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Miscellaneous_Word_Problems/383300: I need this worked out so I can understand. I am to find out which humbers cannot be used in place of the variable the rational expression. Please write it so I can understand it because I do not understand or know how to do this. 2y+1/y^2-y-6 Thank you so much. 1 solutions Answer 271429 by ankor@dixie-net.com(15746)   on 2010-12-08 19:44:33 (Show Source): You can put this solution on YOUR website! find out which numbers cannot be used in place of the variable the rational expression. Assume it is: Remember that division by 0 is not permitted, Therefore the denominator cannot equal 0 Find these forbidden values for y: y^2 - y - 6 = 0 Factors to (y-3)(y+2) = 0 Two solutions y = +3 y = -2 These two values for y cannot be used : : Check this, substitute these two values in y^2 - y + 6, confirm that it equals 0 : Was this understandable to you?

Quadratic-relations-and-conic-sections/382728: Please help me with this: A bridge is to be built in the shape of a parabolic arch and is to have a span of 100 feet. The height of the arch at a distance of 40 ft from the center is to be 10 ft. Find the height of the arch at its center. 1 solutions Answer 271377 by ankor@dixie-net.com(15746)   on 2010-12-08 16:58:59 (Show Source): You can put this solution on YOUR website! A bridge is to be built in the shape of a parabolic arch and is to have a span of 100 feet. The height of the arch at a distance of 40 ft from the center is to be 10 ft. Find the height of the arch at its center. ; Find the equation using the form ax^2 + bx = y : From the information given, we can find two x,y coordinates x = the width of the bridge, y = height of the bridge at x x=100, y=0 and it says,"height of the arch at a distance of 40 ft from the center is to be 10 ft" The center of the bridge = 50 ft, 40 ft to left of center: x=10 x=10, y = 10 and x=100, y=0 100^2a + 100b = 0 10000a + 100b = 0 and x=10, y=10 10^2a + 10b = 10 100a + 10b = 10 Multiply the above equation by 10 subtract from the 1st equation 10000a + 100b = 0 1000a + 100b = 100 -----------------------subtraction eliminates b, find a 9000a = -100 a = a = -.011 : Find b using 100a + 10b = 10 100(-.011) + 10b = 10 -1.11 + 10b = 10 10b = 10 + 1.11 b = b = 1.111 : The equation: y = -.011x^2 + 1.11x, graph would look like this You can see that 40' either side of the center (50') the arch is 10' high : What is the height at the center? Substitute 50' for x in the equation, find y y = -.011(50^2) + 1.11(50) y = -27.5 + 55.5 y = 28 ft, which is about right on the graph

Miscellaneous_Word_Problems/382204: Tom and Jerry share out a certain sum of money in the ratio 5:4 respectively, Tom ends up with 275 $. How much money was shared out?? 1 solutions Answer 271166 by ankor@dixie-net.com(15746)   on 2010-12-07 21:55:16 (Show Source): You can put this solution on YOUR website! Tom and Jerry share out a certain sum of money in the ratio 5:4 respectively, Tom ends up with 275 $. How much money was shared out?? : let x = total amt : Tom's money is of the total, therefore: x = 275 multiply both sides by 9 5x = 9*275 5x = 2475 x = x = $495 total was shared out : : Check by finding Jerry's share: *495 = 220 = 1.25 which is

Travel_Word_Problems/381937: i sailed west to hawaii against the wind at a speed 12 knots/hour. when i returned, i sailed the same route with a wind at a speed of 18 knots/hour. what was my average speed for the entire trip? 1 solutions Answer 271067 by ankor@dixie-net.com(15746)   on 2010-12-07 18:45:02 (Show Source): You can put this solution on YOUR website! i sailed west to Hawaii against the wind at a speed 12 knots/hour. when i returned, i sailed the same route with a wind at a speed of 18 knots/hour. what was my average speed for the entire trip? : Let a = average speed for the entire trip : Let d = the one way distance : Write a time equation: time = dist/speed : to time + return time = total time + = : We don't need d, divide thru by d and you have + = Multiply by 36a to clear the denominators, results 3a + 2a = 36(2) : 5a = 72 a = a = 14.4 knot/hr is the av for the entire trip

Miscellaneous_Word_Problems/382304: solve. henry runs at a speed of 10mph and doug at a speed of 8mph henry gives doug a half mile head start. how long will it take henry to catch doug? show all work please 1 solutions Answer 271062 by ankor@dixie-net.com(15746)   on 2010-12-07 18:04:31 (Show Source): You can put this solution on YOUR website! henry runs at a speed of 10mph and doug at a speed of 8mph henry gives doug a half mile head start. how long will it take henry to catch doug? : You can do this in your head, their relative speed: 10 - 8 = 2mph : How long will it take to cover .5 mile at 2mph : Time = Dist/speed: = .25 hrs or 15 min : : We d catches h, they will have traveled the same dist: 8(.25) + .5 = 2.5 mi 10(.25) + 2.5 mi

Miscellaneous_Word_Problems/381451: i need your help!! can you answer this one? A boat made trip of 9 miles with the tide and back against the tide in 3hrs. If the tide had been half as strong the trip would had been made in 36min. less time. find the rate of the boat in still water and the rate of the stronger tide. 1 solutions Answer 270837 by ankor@dixie-net.com(15746)   on 2010-12-06 19:31:39 (Show Source): You can put this solution on YOUR website! A boat made trip of 9 miles with the tide and back against the tide in 3hrs. If the tide had been half as strong the trip would had been made in 36min. less time. find the rate of the boat in still water and the rate of the stronger tide. : Let s = boat speed in still water Let t = rate of the stronger tide then (s+t) = effective speed with the stronger tide (s-t) = effective speed against the stronger tide : Write a time equation for each scenario; Time = dist/speed : + = 3 hrs 9(s-t) + 9(s-t) = 3(s+t)(s-t) 9s - 9t + 9s + 9t = 3(s^2 - t^2) 18s = 3(s^2 - t^2) Divide both sides by 3 6s = s^2 - t^2 : At half the tide rate; (.5t) + = 3 - + = 3 - .6 + = 2.4 9(s-.5t) + 9(s+.5t) = 2.4(s+.5t)(s-.5t) 9s - 4.5t + 9s + 4.5t = 2.4(s^2 - .25t^2) 18s = 2.4(s^2 - .25t^2) divide both sides by 2.4 7.5s = s^2 - .25t^2 : multiply the above equation by 4, subtract 1st Simplified equation 30s = 4s^2 - t^2 6s = s^2 - t^2 ---------------- subtraction eliminates t^2 24s = 3s^2 simplify, divide by 3s 8 = s Boat speed in still water: 8 mph : Find t using the 1st simplified equation 6s = s^2 - t^2 t^2 = s^2 - 6s Replace s with 8 t^2 = 8^2 - 6(8) t^2 = 64 - 48 t^2 = 16 t = t = 4 mph is rate of the strong tide : : Check solutions in the original half speed tide equation + = 2.4 + = 2.4 + = 2.4 .9 + 1.5 = 2.4; confirms our solutions of s=8; t=4

Polynomials-and-rational-expressions/380798: Solve using the quadratic formula and round your answers to the nearest tenth: 3x^2+4x-2=0 I am so confused and don't even know where to start! Help! 1 solutions Answer 270350 by ankor@dixie-net.com(15746)   on 2010-12-05 10:50:27 (Show Source): You can put this solution on YOUR website! Solve using the quadratic formula and round your answers to the nearest tenth: 3x^2 + 4x - 2 = 0 : Here it is step-by-step the quadratic formula: : The equation is in the form: ax^2 + bx + c = 0;therefore: a=3; b=4; c=-2 : Replace these letters in the formula and you have: Now just do the math Remember minus a minus is a plus Find the square root of 40, there will be two solutions x = x = .3867 ~ .4 and x = x = -1.72 ~ 1.7 : Two solutions: x = .4, x= -1.7 : : It's easy to make a math mistake, so it is a good idea to check your solutions in the original equation. Replace x with .4 3(.4^2) + 4(.4) - 2 = 0 3(.16) + 1.6 - 2 = 0 .48 + 1.6 - 2 = 0 .08 ~ 0, not exact because we rounded off but close enough to check our answer ; Check it with x=-1.7 3(-1.7^2) + 4(-1.7 - 2 = 0 3(2.89) - 6.8 - 2 = 0 8.67 - 6.8 - 2 = 0 .13 ~ 0, also close : : Learn this completely, print it out and study it, it will make life much easier in algebra class. Like giving yourself a lasting Christmas present! Best regards, Carl

Linear_Equations_And_Systems_Word_Problems/380667: The sum of two nubers is 20. Their difference is 4. A. Write a system of equations that describes this situation B. Solve by elimination to find the two numbers. If you could just do A, and set it up that would be amazing 1 solutions Answer 270348 by ankor@dixie-net.com(15746)   on 2010-12-05 10:19:14 (Show Source): You can put this solution on YOUR website! The sum of two numbers is 20. Their difference is 4. A. Write a system of equations that describes this situation : Write an equation for each statement: "The sum of two numbers is 20." x + y = 20 : " Their difference is 4." x - y = 4 : Easy elimination, when you add x + y = 20 x - y = 4

Travel_Word_Problems/380556: A person drives with constant speed and after some time he sees a milestone with 2 digits. Then travels for 1 hours and sees the same 2 digits in reverse order. 1 hours later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car? 1 solutions Answer 270269 by ankor@dixie-net.com(15746)   on 2010-12-04 20:24:52 (Show Source): You can put this solution on YOUR website! A person drives with constant speed and after some time he sees a milestone with 2 digits. Then travels for 1 hour and sees the same 2 digits in reverse order. 1 hours later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car? : Let x = the 1st digit on the first mile stone Let y = the 2nd digit : Let s = speed of the car : "Then travels for 1 hour and sees the same 2 digits in reverse order." 10x + y + 1s = 10y + x 10x - x + s = 10y - y 9x + s = 9y : "1 hours later he sees that the milestone has the same 2 digits with a 0 between them." 10y + x + s = 100x + y 10y - y + s = 100x - x 9y + s = 99x : Rearrange the above two equations for elimination 9x - 9y + s = 0 -99x+9y + s = 0 ----------------adding eliminates y -90x + 2s = 0 2s = 90x s = 45x x has to equal 1, then s = 45 mph (If x=2 and s=90 mph, when added to a two digit milestone, could not be at another two digit milestone.) : Find y 9x + s = 9y 9(1) + 45 = 9y 9 + 45 = 9y simplify divide by 9 1 + 5 = y y = 6 : Speed is 45 mph : Try this: 1st milestone: 16 travel one hr +45 2nd milestone: 61 travel one hr:+45 3rd milestone:106

Travel_Word_Problems/380011: You are on a 650-mile trip by car. Your car used 8 gallons of gas to travel the first 210 miles of the trip. If you stop at this point and fill the car's 18 gallon gas tank, will you make it the rest of the way? 1 solutions Answer 270170 by ankor@dixie-net.com(15746)   on 2010-12-04 12:50:14 (Show Source): You can put this solution on YOUR website! You are on a 650-mile trip by car. Your car used 8 gallons of gas to travel the first 210 miles of the trip. If you stop at this point and fill the car's 18 gallon gas tank, will you make it the rest of the way? : Find the miles per gallon: 210 mi used 8 gallons = 26.25 mi/gal : Find the remaining distance after fill-up 650-210 = 440 mi : Find how far you can go on 18 gallon 18 * 26.25 = 472.5 miles, so you could make it the rest of the way

logarithm/380264: I cannot figure out how to make an equation in order to solve this problem and when I do try I get an outrageously huge number that is wrong. Please help me understand this... The fox polulation in a certain region has a relative growth rate of 9 percent per year. It is estimated that the population in the year 2000 was 15700. (a) Find a function that models the population t years after 2000 (t=0 for 2000). Your answer is P(t) = ____ (b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer must be an integer) _____ 1 solutions Answer 270140 by ankor@dixie-net.com(15746)   on 2010-12-04 08:18:36 (Show Source): You can put this solution on YOUR website! The fox population in a certain region has a relative growth rate of 9 percent per year. It is estimated that the population in the year 2000 was 15700. : Remember that an increase of 9% of a value, is the same as multiplying by 1.09, when the increase is added to what you already have. : (a) Find a function that models the population t years after 2000 (t=0 for 2000). Your answer is: P(t) = 15700*1.09^t You can see when t=0, there will be no change, since 1.09^0 = 1 : (b) Use the function from part (a) to estimate the fox population in the year 2008. t = 8, when the year is 2008 P(t) = 15700*1.09^8 P(t) = 15700*1.99256 P(t) = 31,283 foxes in 2008 : : Was I able to explain this to you in a way, that you understand now?

Linear_Equations_And_Systems_Word_Problems/380060: A car traveled 262 miles on a trip. During 90 miles of the trip, the car traveled through the city and had gas mileage that was 13 fewer miles per gallon than the gas mileage on the highway. If the total amount of gasoline used for the trip was 7 gallons, find the gas mileage of the car on the highway. 1 solutions Answer 270025 by ankor@dixie-net.com(15746)   on 2010-12-03 21:28:25 (Show Source): You can put this solution on YOUR website! A car traveled 262 miles on a trip. During 90 miles of the trip, the car traveled through the city and had gas mileage that was 13 fewer miles per gallon than the gas mileage on the highway. If the total amount of gasoline used for the trip was 7 gallons, find the gas mileage of the car on the highway. : Let x = gas mileage on the highway then (x-13) = gas mileage in the city : Find the number of miles traveled on the highway: 262 - 90 = 172 : gals on hwy + gals in city = 7 gallons + = 7 multiply equation by x(x-13), results 172(x-13) + 90x = 7x(x-13) : 172x - 2236 + 90x = 7x^2 - 91x : 262x - 2236 = 7x^2 - 91x Combine like terms on the right 0 = 7x^2 - 91x - 262x + 2236 A quadratic equation 7x^2 - 353x + 2236 = 0 Use the quadratic formula to find x, a=7; b=-353; c=2236 Do the math, of the two solutions, the reasonable one: x = 43 mpg on highway : : Check this by finding the total gal 172/43 = 4 90/30 = 3 ------------ total; 7 gal

Travel_Word_Problems/380125: If a train A is going 250 mph from a distance of 300 miles away, and train B is going 200 mph from opposite direction 250 miles away. How many miles will train A travel until it hits train B? 1 solutions Answer 270020 by ankor@dixie-net.com(15746)   on 2010-12-03 21:02:29 (Show Source): You can put this solution on YOUR website! If a train A is going 250 mph from a distance of 300 miles away, and train B is going 200 mph from opposite direction 250 miles away. How many miles will train A travel until it hits train B? : We can determine that the two trains are initially; 300 + 250 = 550 mi apart : They will be closing in on each other at: 250 + 200 = 450 mi per hr : Find the elapsed time that this unfortunate collision will occur = 1.22 hrs : Find how far that train A will travel when this happens 1.22(250) = 305.6 mi : : Check this by finding how far train B will travel 1.22(200) 244.4 mi : Add the two distances 305.6 + 244.4 = 550 mi, confirms our solution

Miscellaneous_Word_Problems/380164: Mary starts jogging from her home to the park at the speed of 4kph. Half an hr later, Fred follows running at a speed of 9 kph. How long before Fred overtakes Mary? 1 solutions Answer 269906 by ankor@dixie-net.com(15746)   on 2010-12-03 14:50:19 (Show Source): You can put this solution on YOUR website! Mary starts jogging from her home to the park at the speed of 4kph. Half an hr later, Fred follows running at a speed of 9 kph. How long before Fred overtakes Mary? : Let t = time required for F to catch M : When this happens, they will have traveled the same distance : convert 30 min to .5 hrs : Write a distance equation; dist = speed * time ; F's dist = M's dist 9t = 4(t+.5) 9t = 4t + 2 9t - 4t = 2 5t = 2 t = hr for F to catch M or .4 * 60 = 24 minutes : : Check solution by finding the dist each traveled, should be equal: 9 * .4 = 3.6 mi 4 *(.4 + .5) = 3.6 mi; confirms our solution of t = .4

Travel_Word_Problems/380283: If Denny who walks 60 meters per minute has already walked 1800 meters, how many minutes will it take for John who cycles 210 per minute to catch up with Denny by bike? 1 solutions Answer 269876 by ankor@dixie-net.com(15746)   on 2010-12-03 12:37:10 (Show Source): You can put this solution on YOUR website! If Denny who walks 60 meters per minute has already walked 1800 meters, how many minutes will it take for John who cycles 210 per minute to catch up with Denny by bike? : Let t = no. of minutes for J to catch D : Find out how many minutes that D has walked already = 30 minutes : When J catches D the will have traveled the same dist; Write a dist equation; dist = speed * time : J's dist = D's dist 210t = 60(t+30) 210t = 60t + 1800 210t - 60t = 1800 150t = 1800 t = t = 12 minutes for J to catch D ; : Confirm this by finding the distance of each, should be equal: 210*12 = 2520 meters 60(12+30) = 2520 meters also

Travel_Word_Problems/379790: Scott took an 8 hour trip last Saturday afternoon. He left his house and drove 40 mph to his lunch destination. He returned the same way going 30 mph. How far was the total trip if he stopped for 1 hour to eat lunch? 1 solutions Answer 269764 by ankor@dixie-net.com(15746)   on 2010-12-02 22:00:34 (Show Source): You can put this solution on YOUR website! Scott took an 8 hour trip last Saturday afternoon. He left his house and drove 40 mph to his lunch destination. He returned the same way going 30 mph. How far was the total trip if he stopped for 1 hour to eat lunch? : Let d = the one way distance : Write a time equation, time = dist/speed + = 7, (traveling time) Multiply by 120 to clear the denominators, results: 3d + 4d = 120(7) 7d = 120(7) divide both sides by 7 d = 120 mi is the one way distance then, obviously: 240 mi is the total distance

Quadratic_Equations/379912: The dimensions of Eric’s pool are 9 feet by 7 feet. He wants to build a walkway surrounding the pool so that the square footage of the walkway and pool is 143 square feet. How wide is one side of the walkway? 1 solutions Answer 269758 by ankor@dixie-net.com(15746)   on 2010-12-02 21:51:01 (Show Source): You can put this solution on YOUR website! The dimensions of Eric’s pool are 9 feet by 7 feet. He wants to build a walkway surrounding the pool so that the square footage of the walkway and pool is 143 square feet. How wide is one side of the walkway? : Let x = the width of the pool Since the walkway goes all the way around the pool the over dimensions will be: (2x+9) by (2x+7); then the overall area (pool & walkway) will be: (2x+9)*(2x+7) = 143 FOIL 4x^2 + 14x + 18x + 63 = 143 : 4x^2 + 32x + 63 - 143 = 0 : 4x^2 + 32x - 80 = 0; our old friend, the quadratic equation! Simplify, divide by 4 x^2 + 8x - 20 = 0 Factors to (x+10)(x-2) = 0 The positive solution is what we want here x = 2 ft is the width of the walkway : : Check this solution by finding the area with the overall dimensions: (4+7) * (4+9) = 11 * 13 = 143, confirms our solution of x=2

Quadratic-relations-and-conic-sections/379335: i really need help with this problem. i'm clueless 2Y=3X-Xsquared X+2Y=-12 1 solutions Answer 269746 by ankor@dixie-net.com(15746)   on 2010-12-02 21:15:29 (Show Source): You can put this solution on YOUR website! 2Y = 3X - X^2 X + 2Y = -12 Let's rearrange it like this ------>x + 2y = -12 x^2 - 3x + 2y = 0 --------------------subtraction eliminates y, and we have -x^2 + 4x = -12 Multiply by -1, x^2 - 4x = 12 x^2 - 4x - 12 = 0; a quadratic equation Factors to: (x-6)(x+2) = 0 Two solutions x = 6 x = -2 : Use the 1st original equation to find y, using x=6 2Y = 3X - X^2 2Y = 3(6) - 6^2 2y = 18 - 36 2y = -18 y = y = -9 : 1st solution: x=6; y=-9 : Check this in the original 2nd equation X + 2Y = -12 6 + 2(-9) = -12; confirms this solution : : What about x = -2 Use the 1st original equation to find y, using x=-2 2Y = 3X - X^2 2Y = 3(-2) - (-2^2) 2y = -6 - 4 2y = -10 y = y = -5 : 2nd solution x =-2; y = -5 : Check this in the original 2nd equation X + 2Y = -12 -2 + 2(-5) = -12; confirms this solution also : : Did this provide a clue or two for you, did it make sense?

Travel_Word_Problems/379795: A plane whose air speed is 150 miles per hour flew from Abott to Blair in 2 hours with a tail wind. on the return trip against the same wind, the plane was still 60 miles from abbot after 2 hours. find the wind speed and the distance between abbot and blair? i have no clue how to even begin please help its much appreciated!:) 1 solutions Answer 269697 by ankor@dixie-net.com(15746)   on 2010-12-02 19:18:40 (Show Source): You can put this solution on YOUR website! A plane whose air speed is 150 miles per hour flew from Abott to Blair in 2 hours with a tail wind. on the return trip against the same wind, the plane was still 60 miles from abbot after 2 hours. find the wind speed and the distance between abbot and blair? : Let w = the wind speed then (150+w) = effective speed with the wind and (150-w) = effective speed against the wind : Write a distance equation using both trips. (dist = time * speed) : Outbound dist = return dist + 60 mi 2(150+w) = 2(150-w) + 60 Divide thru by 2, results: 150 + w = 150 - w + 30 w + w = 150 - 150 + 30 2w = 30 w = w = 15 mph is the wind speed : Find the distance d = 2(150+15) d = 2(165 d = 330 mi : Check this on the return trip distance d = 2(150-15) d = 2(135) d = 270, which is 60 mi less as the problem stated

Linear_Equations_And_Systems_Word_Problems/379688: Please Help, I dont have to have an answer maybe just show me how 1 solutions Answer 269663 by ankor@dixie-net.com(15746)   on 2010-12-02 18:02:04 (Show Source): You can put this solution on YOUR website! Creative Mart sells paint supplies at discount prices. On a particular day they sold 238 paint roller covers. some of these were 7' rollers, which sold for $1.97 each, while the rest were for 9' rollers, which sold for $2.29 each. how many types of rollers where sold if the sales totaled 518.78. : You can write two equations from the givien information Let x = 7' rollers Let y = 9' rollers : Total item equation x + y = 238 y = (238-x); use this for substitution in the 2nd equation : 1.97x + 2.29y = 518.78

Travel_Word_Problems/379411: Anna and John both drive to their new home 600 miles away. Anna drives the family car at an average speed of 65 mph. John drives the removal truck at an average speed of 50 mph. During the trip, Anna stops for a total of 2 hours and 20 minutes, John stops for 90 minutes. What is the difference in minutes between their arrival times? 1 solutions Answer 269616 by ankor@dixie-net.com(15746)   on 2010-12-02 14:17:24 (Show Source): You can put this solution on YOUR website! Anna and John both drive to their new home 600 miles away. Anna drives the family car at an average speed of 65 mph. John drives the removal truck at an average speed of 50 mph. During the trip, Anna stops for a total of 2 hours and 20 minutes, John stops for 90 minutes. What is the difference in minutes between their arrival times? : change 2 hr 20 min to hrs change 90 min to hrs : Write a total time equation for each Truck: + = 13.5 Car: + = 11.56 hrs ---------------------------------------------- Time difference between them: 1.1678 hrs Change to minutes 60 + .1678(60) = 70.1 min between them

Exponential-and-logarithmic-functions/379109: Superman has been disabled by a nearby amount of Kryptonite. He cannot regain his power until 90% of the kryptonite disntegrates. If the half life of Kryptonite is 5 days, how long will it be before he regains his powers? 1 solutions Answer 269378 by ankor@dixie-net.com(15746)   on 2010-12-01 22:07:38 (Show Source): You can put this solution on YOUR website! . He cannot regain his power until 90% of the kryptonite disntegrates. If the half life of Kryptonite is 5 days, how long will it be before he regains his powers? : The remaining amt = .1 : The half life equation 2^(-t/5) = .1 = = -3.3212 t = -5*-3.3212 t = 16.6 days : : Check on a calc: enter 2^(-16.6/5}, results .100

Numbers_Word_Problems/379102: seven times the sum of a number and four is the same as eight 1 solutions Answer 269326 by ankor@dixie-net.com(15746)   on 2010-12-01 19:57:52 (Show Source): You can put this solution on YOUR website! 7(x + 4) = 8 7x + 28 = 8 7x = 8 - 28 7x = -20 x = x = -2.857, a disappointing number, let's see if it works in the original eq : 7(-2.857 + 4) = 8 7(1.143) = 8 8.00 = 8; therefore x =-2.857 is correct

Miscellaneous_Word_Problems/379084: solve. the cost of admission to the spring carnival was $50 for a group of 9 children and 2 adults. the admission was $61 for another group of 10 children and 3 adults. what was the admission price for each child? what was the admission price for each adult? this is what i have so far, im stuck. children=c adults=a $50=9c+2a $61=10c+3a 1 solutions Answer 269320 by ankor@dixie-net.com(15746)   on 2010-12-01 19:49:28 (Show Source): You can put this solution on YOUR website! the cost of admission to the spring carnival was $50 for a group of 9 children and 2 adults. the admission was $61 for another group of 10 children and 3 adults. what was the admission price for each child? what was the admission price for each adult? : I would write it like this (but your way is OK too) 9c + 2a = 50 10c + 3a = 61 : To use elimination, multiply the 1st equation by 3, the 2nd equation by 2: 27c + 6a = 150 20c + 6a = 122 ----------------Subtraction eliminates a, find c 7c = 28 c = c = $4 for children : Use the 1st original equation to find a, replace c with 4 9c + 2a = 50 9(4) + 2a = 50 36 + 2a = 50 2a = 50 - 36 2a = 14 a = a = $7 for adults : : We can check these solutions in the 2nd original equation 10c + 3a = 61 10(4) + 3(7) = 61 40 + 21 = 61, confirms our solution : How about this, did it make sense to you now?

Trigonometry-basics/378980: a ferris wheel has a radius of 80 feet. two particular cars are located such that the central angle between them is 165 degrees. to the nearest tenth, what is the measure of the intercepted arc between those two cars on the farris wheel? 1 solutions Answer 269312 by ankor@dixie-net.com(15746)   on 2010-12-01 19:35:26 (Show Source): You can put this solution on YOUR website! a ferris wheel has a radius of 80 feet. two particular cars are located such that the central angle between them is 165 degrees. to the nearest tenth, what is the measure of the intercepted arc between those two cars on the Ferris wheel? : Find the circumference, then find what fraction of that value, is the arc. a = a = 230.4 ft

Problems-with-consecutive-odd-even-integers/378593: can you please help me with this define avariable write an equation and solve each problem:one half of a number decreased by two thirds is two less than one fifth of the number find the number 1 solutions Answer 269307 by ankor@dixie-net.com(15746)   on 2010-12-01 19:27:52 (Show Source): You can put this solution on YOUR website! Let x = "the number" : Write an equation just as it says: "one half of a number decreased by two thirds is two less than one fifth of the number find the number x - = x - 2 If we multiply equation by 30, we can get rid of those annoying fractions, results: 15x - 20 = 6x - 30(2) 15x = 6x - 60 + 20 15x - 6x = -60 + 20 9x = -40 x = x = -4.44, a rather disappointing number, see if it works in the original equation : (-4.44) - = (-4.44) - 2 -2.22 - .67 = -.89 - 2 -2.89 = -2.89; so I guess x = -4.44 is the solutions

Polynomials-and-rational-expressions/378533: How do I solve the equation 5/6 of N= -60 1 solutions Answer 269297 by ankor@dixie-net.com(15746)   on 2010-12-01 19:09:10 (Show Source): You can put this solution on YOUR website! solve the equation 5/6 of N= -60 : N = -60 Multiply both sides by 6, gets rid of the fraction, results 5N = 6(-60) 5N = -360 divide both sides by 5 N = N = -72 : : See if this is true, replace N with 72 in the original equation (-72) = -60 cancel 6 into 72 -12 * 5 = -60

Square-cubic-other-roots/378931: Set up an equation and solve the problem: The sum of the ares of two squares is 4,477 square inches. Each side of the larger square is 6 times the length of a side of the smaller square. Find the length of a side of the smaller square. Thanks in advance! 1 solutions Answer 269288 by ankor@dixie-net.com(15746)   on 2010-12-01 18:45:00 (Show Source): You can put this solution on YOUR website! The sum of the areas of two squares is 4,477 square inches. Each side of the larger square is 6 times the length of a side of the smaller square. Find the length of a side of the smaller square. : Let x = side of the small square then 6x = side of the large square : Large sq area + small sq area = 4477 (6x)^2 + x^2 = 4477 36x^2 + x^2 = 4477 37x^2 = 4477 Divide both sides by 37, results x^2 = 121 x = x = 11 inches is the side of the smaller square : : Check solution by finding the total area 66^2 + 11^2 = 4356 + 121 = 4477, confirms our answer

Linear_Equations_And_Systems_Word_Problems/379009: Plutonium 239 is used as fuel for some nuclear reactors, and also as the fissionable material in atomic bombs. it has a half life of 24400 years. how long would it take 10 grams of plutonium 239 to decay to 1 gram?(round your answer to three significant digits) 1 solutions Answer 269264 by ankor@dixie-net.com(15746)   on 2010-12-01 18:07:18 (Show Source): You can put this solution on YOUR website! Plutonium 239 is used as fuel for some nuclear reactors, and also as the fissionable material in atomic bombs. it has a half life of 24400 years. how long would it take 10 grams of plutonium 239 to decay to 1 gram?(round your answer to three significant digits) : The half life formula: Ao*2^(-t/h) = A where A = resulting amt after t yrs Ao = initial amt t = time in yrs h = half-life of substance : 10*2(-t/24400) = 1 Divide both sides by 10 2(-t/24400) = .1 Using nat logs ln(2(-t/24400)) = ln(.1) ln(2) = ln(.1) = Using a calc = -3.32193 Multiply both sides by -24400 t = 81,055.0456 years : : Check solution on a calc; enter 10*2^(-81055/24400) results: 1.000

Percentage-and-ratio-word-problems/379118: What is the answer to this word problem with work shown? To pass a course, a student must have an average on four exams of at least 70. If a student scores 40, 78, and 88 on the first three tests, what must he earn on the fourth exam to pass the course? 1 solutions Answer 269244 by ankor@dixie-net.com(15746)   on 2010-12-01 17:07:47 (Show Source): You can put this solution on YOUR website! To pass a course, a student must have an average on four exams of at least 70. If a student scores 40, 78, and 88 on the first three tests, what must he earn on the fourth exam to pass the course? : Let x = required grade to average at least 70 : => 70 Multiply both sides by 4, add up the given values x + 206 => 280 x => 280 - 206 x => 74 to pass the course

Age_Word_Problems/379155: Aunt is 7 years younger than uncle and ages total 71. I was thinking A + B - 7 = 71. I added 7 to each side to make it A + B = 71 + 7. A + B = 78. divided 78 by two to make 39 and then subtracted the 7 from 39 to make 32. so one is 32 and one is 39 and it totals 71 but I am thinking that I am making more work than necessary? this is a 4th grade problem and we are just starting. thank you 1 solutions Answer 269242 by ankor@dixie-net.com(15746)   on 2010-12-01 17:01:38 (Show Source): You can put this solution on YOUR website! Do it this way. Let a = Aunt's age then (a+7) = Uncle's age : a + (a+7) = 71 2a = 71 - 7 2a = 64 a = 32 is Aunt's age and 39 = uncles age : Check: 32 + 39 = 71