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 Radicals/290613: 3a^2/a-b minus 3b^2-6ab/b-a1 solutions Answer 210307 by ankor@dixie-net.com(15658)   on 2010-04-10 21:59:33 (Show Source): You can put this solution on YOUR website! - Factor out -1 to make the denominators the same - the minus one changes the sign + Factor out 3 = Can be written Factor and cancel = 3(a-b)
 Miscellaneous_Word_Problems/290584: A farmer ordered 100 animals for 100 dollars from a local mill. he knew he ordered some pigs, calves and chicks but he lost his receipt and forgot how many of each he orderd, he knew pigs were \$3 each calves \$10 each and chicks \$.50 each. using this information determine what the farmers order was.1 solutions Answer 210300 by ankor@dixie-net.com(15658)   on 2010-04-10 19:47:42 (Show Source): You can put this solution on YOUR website!A farmer ordered 100 animals for 100 dollars from a local mill. he knew he ordered some pigs, calves and chicks but he lost his receipt and forgot how many of each he orderd, he knew pigs were \$3 each calves \$10 each and chicks \$.50 each. using this information determine what the farmers order was. : Let c = no. of calves; p = no. of pigs; s = no. chickens : No. of animals equation: c + p + s = 100 : Calves cost \$10, Pigs cost \$3, and chickens cost \$.50. the \$\$ equation: 10c + 3p + .5s = 100 : We have two equations but 3 unknowns, however, we know there can't very many calves, After trying a couple values for no. of cows, came up with 5 cows, they're worth \$50, our two equations then are: : p + s = 100 - 5 p + s = 95 and 3p + .5s = 100 - 50 3p + .5s = 50 : Multiply the 1st equation by 3 and subtract the 2nd equation: 3p + 3s = 285 3p + .5s = 50 ---------------- subtracting eliminates p 0p + 2.5s = 235 s = s = 94 chickens : Find pigs p + 94 = 95 p = 95 - 94 p = 1 pig : We have then: 5 calves, 1 pig, 94 chicken ; ; Check in the cost equation 10(5) + 3(1) + 94(.5) = 50 + 3 + 47 = \$100
 Polynomials-and-rational-expressions/290611: add or subtract your answer -3t/t-4 - 2t+4/4-t1 solutions Answer 210299 by ankor@dixie-net.com(15658)   on 2010-04-10 19:26:34 (Show Source): You can put this solution on YOUR website!When the sum of 8 and a certain number is increased by 12, the result is the same as the product of 3 and the number. (x + 8) + 12 = 3x x + 20 = 3x 20 = 3x - x 20 = 2x x = x = 10 : : Check: 10 + 8 + 12 = 3(10)
 Percentage-and-ratio-word-problems/290453: A speaker was so boring that one-half of the audience left after a few minutes. Five minutes later, one-third of the remaining audience left. Ten minutes later, one-fourth of those remaining left, leaving only nine people in the audience. How many people were in the audience at the beginning of the lecture? (a) 21 (b) 36 (c) 72 (d) 144 (e) 216 1 solutions Answer 210274 by ankor@dixie-net.com(15658)   on 2010-04-10 18:03:10 (Show Source): You can put this solution on YOUR website!one-half of the audience left after a few minutes. Five minutes later, one-third of the remaining audience left. Ten minutes later, one-fourth of those remaining left, leaving only nine people in the audience. How many people were in the audience : Let x = no. in the audience : "one-third of the remaining audience left. that leaves 2/3 *(x) = x = x : "one-fourth of those remaining left," that leave 3/4 *x = x = x : "leaving only nine people in the audience. " x = 9 Multiply by 4 x = 36 people in the audience
 Age_Word_Problems/290341: Mr. King is two times as old as his daughter. Ten years ago he lacked 5 years from being three times as old as his daughter was then. Find each of their ages.1 solutions Answer 210232 by ankor@dixie-net.com(15658)   on 2010-04-10 13:30:22 (Show Source): You can put this solution on YOUR website!Mr. King is two times as old as his daughter. k = 2d : Ten years ago he lacked 5 years from being three times as old as his daughter was then. k - 10 + 5 = 3(d-10) : k - 5 = 3d - 30 : k = 3d - 30 + 5 : k = 3d - 25 : Replace k with 2d 2d = 3d - 25 : 25 = 3d - 2d : d = 25 yrs is the daughter then 2(25) = 50 yrs is Mr K ; : Check solution in the statement: "Ten years ago he lacked 5 years from being three times as old as his daughter was then." 50 - 10 = 3(15) - 5 40 = 45 - 5
 Quadratic-relations-and-conic-sections/290479: I really need help with this question, I'm not understanding it at all, the answer apparently is (-3/2i , 15/4i), (3/2i, -15/4i) Solve this System: 9x^2-4y^2=36 5x+2y=01 solutions Answer 210221 by ankor@dixie-net.com(15658)   on 2010-04-10 11:42:24 (Show Source): You can put this solution on YOUR website!Solve this System: 9x^2 - 4y^2 = 36 5x + 2y = 0 : 2y = -5x y = -x or y = -2.5x : Replace y with -2.5x in the 1st equation 9x^2 - 4(-2.5x)^2 = 36 9x^2 - 4(6.25x^2) = 36 9x^2 - 25x^2 = 36 -16x^2 = 36 16x^2 = -36 4x = +/- 4x = +6i x = i x = i and 4x = -6i x = -i x = -i : Find y using the 2nd equation when x =i 5(i) + 2y = 0 i + 2y = 0 2y = -i y = -i and find y when x = -i 5(i) + 2y = 0 i + 2y = 0 2y = +i y = +i
 Miscellaneous_Word_Problems/290451: Three men can cut 72 trees in three hours. Because of a shortage of space, each time one man is added, each of the workers can cut one less tree per hour. How many trees can 5 men cut in 5 hours? (A)30 (B) 50 (C) 90 (D) 150 (E) 200 1 solutions Answer 210189 by ankor@dixie-net.com(15658)   on 2010-04-10 09:08:57 (Show Source): You can put this solution on YOUR website!Three men can cut 72 trees in three hours. : = 24 trees per man in three hrs = 8 trees per man per hr : : Because of a shortage of space, each time one man is added, each of the workers can cut one less tree per hour. : two men added, therefore each man cuts 6 trees/hr : : How many trees can 5 men cut in 5 hours? 5 * 6 * 5 = 150 trees in 5 hrs
 Exponents/290467: Simplify. Write answer with positive exponents. (b-2) ______-2 (b-5) I can't type this to look right. It should be on top b to the negative 2 power over b to the negative 5 power. The entire fraction is in parenthesis with that to the negative 2 power on the top it shows. Please help me solve. thank you. I thought you multiply so b to the positive 4 over b to the positive 4 would equal 1 but I was marked wrong. 1 solutions Answer 210176 by ankor@dixie-net.com(15658)   on 2010-04-10 08:21:10 (Show Source): You can put this solution on YOUR website!Simplify. Write answer with positive exponents. (b-2) ______-2 (b-5) Assume you mean You can do this a couple ways, here is one way: = = =
 Systems-of-equations/290300: Solve the following systems of equations by graphing: y=5x-7, y-5x=8 A.(3,2) B.(0.5,1.5) C.(1.5,0.5) D.no solution It's not clear to me on how to work these problems. I don't have a graphing calculator, nor do I know how to use one, and neither do I have any graphing paper. Thank you so, so much for all of your help!!!!1 solutions Answer 210150 by ankor@dixie-net.com(15658)   on 2010-04-09 21:07:28 (Show Source): You can put this solution on YOUR website!Solve the following systems of equations by graphing: y= 5x - 7, Arrange this equation to be in the slope/intercept (y=mx+b) form also y-5x=8 add 5x to both sides and you have y = 5x + 8 : Both these equations have a slope of 5, they are parallel line, therefore "there is no solution" : If you did graph them, you could see it, they never intersect
 Square-cubic-other-roots/290326: the cube of a number added to the sum of three times the number and 9 is a prime number 1 solutions Answer 210145 by ankor@dixie-net.com(15658)   on 2010-04-09 20:52:21 (Show Source): You can put this solution on YOUR website!the cube of a number added to the sum of three times the number and 9 is a prime number : x^3 + 3x + 9 = y(prime) Actually for both x=1, and x=2, y is prime
 Quadratic_Equations/290323: Sue rowed her boat across and back lake bend in 3 hours. if her returning rate was 2mph less than the going rate, and if the distance each way was 7 miles find her rate going. would it be 7 over x plus 7 over x-2=3? I have to solve it using the quadratic formula. Thanks1 solutions Answer 210137 by ankor@dixie-net.com(15658)   on 2010-04-09 20:04:37 (Show Source): You can put this solution on YOUR website!Sue rowed her boat across and back lake bend in 3 hours. if her returning rate was 2mph less than the going rate, and if the distance each way was 7 miles find her rate going. : Yes, it could be: + = 3 Multiply by x(x-2), results 7(x-2) + 7x = 3x(x-2) : 7x - 14 + 7x = 3x^2 - 6x : 14x - 14 = 3x^2 - 6x combine like terms to have a quadratic equation 0 = 3x^2 - 6x - 14x + 14 : 3x^2 - 20x + 14 = 0 : the quadratic formula In this problem a=3; b=-20; c=14 : : Two solutions x = x = 5.87 and x = x = .795 : The reasonable solution: x = 5.87 mph, her rate going : : Check solution by finding the times coming and going 7/5.87 = 1.19, going 7/3.87 = 1.81, returning ---------------- total = 3 hrs
 Graphs/290401: Help is very much needed. What is the solution set of the equation 3x^2=48? Graph is needed. If possible please explain?1 solutions Answer 210128 by ankor@dixie-net.com(15658)   on 2010-04-09 19:17:45 (Show Source): You can put this solution on YOUR website!What is the solution set of the equation 3x^2=48? Graph is needed. : 3x^2 = 48 3x^2 - 48 = 0 Can be factored (3x-12)(x+4) = 0 Two solutions 3x = 12 x = 4 and x = -4 : A graph of this:
 Travel_Word_Problems/290314: Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 mph and Train B is traveling at 70 mph. Train A passes a station at 7:15 p.m. If train B passes the same station at 7:27 p.m. Then at what time will train B catch up to train A?1 solutions Answer 210121 by ankor@dixie-net.com(15658)   on 2010-04-09 18:50:56 (Show Source): You can put this solution on YOUR website!Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 mph and Train B is traveling at 70 mph. Train A passes a station at 7:15 p.m. If train B passes the same station at 7:27 p.m. Then at what time will train B catch up to train A? : from the given information, we know that train B is 12 min (1/5 hr) behind train A, when train A passes the station : The distance between the trains at this time: * 70 = 14 mi : Let t = time required for train B to catch train a : write a distance equation: Dist = speed * time : Train B travel dist = Train A travel dist + 14 mi 70t = 60t + 14 70t - 60t = 14 10t = 14 t = t = 1.4 hr or 1 hr 24 min : 7:15 + 1:24 = 8:39 pm, B catches A
 Miscellaneous_Word_Problems/290306: 24 boxes are carried by 24 people. Adults can carry 3 boxes Teenages can carry 2 boxes and 3 children can carry 1 box. How do I figure hown many of which people carried how many boxes. Some thing like 3 adults 2 teenagers and 6 children???1 solutions Answer 210076 by ankor@dixie-net.com(15658)   on 2010-04-09 13:34:58 (Show Source): You can put this solution on YOUR website!24 boxes are carried by 24 people. Adults can carry 3 boxes Teenagers can carry 2 boxes and 3 children can carry 1 box. How do I figure how many of which people carried how many boxes. : Total people equation: a + t + c = 24 : Let each child carry 1/3 of box 3a + 2t + c = 24 Multiply by 3 and use elimination with the first equation: 9a + 6t + c = 72 a + t + c = 24 -------------------subtraction eliminates c 8a + 5t = 48 8a = 48 - 5t Divide eq by 8: a = 6 - t We must have an integer solution; t has to be a multiple of 8, but not 16 t=8 a = 6 - 5 a = 1 : 1 adult, 8 teenagers : Find the number of children 1 + 8 + c = 24 c = 24 - 9 c = 15 children : Check by finding the number of boxes 1(3) + 8(2) + 15 = 24 3 + 16 + 5 = 24 boxes ; 1 adult, 8 teenagers, 15 children
 Travel_Word_Problems/290200: two bicyclists leave town at the same time going in the same direction. one is traveling at 22 km/h and the other at 38 km/h. in how many hours will they be 112 km apart?1 solutions Answer 210037 by ankor@dixie-net.com(15658)   on 2010-04-09 10:19:24 (Show Source): You can put this solution on YOUR website!two bicyclists leave town at the same time going in the same direction. one is traveling at 22 km/h and the other at 38 km/h. in how many hours will they be 112 km apart? ; Use the relative speed, and it's very easy relative speed between the two bikes: 38-22 = 16 : Time = = 7 hrs
 Travel_Word_Problems/289863: Persons A and B are 30 km apart. If they leave at the same time and travel in the same direction, A overtakes Bin 60 hours. If they walk toward each other they meet in5 hours. What is the sum of their rates, measured in km per hour? (a) 6 (b) 7 (c) 8 (d) 9 (e) None of the above 1 solutions Answer 209983 by ankor@dixie-net.com(15658)   on 2010-04-08 21:42:07 (Show Source): You can put this solution on YOUR website!Persons A and B are 30 km apart. If they leave at the same time and travel in the same direction, A overtakes Bin 60 hours. If they walk toward each other they meet in5 hours. What is the sum of their rates, measured in km per hour? : The only part we need to solve this is: "If they walk toward each other they meet in 5 hours. What is the sum of their rates, measured in km per hour?" : 5(A+B) = 30 A + B = A + B = 6 km/hr
 Trigonometry-basics/289726: While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 2.5 degrees. After you drive 17 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain.1 solutions Answer 209973 by ankor@dixie-net.com(15658)   on 2010-04-08 20:59:15 (Show Source): You can put this solution on YOUR website!While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 2.5 degrees. After you drive 17 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain. : represent this with a scalene triangle, where A = 2.5 degrees B = (180-9) = 171 degrees C = 180 - 171 - 2.5 = 6.5 degrees c = 17 Find side b using the law of sines: = = : Sin(6.5)b = 17*sin(171) : .1132b = 2.659 b = b = 23.49 mi (from angle A to the top of the mountains) : Side b is the hypotenuse of a right triangle at the base of the mountain formed by the mountain top and a line to point A : Use the sine of 2.5, height (h) of the mountain will be the side opposite Sin(2.5) = .0436 = h = .0436 * 23.49 h = 1.02462 mi is the mountain height 0r 1.02462 * 5280 = 5410 ft high
 Miscellaneous_Word_Problems/290029: What would be the monthly payment on a \$90,000 mortgage at a rate of 7.5% interest for 30 years?1 solutions Answer 209965 by ankor@dixie-net.com(15658)   on 2010-04-08 19:48:46 (Show Source): You can put this solution on YOUR website!What would be the monthly payment on a \$90,000 mortgage at a rate of 7.5% interest for 30 years? : That's a pretty complicated formula, but using the finance feature on my TI83 monthly payment = \$629.29
 Linear-equations/290060: Two cyclists drive a distance of 15 kilometres. One of the cyclists drives 10 km h faster than the other one and arrives at their destination 20 minutes earlier. What are the speeds of the cyclists?1 solutions Answer 209959 by ankor@dixie-net.com(15658)   on 2010-04-08 19:23:11 (Show Source): You can put this solution on YOUR website!Two cyclists drive a distance of 15 kilometres. One of the cyclists drives 10 km h faster than the other one and arrives at their destination 20 minutes earlier. What are the speeds of the cyclists? : Let s = speed of the slow cyclist then (s+10) = speed of the faster one : Change 20 min to hr : Write a time equation: Time = dist/speed : slow time - fast time = hr - = Multiply by 3s(s+10), results: 3(15)(s-10) - 3(15)s = s(s+10) : 45(s+10) - 45s = s(s+10) : 45s + 450 - 45s = s^2 + 10s : 0 = s^2 + 10s - 450 : Use the quadratic formula to find s: In this equation, x=s; a=1, b=10; c=-450 : ; : Positive solution s = s = 16.7945 ~ 16.8km/h is the slow cyclist and 26.8 km/h is the fast cyclist ; : Check solution by finding the times Slow: 15/16.8 = .89 hrs Fast: 15/26.8 = .56 hrs ------------------------ difference is: .33 hrs which is about 20 min
 Expressions-with-variables/290023: - +3 Could someone help me with this? I need to do this operation and then simplify my answer. Thanks a lot!1 solutions Answer 209927 by ankor@dixie-net.com(15658)   on 2010-04-08 16:11:20 (Show Source): You can put this solution on YOUR website! - + 3 The common denominator is ax - + =
 Rational-functions/289867: Hi, I hope someone can help me. My problem is: Niagara Electric charges a flat fee of \$8.50 for the first 1000 kilowatt hours used, \$0.05 per kilowatt hour for the next 4000 kilowatt hours, and \$.04 per kilowatt hour for each hour used thereafter. What is the expression for the cost function, C(x), using standard notation?1 solutions Answer 209872 by ankor@dixie-net.com(15658)   on 2010-04-08 09:18:41 (Show Source): You can put this solution on YOUR website!Niagara Electric charges a flat fee of \$8.50 for the first 1000 kilowatt hours used, \$0.05 per kilowatt hour for the next 4000 kilowatt hours, and \$.04 per kilowatt hour for each hour used thereafter. What is the expression for the cost function, C(x), using standard notation? : I think you need two expression x =< 5000 kwh C(x) = .05(x-1000) + 8.50 and x > 5000 kwh,(add 1 cent per kwh for 4000 kwh) C(x) = .04(x-1000) + 40.00 + 8.50 C(x) = .04(x-1000) + 48.50
 Polynomials-and-rational-expressions/289797: Good evening, Please help me solve this rational expression. In addition, please provide the steps. x/2 + 1 = x/41 solutions Answer 209817 by ankor@dixie-net.com(15658)   on 2010-04-07 21:53:54 (Show Source): You can put this solution on YOUR website! + 1 = Clear the denominators, multiply by 4 4* + 4(1) = 4* Cancel the denominators 2x + 4 = x Subtract 4 from both sides 2x = x - 4 subtract x from both sides x = -4 ; : Check solution in original problem + 1 = -2 + 1 = -1; equality confirms your solution
 Quadratic_Equations/289772: Hello can anyone help solve this problem with work shown and answers it will help me learn how to do these problems for my upcoming test. Sean's Widget Company has revenue that is modeled by the function R(x) = -4x2 + 35x and costs modeled by the function C(x) = 12x +30. The input variable x is in hundreds of widgets, and the outputs of the functions are in units of thousands of dollars. Construct a profit function P(x) and find the value of x that maximizes the profit. Thank you John1 solutions Answer 209815 by ankor@dixie-net.com(15658)   on 2010-04-07 21:43:00 (Show Source): You can put this solution on YOUR website!Sean's Widget Company has revenue that is modeled by the function R(x) = -4x2 + 35x and costs modeled by the function C(x) = 12x +30. The input variable x is in hundreds of widgets, and the outputs of the functions are in units of thousands of dollars. Construct a profit function P(x) and find the value of x that maximizes the profit. : Profit = Revenue - Cost P(x) = R(x) - C(x) Which is P(x) = -4x^2 + 35x - (12x + 30) Removing the bracket changes the signs P(x) = -4x^2 + 35x - 12x - 30 Combine like terms P(x) = -4x^2 + 23x - 30 : A quadratic equation, we can find the axis of symmetry: x = -b/(2a) That value of x will give us max profit x = x = x = +2.875 hundreds of widgets : 287.5 ~ 288 widgets for max profit (has to be an integer) : : To find the actual profit value (in thousands), substitute 2.88 for x in the equation P(x) = -4(2.88^2) + 23(2.88) - 30
 Linear_Algebra/289736: Soybean meal is 16% protein. Cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320- pound mixture that is 13% protein?? How many pounds of cornmeal?________ How many pounds of soybean meal??_______ 1 solutions Answer 209813 by ankor@dixie-net.com(15658)   on 2010-04-07 21:20:30 (Show Source): You can put this solution on YOUR website!Soybean meal is 16% protein. Cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320 pound mixture that is 13% protein?? : Let x = amt of soy then the total is to be 320lb, therefore: (320-x) = amt of corn : A typical mixture equation: .16x + .08(320-x) = .13(320) .16x + 25.6 - .08 = 41.6 .16x - .08x = 41.6 - 25.6 .08x = 16 x = x = 200 lb of soy then 320 - 200 = 120 lb of corn : : Check solution in original equation .16(200) + .08(120) = .13(320) 32 + 9.6 - 41.6
 Age_Word_Problems/289692: Tamara has 2 sisters. One of the sisters is 7 years older the Tamar. The other sister is 3 years younger then Tamara. The product of her sisters ages is 24. How old is Tamra1 solutions Answer 209803 by ankor@dixie-net.com(15658)   on 2010-04-07 20:07:37 (Show Source): You can put this solution on YOUR website!Tamara has 2 sisters. One of the sisters is 7 years older the Tamar. The other sister is 3 years younger then Tamara. The product of her sisters ages is 24. How old is Tamra : Let t = T's age then (t+7) = older sister's age and (t-3) = younger sister's age : The product of her sisters ages is 24. (t+7)(t-3) = 24 FOIL t^2 - 3t + 7t - 21 = 24 : t^2 + 4t - 21 - 24 = 0 : t^2 + 4t - 45 = 0 factors to (t+9)(t-5) = 0 Positive solution t = 5 yrs is T's age ; : Check solution by find the product of the sisters age (5+7) * (5-3) = 24
 Travel_Word_Problems/289706: George jogged downhill at 6 mi/h and then jogged back up at 4mi/h. If the total jogging time was 1.25 h, how far did he jog in all?1 solutions Answer 209785 by ankor@dixie-net.com(15658)   on 2010-04-07 19:27:53 (Show Source): You can put this solution on YOUR website!George jogged downhill at 6 mi/h and then jogged back up at 4mi/h. If the total jogging time was 1.25 h, how far did he jog in all? : Let d = dist up the hill Same distance down the hill : Write a time equation: Time = dist/speed : down time + up time = 1.25 hr + = 1.25 Multiply by 12 to get rid of the denominators, results 2d + 3d = 12(1.25) 5d = 15 d = 3 mi up and 3 mi down : Total dist = 6 mi : : Check solution, find the time 3/6 + 3/4 = .5 + .75 = 1.25
 Linear-systems/289498: PLease help me with this!!!! The perimeter of a rectangle is 186 inches. The length exceeds the width by 65 inches. Find the length and the width. the length is____ the width is___1 solutions Answer 209768 by ankor@dixie-net.com(15658)   on 2010-04-07 18:46:35 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 186 inches. The length exceeds the width by 65 inches. Find the length and the width. : Perimeter equation: 2L + 2W = 186 : It says,"The length exceeds the width by 65 inches.", therefore: L = W + 65 : Replace L with (W+65) in the perimeter equation 2(W+65) + 2W = 186 Simplify, divide by 2 (W+65) + W = 93 : 2W = 93 - 65 : 2W = 28 W = W = 14 inches is the width : L = W + 65 L = 14 + 65 L = 79 inches is the length : : Check solution, find the perimeter 2(79) + 2(14) = 158 + 28 = 186
 Travel_Word_Problems/289494: Primo Car Rental charges \$39 per day plus \$0.25 per mile. Ultimo Car Rental charges \$28 per day plus \$0.60 per mile. Find the daily mileage for which the Ultimo charge is twice the Primo charge. I need to know how to solve this problem, I don't necessarily need the answer, just the steps to go about solving it. Thank you.1 solutions Answer 209766 by ankor@dixie-net.com(15658)   on 2010-04-07 18:00:14 (Show Source): You can put this solution on YOUR website!Primo Car Rental charges \$39 per day plus \$0.25 per mile. Ultimo Car Rental charges \$28 per day plus \$0.60 per mile. Find the daily mileage for which the Ultimo charge is twice the Primo charge. : Primo equation cost = .25m + 39 : Ultimo equation cost = .60m + 28 : "Find the daily mileage for which the Ultimo charge is twice the Primo charge." Ultimo = twice Primo .60m + 28 = 2(.25m + 39) solve for m
 Triangles/289470: I know that the hypoteneuse of a right triangle is 9.0553. That, and the 90 degree angle is all I know. I need to know the length of the short side to find the solution to the full problem (this is only one little part of it.) This is what I tried to find one side: 2s^2=9.0553^2 2s/2^2=81.99/2 s^2=40.99 SQRT(s^2)=SQRT(40.99) s=6.40 Then I thought I could plug that into the pythagorean theorem (a^2+b^2=c^2; where a=6.40, and c=9.0553) but my answer for the other side was also 6.40 I know this can't be right because it is an iscoseles triangle. What do I need to do to find the lenth of the other two sides, or at least just of the shortest side? Is there a way to find the degree measures of the other angles in case it is a 90-60-30 triangle? 1 solutions Answer 209750 by ankor@dixie-net.com(15658)   on 2010-04-07 17:03:15 (Show Source): You can put this solution on YOUR website!But that is right: Two sides of the iscoseles triangle are equal!
 Miscellaneous_Word_Problems/289652: The half-life of is 1620 years. If 2.1 grams remian after 1000 years, whay is the initial quantity anf how much will remain after 10000 years? I am using the formula and so far have , have I set this up right? If so, where do I go from here? Thanks for your help!1 solutions Answer 209746 by ankor@dixie-net.com(15658)   on 2010-04-07 16:52:21 (Show Source): You can put this solution on YOUR website!The half-life of Pu 230 is 1620 years. If 2.1 grams remain after 1000 years, what is the initial quantity? : The half life equation is: A = Ao*2^(-t/h) where A = the resulting amt after t years Ao = initial amt (t=0) t = time in yrs h = half-life of the substance : Find the initial qty Ao*2^(-1000/1620) = 2.1 Ao*2^-.617284 Using a calc: enter 2^-.617284 and you have: .6519Ao = 2.1 Ao = Ao = 3.22 grams is the initial qty : Check on a calc: enter 3.22*2^(-1000/1620) = 2.099 ~ 2.1, confirms our solution : : how much will remain after 10000 years? Using Ao = 3.22, find A A = 3.22*2^(-10000/1620) using a calc A = .044 grams after 10,000 years
 Miscellaneous_Word_Problems/289573: 1.How long will it take an object to hit ground if it is thrown upward at 47 ft/sec from a height of 63 feet? 2.How do you know ahead of time how many roots a quadratic equation will have?1 solutions Answer 209737 by ankor@dixie-net.com(15658)   on 2010-04-07 16:33:25 (Show Source): You can put this solution on YOUR website!1.How long will it take an object to hit ground if it is thrown upward at 47 ft/sec from a height of 63 feet? : The height of an object thrown upward equation: h = 0 when the object hits the ground -16t^2 + 47t + 63 = 0 Solve this using the quadratic formula a=-16; b=47; c=63 You should get a positive solution: x = 3.9375 sec to hit the ground : 2.How do you know ahead of time how many roots a quadratic equation will have? in the form y = ax^2 + bx + c, the discriminant: D = -b^2 - 4*a*c D > 0; two distinct real root D = 0; one real number solution, a double root D < 0; two complex number solutions