=2l+2W. 74=2l+2W: 74=2w+1. 73=2w. w=36.5. 74=2l+2*36.5. 74=2l+73. 1=2L.1=L. Length=1 inch. Width=36.5inches. My friends say I am wrong. The width CAN NOT be longer than the length. Are they correct? If so, then what are the correct answers? If the answers are correct, but the problem is wrong. How would the problem be changed to make it right? 1 solutions Answer 107377 by edjones(7569)   on 2008-07-01 23:57:50 (Show Source): You can put this solution on YOUR website! P=2w+2L P=2w+1 so 2L=1 L=1/2 inch 2w + (2 * 1/2)=74 2w=73 w=36.5 inches . Ed

test/147055: find the shortest distance between the parallel lines with equations 5x-12y+33=0 and 5x-12y-6=0 PLEASE HELP!!! 1 solutions Answer 107376 by edjones(7569)   on 2008-07-01 23:46:17 (Show Source): You can put this solution on YOUR website! 5x-12y+33=0 5x-12y-6=0 . 5x-12y+33=0 -12y=-5x-33 y=5x/12 + 33/12 . 5x-12y-6=0 -12y=-5x+6 y=5x/12 - 1/2 . The distance between the parallel lines is |33/12 + 1/2|=3.25 This is easier to see if we change the slope from 5x/12 (1st graph) to 0x/12 (2nd graph) . Ed . .

Equations/146811: #13. A car traveling east at 45 miles per hour passes a certain intersection at 3 pm. Another car traveling north at 60 miles per hour passes the same intersection 25 minutes later. To the nearest minute, figure out when the cars are exactly 40 miles apart. 1 solutions Answer 107247 by edjones(7569)   on 2008-06-30 08:07:46 (Show Source): You can put this solution on YOUR website! When the 2nd car reaches the intersection the 1st car is 45*25/60=18.75 miles east of it. We have a right triangle with the hypotenuse=40 d=st d=distance s=speed, t=time Let a=60t b=45t+18.75, c=40 a^2+b^2=c^2 60t^2+(45t+18.75)^2=40^2 3600t^2+2025t^2+1687.5t+351.56=1600 5625t^2+1687.5t-1248.44=0 t=.344414 hr =21 min (approx) . Ed . Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) 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=30937556.25 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.344413681939415, -0.644413681939415. Here's your graph:

Rational-functions/146791: 1/4 = 3 - 2x -1/x + 2 1 solutions Answer 107242 by edjones(7569)   on 2008-06-30 06:57:08 (Show Source): You can put this solution on YOUR website! 1/4 = 3 - 2x - 1/x + 2 x=12x-8x^2-4+8x Multiply each side by 4x (LCM) to eliminate fractions. -8x^2+12x-x+8x-4=0 -8x^2+19x-4=0 8x^2-19x+4=0 . Ed . Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) 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=233 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2.14152109515461, 0.233478904845391. Here's your graph:

Rational-functions/146789: If x=0.4 when y=840 and y varies inversely as x find y when x=2.4 1 solutions Answer 107241 by edjones(7569)   on 2008-06-30 06:42:56 (Show Source): You can put this solution on YOUR website! 2.4/.4=6 If x increases 6 times then y will decrease 6 times. y=840/6=140 . Ed

Polynomials-and-rational-expressions/146751: Work. Henry sold 120 magazine subscriptions in x + 2 days. If he sold at the same rate for another week, then how many magazines did he sell in the extra week? 1 solutions Answer 107239 by edjones(7569)   on 2008-06-30 06:34:35 (Show Source): You can put this solution on YOUR website! 120/(x+2) number he sold in one day. (120*7)/(x+2) 840/(x+2) number he sold in the extra week. . Ed

Polynomials-and-rational-expressions/146752: Barn Painting. Melanie can paint a certain barn by herself in x days. Her helper Melissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that they complete for 1 day by working together. Evaluate the expression for x = 5. 1 solutions Answer 107237 by edjones(7569)   on 2008-06-30 06:24:29 (Show Source): You can put this solution on YOUR website! 1/x + 1/2x =(2+1)/2x LCD=2x =3/2x of the barn painted in 1 day working together. . x=5 3/10 of the barn painted in 1 day working together. . Ed

Proportions/146757: The Golden Ratio. The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ratio. If the length of the rectangular painting is 2 feet longer than its width, then for which dimensions would the length and the width have the golden ratio? 1 solutions Answer 107236 by edjones(7569)   on 2008-06-30 06:12:13 (Show Source): You can put this solution on YOUR website! L/w=8/5 golden ratio L=w+2 (w+2)/w=8/5 Proportion 5(w+2)=8w Multiply each side by the LCM (5w) to eliminate fractions. 5w+10=8w 3w=10 w=10'/3=3' 4" L=5' 4" . Ed

Square-cubic-other-roots/146708: My question says to use the laws of exponents to Simplify and write my answer with positve exponents. I am totally lost on where to start as the negative exponent of 2m and the half exponentof the brackets are throwing me off. Any help would be appreciated. Thanks. (9k^2m^-4)^1/2. 1 solutions Answer 107235 by edjones(7569)   on 2008-06-30 05:54:23 (Show Source): You can put this solution on YOUR website! (9k^2m^-4)^(1/2) =(9k^2/m^4)^(1/2) =3k/m^2 or 3km^-2 . Ed

Geometry_Word_Problems/146825: a painting is 3 inches longer than it is wide. it is set in a rectangular border that is 2 inches wider than the painting on each side. if the area of the border is 100 inch^2 what are the dimensions of the painting 1 solutions Answer 107234 by edjones(7569)   on 2008-06-30 05:47:43 (Show Source): You can put this solution on YOUR website! L*w=A L=w+3 for painting w*(w+3)=w^2+3w Area of the painting. (w+2)(w+5)=w^2+7w+10 Area of border and painting combined. w^2+7w+10-(w^2+3w)=100 w^2+7w+10-w^2-3w=100 4w+10=100 4w=90 w=22.5" L=25.5" . Ed

Travel_Word_Problems/146545: Jennifer traveled at a constant speed on an old road for 160 miles. She then traveled 5 miles per hour faster on a newer road for 90 miles. If she drove for 6 hours, find the car's speed for the part of the trip that was traveled on the new road. While you might find the speed on the old road in your calculations, do not include that in your answer. Do not include units in your answer. 1 solutions Answer 107164 by edjones(7569)   on 2008-06-29 02:02:39 (Show Source): You can put this solution on YOUR website! Let old road speed be s, new road speed be s+5; d=160+90, t=6 d=ts d/s=t 160/s + 90/(s+5)=6 160(s+5)+90s=6s(s+5) Multiply each side by the LCM to eliminate fractions. 160s+800+90s=6s^2+30s 6s^2+30s-160s-90s-800=0 Subtract the left side from the right. 6s^2-220s-800=0 2(3s^2-110s-400)=0 (s-40)(3s+10)=0 Factor (or use the quadratic formula) s=40 s+5=45 mph answer . Ed

Average/146637: Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 80 miles per hour and train B traveling at 100 miles per hour. Train A passes a station at 9:15 pm If train B passes the same station at 9:30 pm at what time will train B catch up to a train A? when will train B catch up with train A? 1 solutions Answer 107163 by edjones(7569)   on 2008-06-29 01:29:33 (Show Source): You can put this solution on YOUR website! d=st When B passes the station, train A 80* 1/4=20 mi ahead of it. The difference in speeds of the trains is 20 mph B will catch A in 1 hr. (10:30 PM) . Ed

Radicals/146715: Perform the indicated operations: 3sqrt[3] + 2sqrt[27] –sqrt[12] 1 solutions Answer 107148 by edjones(7569)   on 2008-06-28 19:21:48 (Show Source): You can put this solution on YOUR website! 3sqrt[3] + 2sqrt[27] –sqrt[12] =3sqrt(3)+2sqrt(9*3)-sqrt(4*3) =3srqt(3)+6sqrt(3)-2sqrt(3) =7sqrt(3) . Ed

Radicals/146716: Multiply: (8sqrt[6] + 3sqrt[2])(4sqrt[6] – 5sqrt[2]) 1 solutions Answer 107147 by edjones(7569)   on 2008-06-28 19:17:52 (Show Source): You can put this solution on YOUR website! (8sqrt[6] + 3sqrt[2])(4sqrt[6] – 5sqrt[2]) F 32*6 O -40sqrt(12) I 12sqrt(12) L -15*2 . 192-28sqrt(4*3)-30 162-56sqrt(3) . Ed

test/146711: can someone please tutor me with this problem ive been trying to solve with my parents find the shortest distance between the parallel lines with equations 5x-12y+33=0 and 5x-12y-6=0 1 solutions Answer 107142 by edjones(7569)   on 2008-06-28 19:06:21 (Show Source): You can put this solution on YOUR website! 5x-12y+33=0 5x-12y-6=0 . 5x-12y+33=0 -12y=-5x-33 y=5x/12 + 33/12 . 5x-12y-6=0 -12y=-5x+6 y=5x/12 - 1/2 . The distance between the parallel lines is |33/12 + 1/2|=3.25 This is easier to see if we change the slope from 5x/12 (1st graph) to 0x/12 (2nd graph) . Ed . .

Miscellaneous_Word_Problems/146645: This question is from textbook New Mexico Edition College Algebra A 39-ounce can of Hills Bros. coffee requires 188.5 square inches of aluminum. If its height is 7 inches, what is its radius? ) 1 solutions Answer 107102 by edjones(7569)   on 2008-06-28 02:52:45 (Show Source): You can put this solution on YOUR website! Lateral surface area of cylinder=2pi*r*h surface area of top and bottom combined=2pi*r^2 2pi*r*7+2pi*r^2=188.5 14pi*r+2pi*r^2=188.5 2pi(7r+r^2)=188.5 r^2+7r=188.5/2pi r^2+7r=30 approx. r^2+7r-30=0 (r+10)(r-3)=0 r=3"

Equations/146660: graph and write the solution in interval notation x<7 and x greater than equal to -4 1 solutions Answer 107101 by edjones(7569)   on 2008-06-28 02:30:36 (Show Source): You can put this solution on YOUR website! X[-4,7)

Parallelograms/146675: if four parallel lines intersect seven parallel lines. how many parallelograms are made? it turns out as a grid with 18 boxes. (3x6). i sure there would be an equation that would short cut actually counting up all the parallelograms. 1 solutions Answer 107100 by edjones(7569)   on 2008-06-28 02:25:28 (Show Source): You can put this solution on YOUR website! (7-1)(4-1)=18

Travel_Word_Problems/146475: I really need help with this word problem I am just totally stuck and confused. I would appreciate any help out there. Thank you so much. The problem is: A long distance trucker traveled 168 miles in one direction during a snow storm. The return trip in rainy weather was accomplished at double the speed and took 3 hours less to find,the speed going. 1 solutions Answer 106983 by edjones(7569)   on 2008-06-26 22:38:48 (Show Source): You can put this solution on YOUR website! d=st st=168 s=168/t . 2s(t-3)=168 s=84/(t-3) . On the graph below of the 2 formulas for s where the lines intersect in positive territory x=t=6, y=s=28 Answer when t=3 s=56 . Check: 6*28=168 mi 3*56=168 mi . Ed .

Radicals/146483: Rationalize the numerator and simplify. 5 sqrt (x) / sqrt (7y) Five sqrt of x divided by sqrt of 7y. I started this problem by mutiplying the numerator of 5 sqrt (x) to the numerator and the denom. Not sure what to do after that. Thanks! 1 solutions Answer 106956 by edjones(7569)   on 2008-06-26 17:22:52 (Show Source): You can put this solution on YOUR website! 5sqrt(x)/sqrt(7y) =5sqrt(x)/sqrt(7y) * sqrt(7y)/sqrt(7y) =5sqrt(7xy)/7y . Ed

Square-cubic-other-roots/146522: X 3/2 = 125 1 solutions Answer 106954 by edjones(7569)   on 2008-06-26 17:10:33 (Show Source): You can put this solution on YOUR website! x^(3/2)=125 x=125^(2/3) Take each side to the 2/3 power. x=25 . Ed