Tutor:

New! Get regular updates about newly solved problems via algebra.com's RSS system.

---

Recent problems solved by 'ankor@dixie-net.com'

ankor@dixie-net.com answered: 15634 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989 , 6990..7019 , 7020..7049 , 7050..7079 , 7080..7109 , 7110..7139 , 7140..7169 , 7170..7199 , 7200..7229 , 7230..7259 , 7260..7289 , 7290..7319 , 7320..7349 , 7350..7379 , 7380..7409 , 7410..7439 , 7440..7469 , 7470..7499 , 7500..7529 , 7530..7559 , 7560..7589 , 7590..7619 , 7620..7649 , 7650..7679 , 7680..7709 , 7710..7739 , 7740..7769 , 7770..7799 , 7800..7829 , 7830..7859 , 7860..7889 , 7890..7919 , 7920..7949 , 7950..7979 , 7980..8009 , 8010..8039 , 8040..8069 , 8070..8099 , 8100..8129 , 8130..8159 , 8160..8189 , 8190..8219 , 8220..8249 , 8250..8279 , 8280..8309 , 8310..8339 , 8340..8369 , 8370..8399 , 8400..8429 , 8430..8459 , 8460..8489 , 8490..8519 , 8520..8549 , 8550..8579 , 8580..8609 , 8610..8639 , 8640..8669 , 8670..8699 , 8700..8729 , 8730..8759 , 8760..8789 , 8790..8819 , 8820..8849 , 8850..8879 , 8880..8909 , 8910..8939 , 8940..8969 , 8970..8999 , 9000..9029 , 9030..9059 , 9060..9089 , 9090..9119 , 9120..9149 , 9150..9179 , 9180..9209 , 9210..9239 , 9240..9269 , 9270..9299 , 9300..9329 , 9330..9359 , 9360..9389 , 9390..9419 , 9420..9449 , 9450..9479 , 9480..9509 , 9510..9539 , 9540..9569 , 9570..9599 , 9600..9629 , 9630..9659 , 9660..9689 , 9690..9719 , 9720..9749 , 9750..9779 , 9780..9809 , 9810..9839 , 9840..9869 , 9870..9899 , 9900..9929 , 9930..9959 , 9960..9989 , 9990..10019 , 10020..10049 , 10050..10079 , 10080..10109 , 10110..10139 , 10140..10169 , 10170..10199 , 10200..10229 , 10230..10259 , 10260..10289 , 10290..10319 , 10320..10349 , 10350..10379 , 10380..10409 , 10410..10439 , 10440..10469 , 10470..10499 , 10500..10529 , 10530..10559 , 10560..10589 , 10590..10619 , 10620..10649 , 10650..10679 , 10680..10709 , 10710..10739 , 10740..10769 , 10770..10799 , 10800..10829 , 10830..10859 , 10860..10889 , 10890..10919 , 10920..10949 , 10950..10979 , 10980..11009 , 11010..11039 , 11040..11069 , 11070..11099 , 11100..11129 , 11130..11159 , 11160..11189 , 11190..11219 , 11220..11249 , 11250..11279 , 11280..11309 , 11310..11339 , 11340..11369 , 11370..11399 , 11400..11429 , 11430..11459 , 11460..11489 , 11490..11519 , 11520..11549 , 11550..11579 , 11580..11609 , 11610..11639 , 11640..11669 , 11670..11699 , 11700..11729 , 11730..11759 , 11760..11789 , 11790..11819 , 11820..11849 , 11850..11879 , 11880..11909 , 11910..11939 , 11940..11969 , 11970..11999 , 12000..12029 , 12030..12059 , 12060..12089 , 12090..12119 , 12120..12149 , 12150..12179 , 12180..12209 , 12210..12239 , 12240..12269 , 12270..12299 , 12300..12329 , 12330..12359 , 12360..12389 , 12390..12419 , 12420..12449 , 12450..12479 , 12480..12509 , 12510..12539 , 12540..12569 , 12570..12599 , 12600..12629 , 12630..12659 , 12660..12689 , 12690..12719 , 12720..12749 , 12750..12779 , 12780..12809 , 12810..12839 , 12840..12869 , 12870..12899 , 12900..12929 , 12930..12959 , 12960..12989 , 12990..13019 , 13020..13049 , 13050..13079 , 13080..13109 , 13110..13139 , 13140..13169 , 13170..13199 , 13200..13229 , 13230..13259 , 13260..13289 , 13290..13319 , 13320..13349 , 13350..13379 , 13380..13409 , 13410..13439 , 13440..13469 , 13470..13499 , 13500..13529 , 13530..13559 , 13560..13589 , 13590..13619 , 13620..13649 , 13650..13679 , 13680..13709 , 13710..13739 , 13740..13769 , 13770..13799 , 13800..13829 , 13830..13859 , 13860..13889 , 13890..13919 , 13920..13949 , 13950..13979 , 13980..14009 , 14010..14039 , 14040..14069 , 14070..14099 , 14100..14129 , 14130..14159 , 14160..14189 , 14190..14219 , 14220..14249 , 14250..14279 , 14280..14309 , 14310..14339 , 14340..14369 , 14370..14399 , 14400..14429 , 14430..14459 , 14460..14489 , 14490..14519 , 14520..14549 , 14550..14579 , 14580..14609 , 14610..14639 , 14640..14669 , 14670..14699 , 14700..14729 , 14730..14759 , 14760..14789 , 14790..14819 , 14820..14849 , 14850..14879 , 14880..14909 , 14910..14939 , 14940..14969 , 14970..14999 , 15000..15029 , 15030..15059 , 15060..15089 , 15090..15119 , 15120..15149 , 15150..15179 , 15180..15209 , 15210..15239 , 15240..15269 , 15270..15299 , 15300..15329 , 15330..15359 , 15360..15389 , 15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659, >>Next

Age_Word_Problems/323329: Ann's age is seven-tenths of Bill's age. In 4 years Ann's age will be eight-elevenths of Bill's age. How old is Bill now? I am having a difficult time with setting up the equation due to the fractions. Any and all help will be appreciated. Thank you. 1 solutions Answer 231438 by ankor@dixie-net.com(15649)   on 2010-07-18 10:42:20 (Show Source): You can put this solution on YOUR website! Let a = Ann's present age Let b = Bill's present age : Write an equation for each statement: : "Ann's age is seven-tenths of Bill's age." a = b or a = .7b : "In 4 years Ann's age will be eight-elevenths of Bill's age." a + 4 = (b + 4) Multiply both sides by 11 11(a+4) = 8(b + 4) 11a + 44 = 8b + 32 11a = 8b + 32 - 44 11a = 8b - 12 Replace a with .7b 11(.7b) = 8b -12 7.7b = 8b - 12 12 = 8b - 7.7b 12 = .3b b = b = 40 is Bills age ; : Find a a = .7(40) a = 28 is Anns age check solution in the statement: "In 4 years Ann's age will be eight-elevenths of Bill's age." 28 + 4 = (40+4) 32 = *44 32 = 32

Miscellaneous_Word_Problems/323221: In Feb 2006 in the Valley of the Kings in Egypt, a team of archaeologists uncovered the first tomb since King Tut's tomb was found in 1922. The tomb contained five wooden sarcophagi that contained mummies. The archaeologists believed that the mummies are from the 18th Dynasty, about 3300 to 3500 years ago. Determine the amount of carbon-14 that the mummies have lost. (Recall the half-life of carbon-14 is 5750 years.) 1 solutions Answer 231411 by ankor@dixie-net.com(15649)   on 2010-07-17 21:46:42 (Show Source): You can put this solution on YOUR website! In Feb 2006 in the Valley of the Kings in Egypt, a team of archaeologists uncovered the first tomb since King Tut's tomb was found in 1922. The tomb contained five wooden sarcophagi that contained mummies. The archaeologists believed that the mummies are from the 18th Dynasty, about 3300 to 3500 years ago. Determine the amount of carbon-14 that the mummies have lost. (Recall the half-life of carbon-14 is 5750 years.) : The carbon 14, formula: A = Ao*2^(-t/5750) where A = amt after t yrs (We will use per cent) Ao = initial amt (let it = 1) t = time in yrs : A = 1*2^(-3400/5750) A = 2^-.5913 A = .6637 or 66.37% remain therefore 100 - 66.37 = 33.63% has been lost

Miscellaneous_Word_Problems/323282: A large pump can fill a 10,000 gallon tank 5 hours faster than a small pump. The large pump outputs water 100 gallons per hour faster than the small pump. Find the number of gallons pumped in 1 hour by each pump. 1 solutions Answer 231410 by ankor@dixie-net.com(15649)   on 2010-07-17 21:23:38 (Show Source): You can put this solution on YOUR website! A large pump can fill a 10,000 gallon tank 5 hours faster than a small pump. The large pump outputs water 100 gallons per hour faster than the small pump. Find the number of gallons pumped in 1 hour by each pump. : Let x = gal/hr of the smaller pump (x+100) = gal/hr of the larger pump : small pump time - large pump time = 5 hrs - = 5 multiply by x(x+100), results 10000(x+100) - 10000x = 5x(x+100) : 10000x + 1000000 - 10000x = 5x^2 + 500x A quadratic equation 0 = 5x^2 + 500x - 1000000 Simplify, divide by 5 x^2 + 100x - 200000 = 0 Factors (x + 500)(x - 400) = 0 x = 400 gal/hr, the rate of the small pump and 400 + 100 = 500 gal/hr, the rate of the large pump : : Check solution, find the time of each pump 10000/400 = 25 hrs 10000/500 = 20 hrs --------------------- difference: 5 hrs

Word_Problems_With_Coins/323171: A group of twenty-five coins, whose total value is $2.75, is composed of nickels, dimes, and quarters. If the nickels were dimes, the dimes were quarters, and the quarters were nickels, the total would be $3.75. How many quarters are there in the collection? 1 solutions Answer 231409 by ankor@dixie-net.com(15649)   on 2010-07-17 20:57:16 (Show Source): You can put this solution on YOUR website! A group of twenty-five coins, whose total value is $2.75, is composed of nickels, dimes, and quarters. If the nickels were dimes, the dimes were quarters, and the quarters were nickels, the total would be $3.75. How many quarters are there in the collection? : Write an equation for each statement: A group of twenty-five coins, n + d + q = 25 : whose total value is $2.75, we can use cents here 5n + 10d + 25q = 275 : If the nickels were dimes, the dimes were quarters, and the quarters were nickels, the total would be $3.75. 10n + 25d + 5q = 375 : Multiply the 1st equation by 5, subtract from 2nd equation 5n + 10d + 25q = 275 5n + 5d + 5q = 125 ---------------------subtraction eliminates n 5d + 20q = 150 : multiply the 1st equation by 10, subtract from the 3rd equation 10n + 25d + 5q = 375 10n + 10d + 10q =250 -------------------------- subtraction eliminates n 15d - 5q = 125 : Multiply 5d + 20q = 150 by 3, subtract the above equation 15d + 60q =450 15d - 5q = 125 ------------------- subtraction eliminates d, find q 65q = 325 q = q = 5 quarters : : To check solution, find d 5d + 20q = 150 replace q with 5 5d + 20(5) = 150 5d = 150 - 100 d = d = 10 then n = 10 also (total coins is 25) : Check in the 2nd equation 5(10) + 10(10) + 25(5) = 50 + 100 + 125 = 275

logarithm/323190: I need help doing this problem. Thank you 6^2t=7200 1 solutions Answer 231352 by ankor@dixie-net.com(15649)   on 2010-07-17 15:54:18 (Show Source): You can put this solution on YOUR website! Assume it's = 7200 = 2t*log(6) = log(7200) : .77815(2t) = 3.857 : 1.5563t = 3.857 t = t = 2.4783 : : Check solution on a calc, enter: 6^(2*2.4783) = 7194 ~ 7200

Numbers_Word_Problems/323053: One number is 3 less than another. If 4 times the smaller number minus 3 times the larger number is 4, find the two numbers. 1 solutions Answer 231289 by ankor@dixie-net.com(15649)   on 2010-07-16 21:53:58 (Show Source): You can put this solution on YOUR website! let x = "One number" let y = "another number" : One number is 3 less than another. x = y - 3 : If 4 times the smaller number minus 3 times the larger number is 4, 4x - 3y = 4 : find the two numbers. Replace x with (y-3) 4(y-3) - 3y = 4 4y - 12 - 3y = 4 4y - 3y = 4 + 12 y = 16 : I'll let you find x

Equations/322943: Find the values of x and y that solve the following system of equations: 8x+7y=12 -7x-4y=-2 1 solutions Answer 231285 by ankor@dixie-net.com(15649)   on 2010-07-16 21:40:40 (Show Source): You can put this solution on YOUR website! +8x + 7y = 12 -7x - 4y = -2 : Multiply the 1st equation by 4, multiply the 2nd equation by 7, results +32x + 28y = 48 -49x - 28y = -14 ---------------------addition eliminates y, find x -17x + 0y = 34 x = x = -2 : Use the 1st original equation to find y 8(-2) + 7y = 12 -16 + 7y = 12 7y = 12 + 16 7y = 28 y = y = 4 : : Check solution in the 2nd original equation: -7(-2) - 4(4) = -2 14 - 16 = -2

Polynomials-and-rational-expressions/323035: t^3w^2x^4 and 5t^7x Can you help me find the least common multipleof these two expressions, then simplify as much as possible? 1 solutions Answer 231282 by ankor@dixie-net.com(15649)   on 2010-07-16 21:23:50 (Show Source): You can put this solution on YOUR website! t^3w^2x^4 and 5t^7x Can you help me find the least common multiple of these two expressions, then simplify as much as possible? : Write an expression which include the term with the highest exponent

Miscellaneous_Word_Problems/322918: The desks in a classroom are arranged in straight rows. John is in the third row from the front and the fourth row from the back. He is also third from the left end of a row and fifth from the right. How many desks are in the classroom? 1 solutions Answer 231261 by ankor@dixie-net.com(15649)   on 2010-07-16 19:14:47 (Show Source): You can put this solution on YOUR website! The desks in a classroom are arranged in straight rows. John is in the third row from the front and the fourth row from the back. He is also third from the left end of a row and fifth from the right. How many desks are in the classroom? : No. of rows: 3 + 4 = 7 but John's row can only be counted once, rows = 6 No. of desk in a row. 3 + 5 = 8 but John's desk counted only once, desk = 7 Therefore: 6 * 7 = 42 desks in the classroom : like this o o o o o o o o o o o o o o o o x o o o o o o o o o o o o o o o o o o o o o o o o o

Polynomials-and-rational-expressions/322942: The question is (p^2q^2/p^-4q^5)^-3. Can you help? 1 solutions Answer 231243 by ankor@dixie-net.com(15649)   on 2010-07-16 16:45:11 (Show Source): You can put this solution on YOUR website! Assume the question is and you want to simplify. : Combine the like terms to give us positive exponents if possible = The reciprocal gets rid of the neg exponent multiply exponents by 3

Geometry_Word_Problems/322961: A cylindrical drum has a diameter of 3 feet and stands 5 feet high. What is the volume of the drum? (Hint: Use 1 solutions Answer 231237 by ankor@dixie-net.com(15649)   on 2010-07-16 16:30:05 (Show Source): You can put this solution on YOUR website! : A cylindrical drum has a diameter of 3 feet and stands 5 feet high. What is the volume of the drum? : A diameter of 3 ft gives us a radius of 1.5 ft : Formula for the volume of cylinder: : Substitute for r and h, to find V

Triangles/322909: how do i calculate the height of a triangle if i have too angles and the length of the base ? 1 solutions Answer 231232 by ankor@dixie-net.com(15649)   on 2010-07-16 16:25:32 (Show Source): You can put this solution on YOUR website! how do i calculate the height of a triangle if i have too angles and the length of the base ? Briefly 1.Find the third angle by subtracting the two from 180 degrees : 2.Find one of the other sides using the law of sines That side will be the hypotenuse of the right triangle formed by the height : 3. Use the sine of one of the given angles to find the height

Expressions-with-variables/322959: Solve for x: 4x(x-6)-5x(x-5)= -2 Simplify and use comma to separate answers. thannk you for your help. 1 solutions Answer 231229 by ankor@dixie-net.com(15649)   on 2010-07-16 16:17:55 (Show Source): You can put this solution on YOUR website! Solve for x: 4x(x-6) - 5x(x-5) = -2 Multiply to eliminate the brackets 4x^2 - 24x - 5x^2 + 25x = -2 Combine like terms 4x^2 - 5x^2 - 24x + 25x + 2 = 0 : -x^2 + x + 2 = 0 Easier to factor if we change the signs, multiply by -1 x^2 - x - 2 = 0 Factors to (x-2)(x+1) = 0 Two solutions x = 2 x = -1 : x: 2, -1 : : Confirm our solution using x=-1, in the original problem 4(-1)(-1-6) - 5(-1)(-1-5) = -2 -4(-7) - (-5) (-6) = -2 +28 + 5(-6) = -2 28 - 30 = -2; confirms our solution of x=-1 : You should confirm the solution x=2, in the same manner

Linear-equations/323011: Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40mph and train b is traveling at 50 mph. Train A passes a station at 11:15 pm. If train B passes the same station at 11:45pm, at what time will train B catch up to train A? 1 solutions Answer 231216 by ankor@dixie-net.com(15649)   on 2010-07-16 15:22:05 (Show Source): You can put this solution on YOUR website! Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40mph and train B is traveling at 50 mph. Train A passes a station at 11:15 pm. If train B passes the same station at 11:45pm, at what time will train B catch up to train A? : from the given information, we know that train B is 30 min (1/2 hr) behind train A, when train A passes the station : The distance between the trains at this time: * 50 = 25 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 + 25 mi 50t = 40t + 25 50t - 40t = 25 10t = 25 t = t = 2.5 hr or 2 hr 30 min : 11:45 pm + 2:30 = 2:15 am, B catches A

Radicals/322952: Subtract. Simplify by collecting like radical terms if possible. 5 square root of 18 - 7 square root of 2 = Simpify and use radicals as needed. Thanks for your help. 1 solutions Answer 231214 by ankor@dixie-net.com(15649)   on 2010-07-16 14:45:33 (Show Source): You can put this solution on YOUR website! Simplify by collecting like radical terms if possible. 5 square root of 18 - 7 square root of 2 = Simplify and use radicals as needed. : Factor inside the 1st radical to reveal a perfect square Extract that perfect square : Now we have like terms, just do the math, and we have: : : Check this on your calc: enter: = 11.313 and enter = 11.313 also

Polynomials-and-rational-expressions/323000: According to the Einstein’s Theory of Relativity, nothing in the universe as we presently know it can exceed the speed of light; in a sense, it is the ultimate cosmic speed limit. Speed of light in vacuum is 300,000 kilometers/second or 671,080,888 miles/hour! Take a moment and think about this tremendously high speed; it is extremely fast; faster than a speeding bullet (speed of a rifle bullet is in the range 400 to 3,350 miles/hour). a) Show the speed of light in scientific notation in units of miles/hr. b) Given that Moon on average is 240,000 miles away from where you are standing on Earth, how long does it take a light ray to travel from the Earth to the Moon? 1 solutions Answer 231213 by ankor@dixie-net.com(15649)   on 2010-07-16 14:19:35 (Show Source): You can put this solution on YOUR website! a) Show the speed of light in scientific notation in units of miles/hr. 6.71(10^8) mi/hr : : b) Given that Moon on average is 240,000 miles away from where you are standing on Earth, how long does it take a light ray to travel from the Earth to the Moon? : Convert to miles per second = 186,411.358 mi/sec : = 1.287 sec

Miscellaneous_Word_Problems/322955: Two positive numbers differ by 6, and their squares differ by 96. Find the numbers. 1 solutions Answer 231211 by ankor@dixie-net.com(15649)   on 2010-07-16 13:56:18 (Show Source): You can put this solution on YOUR website! Two positive numbers differ by 6, x - y = 6 x = (y+6) : and their squares differ by 96. x^2 - y^2 = 96 : replace x with (y+6) (y+6)^2 - y^2 = 96 : FOIL (y+6)(y+6) y^2 + 12y + 36 - y^2 = 96 : Combine like terms y^2 - y^2 + 12y = 96 - 36 : 12y = 60 y = y = 5 then x = 5 + 6 x = 11 : : Check solution by finding the squares 11^2 - 5^2 = 96

Travel_Word_Problems/322988: John and Tony start from the same place at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find the speed of each. 1 solutions Answer 231203 by ankor@dixie-net.com(15649)   on 2010-07-16 13:21:59 (Show Source): You can put this solution on YOUR website! John and Tony start from the same place at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find the speed of each. : Let s = Tony's walking speed then 2s = John's walking speed : Write a time equation: Time = dist/speed : John's time + 3 hrs = Tony's time + 3 = multiply by 2s, results: 10 + 2s(3) = 2(10) 10 + 6s = 20 6s = 20 - 10 6s = 10 s = s = 1 mph is Tony's speed then 2(1) = 3 is John's speed : : Check solution with a calc by finding the times 10/1.67 ~ 6 hrs 10/3.33 ~ 3 hrs; a 3 hr difference

Quadratic_Equations/322818: A rectangular playground 40m by 60m is to be doubled in area by extending the length and width by an equal amount. By how much should the length and the width be lengthened? 1 solutions Answer 231114 by ankor@dixie-net.com(15649)   on 2010-07-15 20:10:07 (Show Source): You can put this solution on YOUR website! A rectangular playground 40m by 60m is to be doubled in area by extending the length and width by an equal amount. By how much should the length and the width be lengthened? : Find the area of the present playground 40 * 60 = 2400 sq/m then 2*2400 = 4800 sq/m is the new area : Let x = amt to extend the length and the width (x+40)*(x+60) = 4800 FOIL x^2 + 60x + 40x + 2400 = 4800 A quadratic equation x^2 + 100x + 2400 - 4800 = 0 x^2 + 100x - 2400 = 0 Factors to (x+120)(x-20) = 0 The positive solution x = 20 m, to extend dimensions to double the area ; : See if that's true, find the area with the new dimensions 60 * 80 = 4800

Quadratic_Equations/322751: A rectangular field is to be enclosed by a fence and then divded into two small plots by a fence parallel to one of the sides. If thre is 1800 m of fencing available, find the dimensions of the field that will give the maximum area. 1 solutions Answer 231104 by ankor@dixie-net.com(15649)   on 2010-07-15 19:46:08 (Show Source): You can put this solution on YOUR website! A rectangular field is to be enclosed by a fence and Ithen divided into two small plots by a fence parallel to one of the sides. If there is 1800 m of fencing available, find the dimensions of the field that will give the maximum area. : 2L + 3W = 1800 2L = 1800-3W Divide both sides by 2 L = (900-1.5W) : Area = L * W Replace L with (900-1.5W) A = W(900-1.5W) A = -1.5W^2 + 900W Find the axis of symmetry, x=-b/(2a); in this equation: a=-1.5, b=900 W = W = W = +300 m is the width for max area then L = 900 - 1.5(300) L = 450 m is the length and 300 * 450 = 135,000 sq/m is max area

Miscellaneous_Word_Problems/322806: Find a number which is decreased by 54 and is 5 times its opposite? 1 solutions Answer 231094 by ankor@dixie-net.com(15649)   on 2010-07-15 19:06:58 (Show Source): You can put this solution on YOUR website! Find a number which is decreased by 54 and is 5 times its opposite? : Let x = "a number then -x = it's opposite : x - 54 = 5(-x) x - 54 = -5x x + 5x = +54 6x = 54 x = x = 9 ; ; Check solution in original statement 9 - 54 = 5(-9) -45 = -45

Linear_Equations_And_Systems_Word_Problems/322644: 1n 2005,a father was 4 times as old as his son.in the year 2015,thrice the son's age will exceed the father's age by ten years,in which year was the son born? 1 solutions Answer 231093 by ankor@dixie-net.com(15649)   on 2010-07-15 18:59:24 (Show Source): You can put this solution on YOUR website! 1n 2005, a father was 4 times as old as his son. In the year 2015,thrice the son's age will exceed the father's age by ten years, in which year was the son born? : In 2005, let; f = father's age, s = son's age: f = 4s : In 2015: f + 10 = 3(s+10) - 10 f + 10 = 3s + 30 - 10 f + 10 = 3s + 20 f = 3s + 20 - 10 f = 3s + 10 Replace f with 4s, find s: 4s = 3s + 10 4s - 3s = 10 s = 10 yrs old in 2005 Son was born in 1995 : : Check solution, fathers age in 2005, 4(10) = 40 In 10 yrs 40 + 10 = 3(10+10) - 10 50 = 3(20) - 10

Linear-systems/322627: why is it that in diff places you do not reciprocate the values that you need to eliminate?for example 1x+2y=3 2x+1y=3 then if youre trying to eliminate y or get it it becomes 1(1x+2y=3) 2(2x+1y=3)then becomes x+2=3 4x+2y=6 1 solutions Answer 231077 by ankor@dixie-net.com(15649)   on 2010-07-15 17:52:47 (Show Source): You can put this solution on YOUR website! why is it that in diff places you do not reciprocate the values that you need to eliminate?for example 1x+2y=3 2x+1y=3 then if youre trying to eliminate y or get it it becomes 1(1x+2y=3) 2(2x+1y=3)then becomes x+2=3 4x+2y=6 : I am not sure what you are trying to say here, but if you want to solve the following by eliminating y: : 1x + 2y = 3 2x + 1y = 3 Multiply the 2nd equation by 2 and you have 1x + 2y = 3 4x + 2y = 6 -------------subtracting eliminates y, find x -3x = -3 x = x = +1 : Find y using the 1st equation 1 + 2y = 3 2y = 3 - 1 2y = 2 y = y = +1 : Check solution in the 2nd original equation 2(1) + 1 = 3

Problems-with-consecutive-odd-even-integers/322593: The product of four different positive integers is 360. what is the maximum possible sum of these four integers ? 1 solutions Answer 231061 by ankor@dixie-net.com(15649)   on 2010-07-15 17:06:14 (Show Source): You can put this solution on YOUR website! The product of four different positive integers is 360. what is the maximum possible sum of these four integers ? : Find the 4th root of 360 = 4.35....... integers above and below this value 3 * 4 * 5 * 6 = 360 : 3 + 4 + 5 + 6 = 18 is max

Quadratic_Equations/322752: Ethan cuts half a rectangular lawn 40 m by 30 m by mowing a strip of equal width around the perimeter. Julia cuts the small rectangle left. How wide a strip does Ethan cut so that they share the work equally? 1 solutions Answer 231059 by ankor@dixie-net.com(15649)   on 2010-07-15 16:56:23 (Show Source): You can put this solution on YOUR website! Ethan cuts half a rectangular lawn 40 m by 30 m by mowing a strip of equal width around the perimeter. Julia cuts the small rectangle left. How wide a strip does Ethan cut so that they share the work equally? : Let x = the width of the strip cut by E : Find the total area of the lawn; 40 * 30 = 1200 sq/m Each will mow an area of 600 sq/m : Dimension of the small rectangle which is 600 sq/ft: (40-2x) by (30-2x) ; Write an area equation of this rectangle. find x, which is the width of the strip (40-2x)(30-2x) = 600 FOIL 1200 - 80x - 60x + 4x^2 = 600 Arrange as a quadratic equation 4x^2 - 140x + 1200 - 600 = 0 4x^2 - 140x + 600 = 0 Simplify divide by 4 x^2 - 35x + 150 0 = Factor (x - 5)(x - 30) = 0 The reasonable solution x = 5 ft is the width of the strip : : Check solution by finding the area of the inside rectangle (40-10)*(30-10) = 600

Geometry_Word_Problems/321933: triangle has a perimeter of 36 centimeters. If the length of each side is increased by 50% 1 solutions Answer 230655 by ankor@dixie-net.com(15649)   on 2010-07-13 19:25:47 (Show Source): You can put this solution on YOUR website! triangle has a perimeter of 36 centimeters. If the length of each side is increased by 50% : Assume it is an equilateral triangle, each side 36/3 = 12 Increase each side by 50%, 18 cm, new perimeter, 3*18 = 54 cm

Miscellaneous_Word_Problems/321711: Phone was thrown from top of a building. The height h(t) of the cell phone at time (t) is described by the function h(t) = -16tsquared +96t+112. When will the phone be at a height of 192 feet and how many seconds will it take to hit the ground? I have tried putting the numbers in and just cannot figure this out. Can you help please? Thanks 1 solutions Answer 230425 by ankor@dixie-net.com(15649)   on 2010-07-12 19:54:32 (Show Source): You can put this solution on YOUR website! Phone was thrown from top of a building. The height h(t) of the cell phone at time (t) is described by the function h(t) = -16tsquared +96t+112. When will the phone be at a height of 192 feet and how many seconds will it take to hit the ground? : -16t^2 + 96t + 112 = h(t) The phone will be at 192 ft when h(t) = 192 -16t^2 + 96t + 112 = 192 Subtract 192 from both sides -16t^2 + 96t + 112 - 192 -16t^2 + 96t - 80 = 0; a quadratic equation Simplify, and change the signs, divide each term by -16 t^2 - 6t + 5 = 0 Factors to (t - 5)(t + 1) = 0 The positive solution t = 5 sec , tel at 192 ft : Phone will hit the ground when h(t) = 0 -16t^2 + 96t + 112 = 0 Simplify again, divide by -16 t^2 - 6t - 7 = 0 Factors to (t - 7)(t + 1) = 0 positive solution t = 7 sec, phone strikes the ground

Linear_Equations_And_Systems_Word_Problems/321836: Bob received $14,000 inheritance and divided it between a mutual fund that yielded a yearly return of 5% and a 1-year CD that paid 3.5% annually. If his total earnings for the year on this investment was $640, how much did he invest in each of these two funds? 1 solutions Answer 230414 by ankor@dixie-net.com(15649)   on 2010-07-12 19:03:23 (Show Source): You can put this solution on YOUR website! Bob received $14,000 inheritance and divided it between a mutual fund that yielded a yearly return of 5% and a 1-year CD that paid 3.5% annually. If his total earnings for the year on this investment was $640, how much did he invest in each of these two funds? : Let x = amt invested at 5% The total was given as 14000, therefore (14000-x) = amt invested at 3.5% : Write a total interest equation in decimal form .05x + .035(14000-x) = 640 : .05x + 490 - .035x = 640 : .05x - .035x = 640 - 490 : .015x = 150 x = x = $10,000 amt invested at 5% : I'll let you find out the amt invested a 3.5% : Check solution by finding the total interest using the two values

Quadratic_Equations/321789: Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2 + bx + c = 0 Problem: Solution: 2, (only solution) Thank you!! 1 solutions Answer 230405 by ankor@dixie-net.com(15649)   on 2010-07-12 18:11:07 (Show Source): You can put this solution on YOUR website! Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2 + bx + c = 0 Problem: Solution: 2, (only solution) : A solution of 2 will come from factors: (x-2), (x-2) FOIL (x-2)(x-2) = x^2 - 4x + 4 = 0

Linear_Equations_And_Systems_Word_Problems/321698: . Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 60 cups. But when you raise your price to $1.50 you only sell 30 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear. 1 solutions Answer 230400 by ankor@dixie-net.com(15649)   on 2010-07-12 17:20:14 (Show Source): You can put this solution on YOUR website! you charge $1 per cup of lemonade you sell 60 cups. But when you raise your price to $1.50 you only sell 30 cups Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge : the slope of the equation: m = Assign the given values as follows: x1=1.00, y1=60 x2=1.50, y2=30 Find the slope m = = = -60 is the slope : Use the point/slope formula: y - y1 - m(x - x1) y - 60 = -60(x - 1) y - 60 = -60x + 60 y = -60x + 60 + 60 y = -60x + 120 : c = -60p + 120, is the equation

Numbers_Word_Problems/321696: Three consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. Find the middle number 1 solutions Answer 230399 by ankor@dixie-net.com(15649)   on 2010-07-12 17:08:00 (Show Source): You can put this solution on YOUR website! Three consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. Find the middle number: There is no unique solution : let x = the middle number then (x-1) = the 1st number and (x+1) = the 3rd number : x^2 = ((x-1)*(x+1)) + 1 FOIL x^2 = x^2 - 1 + 1 : x^2 = x^2 Which means this is true for any 3 consecutive numbers even, -1, 0 +1 : Try a few like; 142, 143, 144: 143^2 = 20449, 142*144 = 20448