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 Sequences-and-series/222358: hey there thanks ,the question is- the difference between two numbers is 4 and the sum of their squares is80 less than three times their product. Find the numbers thanks again. xx 1 solutions Answer 166605 by ankor@dixie-net.com(15645)   on 2009-10-06 15:45:55 (Show Source): You can put this solution on YOUR website!the difference between two numbers is 4 x - y = 4 or x = (y + 4) : "the sum of their squares is 80 less than three times their product." x^2 + y^2 = 3xy - 80 x^2 - 3xy + y^2 = -80 ; replace x with (y+4) (y+4)^2 - 3y(y+4) + y^2 = -80 y^2 + 8y + 16 - 3y^2 - 12y + y^2 = -80 : Combine like terms y^2 + y^2 - 3y^2 + 8y - 12y + 16 + 80 = 0 : -y^2 - 4y + 96 = 0 : Multiply by -1 y^2 + 4y - 96 = 0 : Factor: (y+12)(y-8) = 0 : Positive solution y = 8 find x x = 8 + 4 x = 12 : Check 12^2 + 8^2 = 3*12*8 - 80 144 + 64 = 288 - 80 208 = 208 : : How about the solution y = -12? then x = -12 - 4 x = -16 : -16^2 + -12^2 = 3*-16*-12 - 80 256 + 144 = 576 - 80 not a solution
 Percentage-and-ratio-word-problems/222147: If a 5'10" man is 350% of his length as a newborn baby, how many inches long was he when he was born?1 solutions Answer 166592 by ankor@dixie-net.com(15645)   on 2009-10-06 15:16:35 (Show Source): You can put this solution on YOUR website!If a 5'10" man is 350% of his length as a newborn baby, how many inches long was he when he was born? : Convert 5'10" to inches: 5*12 + 10 = 70 inches : Let b = length of baby 3.5b = 70 b = b = 20" long
 Inequalities/222057: adele went to the post office to buy stamps and postcards. she bought a total of 25 stamps some 39 cent stamps and the rest 23 cent postcards. if she paid \$8.47 altogether, how many 39 cent stamps did she buy?1 solutions Answer 166589 by ankor@dixie-net.com(15645)   on 2009-10-06 14:59:00 (Show Source): You can put this solution on YOUR website! she bought a total of 25 stamps some 39 cent stamps and the rest 23 cent postcards. if she paid \$8.47 altogether, how many 39 cent stamps did she buy? : Let s = no. of 39 cent stamps and Let p = no. of 23 cent stamps ; write an equation for each statement: : "she bought a total of 25 stamps some 39 cent stamps and the rest 23 cent" s + p = 25 arrange for use as substitution p = (25-s) : "if she paid \$8.47 altogether," let's just deal in cents 39s + 23p = 847 : Replace p with (25-s) in the above equation, find s 39s + 23(25-s) = 847 39s + 575 - 23s = 847 39s - 23s = 847 - 575 16s = 272 s = s = 17 ea 39 cent stamps and 25 - 17 = 8 ea 23 cent stamps ; ; Is this true? .39(17) + .23(8) = 6.63 + 1.84 = 8.47, seems to be
 Numbers_Word_Problems/222054: what is the answer to this word problem "The Difference between two numbers is 16. Five times the smaller is the same as 8 less than twice the larger. find the numbers?" And this one also please, The sum of two numbers is the same as four times the smaller number, if twice the larger is decreased by the smaller, the result is 30. find the numbers?1 solutions Answer 166585 by ankor@dixie-net.com(15645)   on 2009-10-06 14:43:50 (Show Source): You can put this solution on YOUR website!I am going to do better than give you the answer, I am going to show you how to do it. : write an equation for each statement, let the numbers be x & y : "The Difference between two numbers is 16." x - y = 16 Arrange this to be used for substitution x = y + 16 : Five times the smaller is the same as 8 less than twice the larger." 5y = 2x - 8 : Replace x in the above with (y+16). find y 5y = 2(y+16) - 8 5y = 2y + 32 - 8 5y - 2y = 24 3y = 24 y = y = 8 : You should be able to find x now ; : "The sum of two numbers is the same as four times the smaller number," x + y = 4y x = 4y - y x = 3y : "twice the larger is decreased by the smaller, the result is 30. 2x - y = 30 : Replace x with 3y in the above 2(3y) - y = 30 6y - y = 30 5y = 30 You should be able to handle it now.
 Polynomials-and-rational-expressions/222153: Can someone please assist me with this equation? I need to find the GCF but I am not sure what to do after that point. 22uw^7z^8 and 20u^3w^4 I believe the GCF is 2 this one find the least common multiple 8tuz^9 and 2t^3u^7 (this one has me completely lost)1 solutions Answer 166581 by ankor@dixie-net.com(15645)   on 2009-10-06 14:31:00 (Show Source): You can put this solution on YOUR website!find the GCF 22uw^7z^8 and 20u^3w^4 : 2uw^4 would be the GCF : 2uw^4(11w^3z^8) and 2uw^4(10u^2) ; : least common multiple 8tuz^9 and 2t^3u^7 : Each term has to go into the multiple at least 1 time, so that would be: 8t^3u^7z^9
 Travel_Word_Problems/222018: Juan drives to work. Because of traffic conditions, he averages 22 mph. He retunrs home averaging 32 mph. The total travel time is 2 1/4 hours. Write the equation to find the time Juan spends driving to work.1 solutions Answer 166574 by ankor@dixie-net.com(15645)   on 2009-10-06 14:20:40 (Show Source): You can put this solution on YOUR website!Because of traffic conditions, he averages 22 mph. He returns home averaging 32 mph. The total travel time is 2 1/4 hours. Write the equation to find the time Juan spends driving to work. : Change 2 hrs to 2.25 hrs : Let t = His time to work then (2.25-t) = His time from work : Distance and to and from is equal. Write a distance equation and find t 22t = 32(2.25-t)
 Graphs/222022: okay, i just dont know how to graph this problem. |n+8|>=3 my work was: n+8>=3 n+8>=-3 -8 -8 -8 -8 n>=-5 n>=-11 now what?1 solutions Answer 166567 by ankor@dixie-net.com(15645)   on 2009-10-06 14:12:49 (Show Source): You can put this solution on YOUR website!|n+8| > = 3 my work was: n + 8 > = 3; this right, so you have; n >= 3 -8 n >= -5 which you have and n + 8 <= -3; when you make 3 negative, you have to reverse the inequality sign n <= -3 - 8 n <= -11 : The solution: n >= -5 n <= -11 : : Note that any value between -11 and -5 would not satisfy the inequality But any value below -11 and above -5 would satisfy
 Finance/222144: I need help in my algebra class setting up this word problem. Jake invested \$6,000, part at 6% simple interest and part at 4%simple interest for a period of 1 year. How much did she invest at each rate if each account earned the same interest? 1 solutions Answer 166556 by ankor@dixie-net.com(15645)   on 2009-10-06 13:49:32 (Show Source): You can put this solution on YOUR website!Jake invested \$6,000, part at 6% simple interest and part at 4%simple interest for a period of 1 year. How much did she invest at each rate if each account earned the same interest? ; Let x = amt invested at 6% then (6000-x) = amt invested a 4% : int at 6% = int at 4% .06x = .04(6000-x) .06x = 240 - .04x .06x + .04x = 240 .10x = 240 x = x = \$2400 invested at 6% then 6000 - 2400 = \$3600 invested at 4% ; : Check solution by find that amt of interest earned by each .06(2400) = \$144 .04(3600) = \$144
 Equations/222031: I have a graph that shows the wind speed for an F4 Tornado is 207-260mph. My question is: Write a pair of inequalities that best represents the wind speed (w) for an F4 tornado. Is the answer w207-w260?1 solutions Answer 166553 by ankor@dixie-net.com(15645)   on 2009-10-06 13:43:05 (Show Source): You can put this solution on YOUR website!Write a pair of inequalities that best represents the wind speed (w) for an F4 tornado. wouldn't be: w =< 260 and w => 207
 Polynomials-and-rational-expressions/222189: factor completely 27x^3+1251 solutions Answer 166545 by ankor@dixie-net.com(15645)   on 2009-10-06 13:29:02 (Show Source): You can put this solution on YOUR website!27x^3 + 125 : You can see both coefficients are perfect cubes, 3 and 5 : Use the special factoring form for the "sum of cubes" (x + y)(x^2 - xy + y^2) : In this problem: (3x + 5)(9x^2 - 15x + 25)
 Numbers_Word_Problems/222026: find four consecutive ODD integers such that four less than twice the second has the same value as three times the number that is one more than the third. 1 solutions Answer 166535 by ankor@dixie-net.com(15645)   on 2009-10-06 13:06:01 (Show Source): You can put this solution on YOUR website!find four consecutive ODD integers x, x+2, x+4, x+6 ; such that four less than twice the second has the same value as three times the number that is one more than the third. 2(x+2) - 4 = 3((x+4)+1) 2x + 4 - 4 = 3(x+5) 2x = 3x + 15 -15 = 3x - 2x x = -15 : The four numbers: -15, -13, -11, -9 : : Check solution in the given statement: "four less than twice the second has the same value as three times the number that is one more than the third." 2(-13) - 4 = 3(-11 + 1) -26 - 4 = 3(-10)
 Miscellaneous_Word_Problems/221967: two trains depart from a station, traveling in opposite directions. the train that departs at 6:30 AM travels 15 km/h faster than the train that departs at 6 AM. At 7 AM they are 135 km apart. Determine the rate of each train.1 solutions Answer 166500 by ankor@dixie-net.com(15645)   on 2009-10-06 09:57:27 (Show Source): You can put this solution on YOUR website!two trains depart from a station, traveling in opposite directions. the train that departs at 6:30 AM travels 15 km/h faster than the train that departs at 6 AM. At 7 AM they are 135 km apart. Determine the rate of each train. : Let s = speed of the train that departs at 6 AM then (s+15) = speed of the train that departs at 6:30 : At 7 AM: the 1st train travel time is 1 hr the 2nd train travel time is .5 hr : Write a distance equation: Dist = time * speed : 1s + .5(s+15) = 135 1s + .5s + 7.5 = 135 1s + .5s = 135 - 7.5 1.5s = 127.5 s = s = 85 mph is the speed of the 6 AM train : 85 + 15 = 100 mph is the speed of the 6:30 train ; ; Check solution in the distance equation 1*85 + .5*100 = 85 + 50 = 135
 Linear-systems/222186: Solve the system by the addition method showing all work: (1/6)x + (1/4)y = -2 x – y = -6 1 solutions Answer 166499 by ankor@dixie-net.com(15645)   on 2009-10-06 08:48:52 (Show Source): You can put this solution on YOUR website!Solve the system by the addition method showing all work: (1/6)x + (1/4)y = -2 x – y = -6 multiply the 1st equation by 4. In the 2nd equation change coefficient of x to 6/6 x + y = -8 x - y = - 6 -----------------addition eliminates y and you have: x = -14 Multiply both sides by 6 10x = 6(-14) 10x = -84 x = x = -8.4 : Find y using x - y = -6 -8.4 - y = -6 Multiply equation by -1 8.4 + y = 6 y = 6 - 8.4 y = -2.4 ; : Check solution in the 1st equation (1/6)(-8.4) + (1/4)(-2.4) = -2 -1.4 + -.6 = -2
 Length-and-distance/222064: please help me find this answer. A is the midpoint of segment DE, and DA=12. I and N are trisection points of segment DE. Find segment AN. There is also a diagram that shows a line and points which are in this order: D, I, A, N, E.1 solutions Answer 166438 by ankor@dixie-net.com(15645)   on 2009-10-05 21:35:10 (Show Source): You can put this solution on YOUR website!A is the midpoint of segment DE, and DA=12. I and N are trisection points of segment DE. Find segment AN. There is also a diagram that shows a line and points which are in this order: D, I, A, N, E. : From the information given we know that DE = 2*12 = 24 Trisect 24: 24/3 = 8 : If D=0, I=8, A=12, N=16, E= 24 therefore AN = 4
 Travel_Word_Problems/222063: Debbie traveled by Boat 5 miles upstream to fish. Because of the 4mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water?1 solutions Answer 166436 by ankor@dixie-net.com(15645)   on 2009-10-05 21:23:08 (Show Source): You can put this solution on YOUR website!Debbie traveled by boat 5 miles upstream to fish. Because of the 4 mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water? : Let s = boat speed in still water then (s-4) = speed upstream and (s+4) = speed down stream : Convert 20 min to hrs: 20/60 = hr : Write a time equation: time = Upstream time = downstream time + 20 minutes (1/3 hr) = + : To clear out these denominators, multiply equation by 3(s+4)(s-4) 3(s+4)(s-4)* = 3(s+4)(s-4)* + *3(s+4)(s-4) Results in : 15(s+4) = 15(s-4) + (s+4)(s-4) : 15s + 60 = 15s - 60 + s^2 - 16 : 0 = 15s - 15s - 60 - 60 + s^2 - 16 : 0 = s^2 - 136 : s^2 = 136 s = s = 11.66 mph speed in still water : : Check solution on calc: (speed up = 7.66 and speed down = 15.66) 5/7.66 - 5/15.66 = .3333 which is 1/3 of an hr
 Mixture_Word_Problems/222048: How many grams of pure silver must a silversmith mix with a 45% silver alloy to produce 200 grams of a 50% alloy?1 solutions Answer 166434 by ankor@dixie-net.com(15645)   on 2009-10-05 21:16:30 (Show Source): You can put this solution on YOUR website!How many grams of pure silver must a silversmith mix with a 45% silver alloy to produce 200 grams of a 50% alloy? : Let x = amt of pure silver required to do this Then (200-x) = amt of 45% silver alloy required ; x + .45(200-x) = .50(200) : x + 90 - .45x = 100 x - .45x = 100 - 90 .55x = 10 x = x = 18.2 grams of pure silver : : Check solution: 200-18.2 = 181.8 grams of 45% silver 18.2 + .45(181.8) = .5(200) 18.2 + 81.8 = 100 100 = 100
 Travel_Word_Problems/222124: Train A and B are traviling the same direction on parallel tracks. Train A is traviling at 100 miles per hour and train B is traviling at 120 miles per hour. Train A passes a station at 5:25 p.m. If train B passes the same station at 5:40 p.m., at what time will train B catch up with train A?1 solutions Answer 166431 by ankor@dixie-net.com(15645)   on 2009-10-05 21:08:31 (Show Source): You can put this solution on YOUR website!Train A and B are traveling the same direction on parallel tracks. Train A is traveling at 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes a station at 5:25 p.m. If train B passes the same station at 5:40 p.m., at what time will train B catch up with train A? : from the given information, we know that train B is 15 min (.25 hr) behind train A, when train A passes the station : The distance between the trains at this time: .25 * 120 = 30 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 + 30 mi 120t = 100t + 30 120t - 100t = 30 20t = 30 t = t = 1.5 hr or 1 hr 30 min : 5:25 + 1:30 = 6:55 pm, B catches A : : Check solution by finding the distances (train b travels 30 mi more than train b) 120 * 1.5 = 180 mi 100 * 1.5 = 150 mi ------------------- difference = 30 mi
 Miscellaneous_Word_Problems/221986: a rescue helicopter is flying from an aircraft carrier 350 mi to peral harbor hospital. the point of no return is the point here it would take as much time to fly back to the aircraft carrier as it would to fly on to pearl harbor. the airspeed of the helicopter is 175 mi/h and it is flying into a 25 mi/h headwind. a. calculate the total time for the helicopter to fly to pearl harbor b. once the helicopter is at the point of no return, determine the time it will take to complete the trip. c. use the results from part a and b to determine the time for the helicopter to reach the point of no return.1 solutions Answer 166404 by ankor@dixie-net.com(15645)   on 2009-10-05 19:22:23 (Show Source): You can put this solution on YOUR website!a rescue helicopter is flying from an aircraft carrier 350 mi to Pearl harbor hospital. The point of no return is the point where it would take as much time to fly back to the aircraft carrier as it would to fly on to pearl harbor. The airspeed of the helicopter is 175 mi/h and it is flying into a 25 mi/h headwind. a. calculate the total time for the helicopter to fly to pearl harbor t = t = t = 2 hrs (2 hrs 20 min) : b. once the helicopter is at the point of no return, determine the time it will take to complete the trip. : Let p = point of no return (miles from carrier) Then (350-p) = miles from Pearl Harbor : return to carrier = continue to Pearl = = Cross multiply 150p = 200(350-p) 150p = 70000 - 200p 150p + 200p = 70000 350p = 70000 p = p = 200 mi from carrier is point of no return. (150 mi from Pearl) : c. use the results from part a and b to determine the time for the helicopter to reach the point of no return. t = t = t = 1 hrs : : This checks out, it would take 1 hr to cover the remaining 150 mi at 150 mph 1 + 1 = 2 as found in part a and to return to the carrier, with the wind, 200 mi at 200 mph = 1 hr also
 Linear-equations/221859: Find three consecutive even integers such that if the largest integer is subtracted from four times the smallest , the result is 6 more than twice the sum of the two smallest integers 1 solutions Answer 166318 by ankor@dixie-net.com(15645)   on 2009-10-05 16:21:38 (Show Source): You can put this solution on YOUR website!Find three consecutive even integers x, (x+2), (x+4) : the largest integer is subtracted from four times the smallest, the result is 6 more than twice the sum of the two smallest integers. : 4x - (x+4) = 2(x + (x+2)) + 6 Remove the brackets 4x - x - 4 = 2(2x+2) + 6 3x - 4 = 4x + 4 + 6 3x - 4 = 4x + 10 3x - 4x = 10 + 4 -x = 14 x = -14 : -14, -12, -10 are the three integers : check solution in the statement: "the largest integer is subtracted from four times the smallest, the result is 6 more than twice the sum of the two smallest integers" 4(-14) - (-10) = 2(-14 + -12) + 6 -56 + 10 = 2(-26) + 6 -56 + 10 = -52 + 6 -46 = -46
 Quadratic_Equations/221675: Hi, I am having a problem with a question that reads the following: Use the quadratic formula to solve the equation for x in terms of y. 8x^2-8xy+6(1-y^2)=0 Thanks in advance. 1 solutions Answer 166312 by ankor@dixie-net.com(15645)   on 2009-10-05 15:56:54 (Show Source): You can put this solution on YOUR website!Use the quadratic formula to solve the equation for x in terms of y. : : In this problems a=8; b=-8y; c=6(1-y^2) : : : ; combine like terms : ; factor out 64 : ; extract square root of 64 : ; divide both 8's into 16
 Miscellaneous_Word_Problems/221798: Please help me solve this problem...I dont know how to start solving this.. A 10-quart container is filled with water. One quart of water is drained out and replaced with alcohol. After mixing, a quart of the soluti0n is drained out and replaced with alcohol. This process continued until 5quarts of alcohol have been put into the container. The solution in the container is then what percent of alcohol? Thank you in advance..1 solutions Answer 166271 by ankor@dixie-net.com(15645)   on 2009-10-05 12:47:48 (Show Source): You can put this solution on YOUR website!A 10-quart container is filled with water. One quart of water is drained out and replaced with alcohol. After mixing, a quart of the soluti0n is drained out and replaced with alcohol. This process continued until 5quarts of alcohol have been put into the container. The solution in the container is then what percent of alcohol? : try it step by step : After the 1st replacement, its a .1(10) mixture : 2nd replacement: .1(10-1) + 1 = .1(9) + 1 = .9 + 1 = 1.9 = 1.9 qt of alcohol that's a = .19(10) mixture : 3rd replacement .19(10-1) + 1 .19(9) + 1 1.71 + 1 = 2.71 qt of alcohol that's = .27(10) mixture : 3rd replacement .27(10-1) + 1 = .27(9) + 1 = 2.44 + 1 = 3.44 gt of alcohol that's = .344(10) mixture : 4th replacement .344(10-1) + 1 = .344(9) + 1 = 3.096 + 1 = 4.096 gt of alcohol that's = .4096(10) mixture : 5th replacement .4096(10-1) + 1 = .4096(9) + 1 = 3.6864 + 1 = 4.6864 qt of alcohol that's = .46864(10) mixture : we can say 46.864% alcohol now
 Equations/221662: Hi, I am having trouble with a word problem. The problem states "When a rock is dropped from a cliff into an ocean, it travels approximately 16t^2 ft in t seconds. If the splash is heard 4.5 seconds later and the speed of sounds is 1100ft/sec, approximate the height of the cliff." Thanks in advance.1 solutions Answer 166247 by ankor@dixie-net.com(15645)   on 2009-10-05 08:21:04 (Show Source): You can put this solution on YOUR website!When a rock is dropped from a cliff into an ocean, it travels approximately 16t^2 ft in t seconds. If the splash is heard 4.5 seconds later and the speed of sounds is 1100ft/sec, approximate the height of the cliff." : t = time for the rock to reach the water then (4.5-t) = time for the sound to reach the top of the cliff : Both the rock and the sound will travel the same distance. Write a distance equation : 16t^2 = 1100(4.5-t) 16t^2 = 4950 - 1100t : Arrange as a quadratic equation 16t^2 + 1100t - 4950 = 0 ; Simplify, divide by 2 8t^2 + 550t - 2475 : Use the quadratic formula to find t: in this problem x=t; a=8; b=550; c=-2475 : : : we only want the positive solution here t = t = 4.239 sec for the rock to hit the water and 4.5 - 4.238 = .261 sec for the sound to come back : : You can use either value to find the height of the cliff 16(4.238^2) = 287 ft and 1100(.261) = 287 ft : : Make sense to you?
 Equations/221380: Can someone please solve this sum for me and explain how you got to the answer? Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass beofre the second cyclist catches up with the first from the time the second cyclist started biking? muchos gracias (:1 solutions Answer 166173 by ankor@dixie-net.com(15645)   on 2009-10-04 20:20:28 (Show Source): You can put this solution on YOUR website!Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking? ; Let t = travel time of the 2nd cyclist then (t+3) = travel time of the 1st cyclist : When the 2nd overtakes the 1st, they will have traveled the same distance. Write a distance equation using this fact: Dist = speed * time : 2nd cyclist dist = 1st cyclist dist 10t = 6(t+3) 10t = 6t + 18 10t - 6t = 18 4t = 18 t = t = 4.5 hrs from the time the 2nd cyclist starts ; : Check solution by finding the distance traveled by each (should be equal) 10*4.5 = 45 mi 6*7.5 = 45 mi; confirms our solution : : Answering your question about the time. it should be apparent to you that the 1st cyclist was on the road 3 hr longer than the 2nd cyclist "t", hence we call 1st cyclist time "t+3"
 Miscellaneous_Word_Problems/221465: It takes a train 7 seconds to pass by a stationary observer and 26 seconds to travel the length of a station 380 meters long. What is the speed of the train and its length? 1 solutions Answer 166169 by ankor@dixie-net.com(15645)   on 2009-10-04 20:10:00 (Show Source): You can put this solution on YOUR website!It takes a train 7 seconds to pass by a stationary observer and 26 seconds to travel the length of a station 380 meters long. What is the speed of the train and its length? : let s = speed of the train in meters/sec : 7s = length of the train : time of the front of the train passing the platform It passes the platform 26-7 = 19 sec : s = s = 20 meters/sec : Train length = 7s 7(20) = 140 meters long : The speed of train in km/hr = = 72 km/hr
 Linear_Equations_And_Systems_Word_Problems/221258: Diophantus a greek mathematician is considered by many as the "Father of Algeria" because of his works in the syncopation of algebra. In his epitaph, the following is scripted. "A sixth of his life was spent in childhood. A twelfth as a youth, and a seventh as a bachelor. Five years after his marriage, his son was born but died four years before his own death at half his age".1 solutions Answer 166132 by ankor@dixie-net.com(15645)   on 2009-10-04 18:00:17 (Show Source): You can put this solution on YOUR website!Diophantus passed one-sixth of his life in childhood, one-twelfth in youth, one-seventh more as a bachelor. Five years after his marriage, a son was born who died four years before his father, at half his father's [final] age. How old was Diophantus when he died. : Let x = his final age : a lengthy but simple equation Final age = child + youth + bach + marriage + son's age + 4 x = x + x + x + 5 + x + 4 : Common denominator of 12*7 = 84 x = x + x + x + 5 + x + 4 : x = x + 9 : x - x = 9 : x = 9 : x = 84 is his final age : Check: 14 + 7 + 12 + 5 + 42 + 4 = 84
 Human-and-algebraic-language/221446: A colonel, on attempting to draw up his regiment in the form of a solid square, finds that he has 30 men left over, and that he would require 25 soliders in his regiment to increase the side of the square by one soldier. How many soldiers are there in the regiment?1 solutions Answer 166101 by ankor@dixie-net.com(15645)   on 2009-10-04 16:54:00 (Show Source): You can put this solution on YOUR website!A colonel, on attempting to draw up his regiment in the form of a solid square, finds that he has 30 men left over, and that he would require 25 solders in his regiment to increase the side of the square by one soldier. How many soldiers are there in the regiment? ; Let (x^2 + 30) = no. of soldiers in the regiment : It says that 25 more would give him one more in each side: We can write that (x + 1)^2 = x^2 + 30 + 25 : x^2 + 2x + 1 = x^2 + 55 ; x^2 - x^2 + 2x = 55 - 1 : 2x = 54 x = x = 27 therefore 27^2 + 30 = 759 soldiers : Is this true? 28^2 - 759 = 25
 test/221116: Rus and dufus each took some money froma piggy bank to buy an ice cream cone but rufus was 24 cent short and dufus was 2 cent short of the price of cone. they decided to pool their resources, but found they still could not afford to buy the cone. how many cents did the ice cream cost?1 solutions Answer 166086 by ankor@dixie-net.com(15645)   on 2009-10-04 16:20:47 (Show Source): You can put this solution on YOUR website!Rus and dufus each took some money from a piggy bank to buy an ice cream cone but rufus was 24 cent short and dufus was 2 cent short of the price of cone. they decided to pool their resources, but found they still could not afford to buy the cone. how many cents did the ice cream cost? : Let the cost of the cone = x then x - 24 = R's amt and x - 2 = D's amt : The total amt of both: (x-24) + (x-2) = (2x - 26) : Total amt was not enough to buy a cone, write an inequality 2x - 26 < x 2x - x < 26 x < 26 cents Let x = 25 cents be the price of a cone ; Is this true? 25 - 24 = 1 cents for R and 25 - 2 = 23 cents for D : Together they had 24 cents, not enough for a 25 cent cone
 Geometry_Word_Problems/221381: A red ball and a green ball are simultaneously tossed in to the air. The red bass is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is -16^2+96tfeet. The green ball is given an initial velocity of 80 feet persecond, and its height t seconds after it is tossed is -16t^2+80t feet. Find a polynomial d(t) that represents the fiddference in the heights of the two balls, how much higher is the reball 2 seconds after the balls are tossed. In reality, when does the difference in the deights stop increasing? 1 solutions Answer 166075 by ankor@dixie-net.com(15645)   on 2009-10-04 15:30:07 (Show Source): You can put this solution on YOUR website!A red ball and a green ball are tossed into the air. The red ball is given an initial velocity of 96 feet per second and its height "t" seconds after it is tossed is -16t^2 + 96t feet. The green ball is given an initial velocity of 80 feet per second and its height "t" seconds after being tossed is -16t^2 +80t feet. : Find a polynomial D(t) that represents the difference in the heights of the two balls. D(t) = (-16t^2 + 96t) - (-16t^2 +80t) : Remove brackets D(t) = -16t^2 + 96t + 16t^2 - 80t : combine like terms: D(t) = 16t : How much higher is the red ball 2 seconds after the balls are tossed? D(t) = 16(2) D(t) = 32 ft difference after 2 seconds : When does the difference in the heights stop increasing? : Obviously, when one of the balls hits the ground : Find when the lowest ball hits the ground (h=0) -16t^2 + 80t = 0 Factor out -16t -16t(t - 5) = 0 t = 5 seconds when the difference stops increasing; : A graph illustrates this well
 Linear-equations/221070: What would the answer be if i need to write an equation for the line in slope intercept-form when it passes throught (5,-2) and is parallel to y=-9x+6?1 solutions Answer 166035 by ankor@dixie-net.com(15645)   on 2009-10-04 11:41:44 (Show Source): You can put this solution on YOUR website!What would the answer be if i need to write an equation for the line in slope intercept-form when it passes through (5,-2) and is parallel to y=-9x+6? ; remember that parallel lines have the same slope, here it is -9. : Use point/slope formula; y - y1 = m(x - x1) our equation: y - (-2) = -9(x - 5) y + 2 = -9x + 45 y = -9x + 45 - 2 y = -9x + 43, is the equation in the slope/intercept form
 Circles/221262: I have four circles each with a 10 foot radius, they are put togeather to form a squire of circles what I need to know is the squire foot of the waste in the very middle1 solutions Answer 166027 by ankor@dixie-net.com(15645)   on 2009-10-04 11:29:38 (Show Source): You can put this solution on YOUR website!I have four circles each with a 10 foot radius, they are put together to form a square of circles. What I need to know is the square foot of the waste in the very middle. : Picture a single circle a radius of 10, inscribed in a single square, a side of 20 Find the area of the square, subtract the area of the circle : (20^2) - (pi*10^2) = 400 - 314.159 = 85.84 sq/ft; the total wasted in a all 4 corners : This is also the total of the 4 corners from the 4 circles described therefore 85.84 sq/ft wasted ; Did this make sense to you?
 Numbers_Word_Problems/221245: i am less than 500. i am divisible 11 and 5. i have three digits. the sum of my digits is 14?1 solutions Answer 166002 by ankor@dixie-net.com(15645)   on 2009-10-04 09:53:35 (Show Source): You can put this solution on YOUR website!i am less than 500. i am divisible 11 and 5. i have three digits. the sum of my digits is 14? : with a calc: multiply 55 * 9 = 495 subtract 55 until the digits add up to 14 440 385 330 275 digits add up to 14