# See tutors' answers!

Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

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

ankor@dixie-net.com answered: 15630 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

 logarithm/448980: Determine the solution to the following equation: log(a) + log(a + 12) = 2 log(a + 4). 1 solutions Answer 308981 by ankor@dixie-net.com(15645)   on 2011-05-13 18:48:26 (Show Source): You can put this solution on YOUR website!Determine the solution to the following equation: log(a) + log(a + 12) = 2 log(a + 4). log(a(a+12)) = log ((a+4)^2) therefore a(a+12) = (a+4)^2 : a^2 + 12a = a^2 + 8a + 16 : a^2 - a^2 + 12a - 8a = 16 4a = 16 a = a = 4 : Check: log(4) + log(4 + 12) = 2 log(4 + 4). log(4) + log(16) = 2 log(8). log(4) + log(16) = log(8^2). log(4*16) = log(64)
 Geometry_Word_Problems/449030: Kumar walks around a rectangular field the length of which is twice its width. He then walks around another rectangular field half as wide but having the same perimeter as the first field. If the difference in area between the two fields is 432 m, find the length of the second field.1 solutions Answer 308956 by ankor@dixie-net.com(15645)   on 2011-05-13 15:59:39 (Show Source): You can put this solution on YOUR website!Kumar walks around a rectangular field the length of which is twice its width. He then walks around another rectangular field half as wide but having the same perimeter as the first field. If the difference in area between the two fields is 432 m, find the length of the second field. : Let x = width of original field then 2x = length of original field and 2x + 2(2x) = 6x = perimeter of the original field and 2x^2 = area of original field : L = length of the 2nd field and .5x = width of the 2nd field and 2L + 2(.5x) = 2L + x = perimeter of the 2nd field and .5x*L = area of the 2nd field : Perimeter the same, therefore: 2L + x = 6x 2L = 6x - x 2L = 5x L = x L = 2.5x : "If the difference in area between the two fields is 432 m," 2x^2 - .5x*L = 432 Replace L with 2.5x 2x^2 - .5x(2.5x) = 432 2x^2 - 1.25x^2 = 432 .75x^2 = 432 x^2 = x^2 = 576 x = x = 24 m the width of the original width 2(24) = 48 m the length of the original field then L = 2.5(24) L = 60 m is the length of the 2nd field : : Check this 1st field 48 by 24, 2nd field: 60 by 12 Check solution by finding the perimeter of each 2(48) + 2(24) = 144 2(60) + 2(12) = 144, confirms our solution
 test/448550: Practice Test Question. Find an aproximate equation y=ab^x of the exponential curve that contains the given points. Round the values of a and or b to two decimal places if necessary. (0,4)(3,79)1 solutions Answer 308824 by ankor@dixie-net.com(15645)   on 2011-05-13 08:29:52 (Show Source): You can put this solution on YOUR website!Find an approximate equation y=ab^x of the exponential curve that contains the given points. Round the values of a and or b to two decimal places if necessary. (0,4)(3,79) : Replacing x and y with 0, 4 4 = ab^0 4 = a*1; (any term with a 0 exponent equals 1) a = 4 : replacing a, x, y with 4, 3, 79, find b 4*b^3 = 79 b^3 = b = , find the cube root b = 2.703 : the equation for this curve: to two decimal places looks like this:
 Expressions-with-variables/448873: Soybean meal is 14% protein, cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280-lb mixture that is 13% protein. How many pounds of cornmeal? How many pounds of soybean?1 solutions Answer 308818 by ankor@dixie-net.com(15645)   on 2011-05-13 08:02:48 (Show Source): You can put this solution on YOUR website!Soybean meal is 14% protein, cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280-lb mixture that is 13% protein. How many pounds of cornmeal? How many pounds of soybean? : Let x = amt of soy the states that the resulting total will equal 280 lb, therefore (280-x) = amt of cornmeal : Write a per-cent protein equation in decimal form: : .14x + .07(280-x) = .13(280) .14x + 19.6 - .07x = 36.4 .14x - .07x = 36.4 - 19.6 .07x = 16.8 x = x = 240 lb of soy then 280 - 240 = 40 lb of corn meal : : Check this .14(240) + .07(40) = 33.6 + 2.8 = 36.4
 Mixture_Word_Problems/448693: I have another question that requires help The maximum number of grams of fat (F) that should be in a diet varies directly as a person's weight (w). A person weighing 129 lb should have no more than 86 g of fat per day. What is the maximum daily fat intake for a person weighing 114 lb?1 solutions Answer 308780 by ankor@dixie-net.com(15645)   on 2011-05-12 21:47:20 (Show Source): You can put this solution on YOUR website!The maximum number of grams of fat (F) that should be in a diet varies directly as a person's weight (w). A person weighing 129 lb should have no more than 86 g of fat per day. What is the maximum daily fat intake for a person weighing 114 lb? : Write a ratio equation: let x = 114 lb person fat max = Cross multiply 129x = 114 * 86 129x = 9804 x = x = 76 grams of the good stuff
 Human-and-algebraic-language/448813: The ages of a mother and daughter are the same but the digits are reversed.Twelve years ago, the mother was twice as old as the daughter. How old are they now?1 solutions Answer 308779 by ankor@dixie-net.com(15645)   on 2011-05-12 21:42:40 (Show Source): You can put this solution on YOUR website!The ages of a mother and daughter are the same but the digits are reversed. Let 10x+y = mom's age then 10y+x = daughter's age : Twelve years ago, the mother was twice as old as the daughter. 10x+y - 12 = 2(10y+x-12) 10x + y - 12 = 20y + 2x - 24 10x - 2x = 20y - y - 24 + 12 8x = 19y - 12 Divide by 8 x = y - x = y - only one value for y gives an integer value for x, that is y = 4 then x = (4) - x = - x = 9.5 - 1.5 x = 8 : Mom's age: 84, Daughter 48 : : See if that's true in the statement "Twelve years ago, the mother was twice as old as the daughter." 84 - 12 = 2(48 - 12) 72 = 2(36)
 Radicals/448756: Please help me solve this equation: 1 solutions Answer 308775 by ankor@dixie-net.com(15645)   on 2011-05-12 21:24:28 (Show Source): You can put this solution on YOUR website! square both sides = 0 : Solve this equation on a graphing calc Two solutions x=+2.17 x=-2.058 : You can check both solutions in the original problem
 Radicals/448614: Please help me solve this equation: 1 solutions Answer 308707 by ankor@dixie-net.com(15645)   on 2011-05-12 17:13:32 (Show Source): You can put this solution on YOUR website!Please help me solve this equation: Square both sides : FOIL (x+3)(x+3) on the right 5x + 39 = x^2 + 6x + 9 : Combine like terms on the right 0 = x^2 + 6x - 5x + 9 - 39 : A quadratic equation x^2 + x - 30 = 0 : Factors to (x+6)(x-5) = 0 : Two solutions x = -6 x = +5 : Check both solution in the original problem : : 3 does not = -3, x=-6 is not a solution : try x=5 : x=5 is a valid solutions
 Linear-equations/448387: Find the y-intercept for -3x – 2y = 121 solutions Answer 308630 by ankor@dixie-net.com(15645)   on 2011-05-12 12:54:45 (Show Source): You can put this solution on YOUR website!Find the y-intercept for: -3x – 2y = 12 : Y intercept occurs when x = 0 -3(0) - 2y = 12 -2y = 12 y = y = -6 the y intercept
 Mixture_Word_Problems/448389: an isotope of Strontium 90 has a half life of 38 years. if you have 500mg of this isotope today how many milligrams will you have in 19 years1 solutions Answer 308627 by ankor@dixie-net.com(15645)   on 2011-05-12 12:46:06 (Show Source): You can put this solution on YOUR website!an isotope of Strontium 90 has a half life of 38 years. if you have 500mg of this isotope today how many milligrams will you have in 19 years. : The radioactive decay formula: A = Ao*2(-t/h), where: A = amt after t yrs Ao = initial amt t = time h = half-life of substance : A = 500*2(-19/38) A = 500*2(-1/2} A = 500 * .7071 A = 353.55 milligrams after 19 yrs :
 Graphs/448427: I have one more question. How would you do this in steps? Graph y-5x=-4 and 5x=5+y to find the solution? Just the two equations I need to know how to break it down? Such as what would you do to the numbers? Would you subtract anything? I'll really appreciate it. :) God Bless You!!! -Thank You. :) 1 solutions Answer 308620 by ankor@dixie-net.com(15645)   on 2011-05-12 11:33:48 (Show Source): You can put this solution on YOUR website!Graph y - 5x =-4 and 5x = 5 + y to find the solution? : Put both equations into the slope intercept form (y = mx + b) y - 5x = -4 add 5x to both sides; y = 5x - 4 and 5x = 5 + y subtract 5x from both sides 0 = -5x + y + 5 subtract y from both sides -y = -5x + 5 y has to be positive, multiply both sides by -1 y = 5x - 5 : Both these equations have the same slope m=5, therefore the lines are parallel there is no solution : Prove this to yourself by plotting each equation on the same grid. : Plot these for x = -1 and x = +2 1st equation y = 5(-1) -4 y = -9 : y = 5(2) -4 y = 6 : Plot the two ordered pairs -1.-9 and +2, +6 (red graph) Plot the 2nd equation for x =-1, x=+2 the same way y = 5x - 5 you should get ordered pairs of -1, -10 and +2, +5 (green graph) Plot this on the same system : You can see that these lines are parallel, never intersect, so no solution for this system of equations
 Evaluation_Word_Problems/448365: A boy walked over hills at 3 kilometers per hour and on flat roads at 4 kilometers per hour. He walked 18 kilometers in five hours. How much of his trip is over hills?1 solutions Answer 308611 by ankor@dixie-net.com(15645)   on 2011-05-12 11:03:23 (Show Source): You can put this solution on YOUR website!A boy walked over hills at 3 kilometers per hour and on flat roads at 4 kilometers per hour. He walked 18 kilometers in five hours. How much of his trip is over hills? : Let h = distance over hills then (18-h) = distance on flat roads : Write a time equation, time = dist/speed : hill time + flat time = 5 hrs + = 5 : Multiply by the common denominator, 12: 12* + 12* = 12(5) : Cancel the denominators, results 4h + 3(18-h) = 60 4h + 54 - 3h = 60 4h - 3h = 60 - 54 h = 6 km on the hills : Check by finding the times (flat dist = 12 km) 6/3 + 12/4 = 5 hrs
 Rate-of-work-word-problems/448312: Any help would surely be appreciated. "If Cody and Hunter painted the room together, it would take them 4 hours and 57 minutes. Cody would be able to paint a room 3 hours and 3 minutes faster if Hunter helped. Figure out how long each person needs to paint a room alone". Thanks.1 solutions Answer 308575 by ankor@dixie-net.com(15645)   on 2011-05-12 07:55:06 (Show Source): You can put this solution on YOUR website!"If Cody and Hunter painted the room together, it would take them 4 hours and 57 minutes. Cody would be able to paint a room 3 hours and 3 minutes faster if Hunter helped. Figure out how long each person needs to paint a room alone". : Let's do this in minutes. 4 hrs 57 min = 297 min 3 hrs 3 min = 183 min : Let c = Cody's time alone Let h = Hunter's time alone : Let the completed job = 1 (a painted room) : + = 1 : "Cody would be able to paint a room 3 hours and 3 minutes faster if Hunter helped." So we can say: c - 183 = 297 c = 297 + 183 c = 480 min Cody alone (8 hrs) : Replace c with 480, find h: + = 1 Multiply by 480h, results 297h + 480(297) = 480h 142560 = 480h - 297h 183h = 142560 h = h = 779 min Hunter alone (12 hrs, 59 minutes) : : See if that checks out + = 1 .61875 + .38126 ~ 1, so we can say : Cody, 8 hrs alone Hunter, 12 hr 59 min alone
 Inequalities/447945: please help me solve this word problem. teenagers need at least 1200 mg of calcium a day. one cup of milk cantains 300 mg of calcium. one cup of ice cream contains 150 mg of calcium. suppose a teenager drinks 2 cups of milk a day, how many sups of ice cream could he eat? i need to write an inequality1 solutions Answer 308457 by ankor@dixie-net.com(15645)   on 2011-05-11 17:02:16 (Show Source): You can put this solution on YOUR website!teenagers need at least 1200 mg of calcium a day. one cup of milk cantains 300 mg of calcium. one cup of ice cream contains 150 mg of calcium. suppose a teenager drinks 2 cups of milk a day, how many cups of ice cream could he eat? : Let c = cups of ice cream required : Milk + ice cream => 1200 mg 300(2) + 150c => 1200 600 + 150c => 1200 Subtract 600 from both sides 150c => 1200 - 600 150c => 600 divide both sides by 150 c = c => 4 cups of ice cream : We can say if he consumes 2 cups of milk, he should have 4 or more cups of ice cream
 Numbers_Word_Problems/447887: find two numbers whose difference is 18 and 1/4 of whose sum is 9.1 solutions Answer 308437 by ankor@dixie-net.com(15645)   on 2011-05-11 15:46:17 (Show Source): You can put this solution on YOUR website!find two numbers whose difference is 18 and 1/4 of whose sum is 9. : Two numbers, x & y : "difference is 18" x - y = 18 : and 1/4 of whose sum is 9. (x + y) = 9 multiply both sides by 4 x + y = 4(9) x + y = 36 add to the 1st equation x - y = 18 x + y = 36 -----------adding eliminates y find x 2x = 54 x = x = 27 then 27 + y = 36 y = 36 - 27 y = 9 : : Check solution in original 2nd equation (27 + 9) = (36) = 9
 Rate-of-work-word-problems/447908: this morning it took armenta 45min, to drive to work.During the first half hour he traveled 25miles.He drove at an average speed of 65miles per hour the rest of the work to work.How many miles in all did Armenta drive?1 solutions Answer 308432 by ankor@dixie-net.com(15645)   on 2011-05-11 15:35:03 (Show Source): You can put this solution on YOUR website!this morning it took armenta 45 min, to drive to work. During the first half hour he traveled 25 miles. He drove at an average speed of 65 miles per hour the rest of the work to work. How many miles in all did Armenta drive? : Let d = total dist to work then (d-25) = dist driven at 65 mph : Change 45 min to .75 hr : Write a time equation: .5 + = .75 multiply by 65, results 65(.5) + (d-25) = 65(.75) 32.5 + d - 25 = 48.75 d + 7.5 = 48.75 d = 48.75 - 7.5 d = 41.25 mi to work : : Check this by finding the time at 65 mph (41.25-25)/65 = .25 hrs plus .5 hrs = .75 hr
 Rectangles/447872: If I have a rectangular 5 acre piece of land and its length is 568 feet , what will be its width?1 solutions Answer 308426 by ankor@dixie-net.com(15645)   on 2011-05-11 15:17:05 (Show Source): You can put this solution on YOUR website!If I have a rectangular 5 acre piece of land and its length is 568 feet , what will be its width? : 1 acre = 43,560 sq/ft : = 383.45 ft is the width
 real-numbers/448102: how do i solve the equation? 3|x-4|=10 i no there are two solutions, 2/3 and 22/3, i know how to solve the equation to get 22/3 but i dont know how to get 2/3? How would i do this? Thanks for all your help! 1 solutions Answer 308423 by ankor@dixie-net.com(15645)   on 2011-05-11 15:11:23 (Show Source): You can put this solution on YOUR website!3|x-4| = 10 Divide both sides by 3 |x-4| = Remove absolutes, solve for two solutions x - 4 = x = + 4 x = + x = and x - 4 = x = + 4 x = + x =
 Miscellaneous_Word_Problems/447938: I HAVE A 2,700 GALLONS WATER POND. HOW MUCH SOLUTION DO I PUT INTO MY POND IF 1 GALLON OF THIS SOLUTION IS USED FOR 500,000 GALLONS OF WATER? THANK YOU, JOANNE1 solutions Answer 308384 by ankor@dixie-net.com(15645)   on 2011-05-11 13:19:33 (Show Source): You can put this solution on YOUR website!I HAVE A 2,700 GALLONS WATER POND. HOW MUCH SOLUTION DO I PUT INTO MY POND IF 1 GALLON OF THIS SOLUTION IS USED FOR 500,000 GALLONS OF WATER? : There are 32 * 4 = 128 oz in a gallon : * 128 = .69 ~ .7 oz
 Linear_Equations_And_Systems_Word_Problems/447762: Please help me!!!!!!!! Solve. Please show the algebraic inequality you used and show all of your work. Two cell phone companies are advertising rates. Company A charges a rate of \$20 per month plus \$0.05 per minute. Company B charges a rate of \$10 per month plus \$0.10 per minute. What is the number of minutes used above which Company A costs more than Company B?1 solutions Answer 308312 by ankor@dixie-net.com(15645)   on 2011-05-11 08:10:37 (Show Source): You can put this solution on YOUR website!Two cell phone companies are advertising rates. Company A charges a rate of \$20 per month plus \$0.05 per minute. Company B charges a rate of \$10 per month plus \$0.10 per minute. What is the number of minutes used above which Company A costs more than Company B? : Let m = no. of minutes for this to be true : Write an cost equation for each plan : "Company A charges a rate of \$20 per month plus \$0.05 per minute." Cost A = .05m + 20 : "Company B charges a rate of \$10 per month plus \$0.10 per minute." Cost B = .10m + 10 : What is the number of minutes used above which Company A costs more than Company B? Cost A > Cost B which is .05m + 20 > .10m + 10 .05m - .10m > 10 - 20 -.05m > -10 We need to get rid of the negatives, multiply by -1, this reverses the inequality sign .05m < 10 m < m < 200 We can translate this to the statement "Plan A cost more than Plan B when you use less than 200 min" or "Plan A cost less than Plan B when you exceed 200 min" : Let's see if that is true: If you use 201 min A = .05(201) + 20 = \$30.05 B + .10(201) + 10 = \$30.10
 Travel_Word_Problems/447812: A boat took 2 hours to make a trip down river. The same boat took 10 hours to make the return trip upstream. The river current is moving at a constant rate of 8 miles per hour. What is the average speed of the boat in still water?1 solutions Answer 308250 by ankor@dixie-net.com(15645)   on 2011-05-10 21:54:14 (Show Source): You can put this solution on YOUR website!A boat took 2 hours to make a trip down river. The same boat took 10 hours to make the return trip upstream. The river current is moving at a constant rate of 8 miles per hour. What is the average speed of the boat in still water? : Let s = still water speed of the boat then (s-8) = effective speed upstream and (s+8) = effective speed downstream ; Write a distance equation, dist = speed * time : upstream dist = downstream dist 10(s-8) = 2(s+8) 10s - 80 = 2s + 16 10s - 2s = 16 + 80 8s = 96 s = s = 12 mph in still water : : Check solution by finding the distances, they should be equal 2(12+8) = 40 mi 10(12-8) = 40 mi
 logarithm/447700: solve for x; 9 to the x power = .751 solutions Answer 308228 by ankor@dixie-net.com(15645)   on 2011-05-10 20:53:01 (Show Source): You can put this solution on YOUR website!solve for x; 9 to the x power = .75 = .75 Using nat logs = ln(.75) log equiv of exponents x*ln(9) = ln(.75) x = x = -.131 : : Check on a calc: enter 9^-.131, results .74988 ~.75
 Quadratic-relations-and-conic-sections/447148: Hi, i'm really stuck on this problem for partial fractions and would really appreciate the help! Find the partial fraction decomposition of the following rational expression: 5x^2+x+5/x^3+x^2+2x+2 Thanks!1 solutions Answer 308219 by ankor@dixie-net.com(15645)   on 2011-05-10 20:17:27 (Show Source): You can put this solution on YOUR website!Find the partial fraction decomposition of the following rational expression: Factor the denominator, I used synthetic division ________________ -1|1 + 1 + 2 + 2 and got = + = If the denominators are equal the numerators equal, so we have: 5x^2 + x + 5 = A(x+1) + B(x^2+2) : let x=-1, then one factor will drop out, we can solve for B 5(-1)^2 - 1 + 5 = A(-1+1) + B(-1^2+2) 5 - 1 + 5 = 0 + 3B 9 = 3B B = 3 : Replace B with 3, Find A 5x^2 + x + 5 = A(x+1) + 3(x^2+2) 5x^2 + x + 5 = A(x+1) + 3x^2 + 6 5x^2 - 3x^2 + x + 5 - 6 = A(x+1) 2x^2 + x - 1 = A(x+1) Factor (2x-1)(x+1) = A(x+1) Divide both sides by (x+1) (2x - 1) = A : so we have = +
 Quadratic_Equations/447407: A gound base missile is launched from the origin (0,0), it reaches a maximum height of 10km and lands 200km away at the point (200,0) determine the quadratic equation. The missiles flight path is a parabola.1 solutions Answer 308133 by ankor@dixie-net.com(15645)   on 2011-05-10 16:13:35 (Show Source): You can put this solution on YOUR website!A gound base missile is launched from the origin (0,0), it reaches a maximum height of 10km and lands 200km away at the point (200,0) determine the quadratic equation. The missiles flight path is a parabola. : The max height is halfway between launch and impact point: 100 km : Two ordered pairs: 100, 10 and 200, 0 Using the form ax^2 + bx + c = y; c = 0 here so we have: 100, 10 100^2*a + 100b = 10 10000a + 100b = 10 and 200, 0 200^2*a + 200b = 0 40000a + 200b = 0 multiply the 1st equation by 2, subtract from the above equation 40000a + 200b = 0 20000a + 200b = 20 ---------------------subtraction eliminates b, find a 20000a = -20 a = a = -.001 : Find b using the 1st equation 10000(-.001) + 100b = 10 -10 + 100b = 10 100b = 10 + 10 100b = 20 b = b = .2 : The equation: y = -.001x^2 + .2x : looks like this;
 Equations/447300: Two cyclists leave town at the same time on the same road going in the same direction. Cyclist A is going 6 miles per hour faster than cyclist B. After 8 hours cyclist A has traveled three times the distance as cyclist B. How fast is cyclist B traveling?1 solutions Answer 307964 by ankor@dixie-net.com(15645)   on 2011-05-09 22:10:43 (Show Source): You can put this solution on YOUR website!Two cyclists leave town at the same time on the same road going in the same direction. Cyclist A is going 6 miles per hour faster than cyclist B. After 8 hours cyclist A has traveled three times the distance as cyclist B. How fast is cyclist B traveling? : Let s = speed of B cyclist then (s+6) = speed of A cyclist : Write a dist equation, Dist = time * speed A's dist = 3 times B's dist 8(s+6) = 3(8s) 8s + 48 = 24s 48 = 24s - 8s 48 = 16s s = 48/16 s = 3 mph is B's speed : : Check by finding the actual dist each traveled A: 9*8 = 72 mi B: 3*8 = 24 mi
 Quadratic_Equations/447227: Well, I have a math problem that say," Yoy have 180 feet of fence to make a rectangular pen. One side of the pen will be against a 200 foot wall, so it requires no fence. What are the dimensions of the rectangle with the maximum area?" and i would like for you to help me on it.1 solutions Answer 307961 by ankor@dixie-net.com(15645)   on 2011-05-09 22:02:27 (Show Source): You can put this solution on YOUR website!You have 180 feet of fence to make a rectangular pen. One side of the pen will be against a 200 foot wall, so it requires no fence. What are the dimensions of the rectangle with the maximum area?" : The perimeter equation for a 3 sided pen L + 2W = 180 L = (180-2W) : The area equation: A = L*W replace L with (180-2W) A = W(180-2W) A = -2W^2 + 180W Max area occurs at the axis of symmetry, formula for that: x=-b/(2*a) In this equation W = W = W = +45 ft is the width for the max area Find the Length L = 180 - 2(45) L = 180 - 90 L = 90 ft is the length for max area : Actual area 45*90 = 4050 sq/ft
 Travel_Word_Problems/447146: Two three year olds, Adam and Louis, are riding their super speeders tricycles back and forth across a playground. Both of them ride at a constant speed (although their speeds are not equal to each other), and they each take no time to turn around at either end of the playground. Adam starts at the west end and louis starts at the east end. they start at the same time and ride toward each other. They meet and pass each other 30 feet from the east end of the playground. When they reach the opposite end of the playground, they turn and ride back toward each other. They meet again 14 feet from the west end of the playground. What is the length of the playground?1 solutions Answer 307925 by ankor@dixie-net.com(15645)   on 2011-05-09 19:49:22 (Show Source): You can put this solution on YOUR website! Both of them ride at a constant speed (although their speeds are not equal to each other), and they each take no time to turn around at either end of the playground. Adam starts at the west end and louis starts at the east end. they start at the same time and ride toward each other. They meet and pass each other 30 feet from the east end of the playground. When they reach the opposite end of the playground, they turn and ride back toward each other. They meet again 14 feet from the west end of the playground. What is the length of the playground? : Let d = distance across the playground : First meeting: L travels 30' A travels (d-30) : Second meeting L travels: (d-30) + 14 = (d-16) A travels: 30 + (d-14) = (d+16) : The relationship of the distance each traveled remains the same. Ratio L:A = Cross multiply 30(d+16) = (d-30)(d-16) 30d + 480 = d^2 - 16d - 30d + 480 Combine like term on the right 0 = d^2 - 16d - 30d - 30d + 480 - 480 which is d^2 - 76d = 0 factor out d d(d - 76) = 0 Two solution d = 0 and d = 76 ft is the length of the playground : : Confirm this relationship = = .652 = .652
 Equations/447221: Pasha is thinking of a number such that when twice the number is added to three times one more than the number seh gets the same result as when she multiplies four times one less than the number. What number is Pasha thinking about?1 solutions Answer 307914 by ankor@dixie-net.com(15645)   on 2011-05-09 19:23:02 (Show Source): You can put this solution on YOUR website!Pasha is thinking of a number such that when twice the number is added to three times one more than the number he gets the same result as when he multiplies four times one less than the number. What number is Pasha thinking about? : Let x = "a number" : 2x + 3(x+1) = 4(x-1) 2x + 3x + 3 = 4x - 4 5x - 4x = -4 - 3 x = -7 is the number ; : See if that works 2(-7) + 3(-7+1) = 4(-7-1) -14 + 3(-6) = 4(-8) -14 - 18 = -32
 Triangles/447049: The diameter of a ferris wheel is 80 feet. a) if the ferris wheel make one revolution every 45 seconds, find the linear velocity of a person riding in the ferris wheel. b) suppose the linear velocity of a person riding in the ferris wheel is 8 feet per second. what is the time for one revolution of the ferris wheel. please show all work so i can understand better1 solutions Answer 307911 by ankor@dixie-net.com(15645)   on 2011-05-09 19:15:04 (Show Source): You can put this solution on YOUR website!The diameter of a ferris wheel is 80 feet. Find the total distance traveled in one revolution, that would be the circumference ; C = 251.33 ft; distance a person travels in one revolution : a) if the ferris wheel make one revolution every 45 seconds, find the linear velocity of a person riding in the ferris wheel. Using velocity of ft/sec Velocity = dist/time v = v = 5.585 ft/sec is the linear velocity : b) suppose the linear velocity of a person riding in the ferris wheel is 8 feet per second. what is the time for one revolution of the ferris wheel. time = dist/velocity t = 251.33/8 t = 31.4 sec per revolution
 Money_Word_Problems/447073: Upon his death Mr. Money Bags left 1/2 of his eastate to his wife, 1/8 to each of his two children, 1/10 to each of his two grandchildren and \$10,000 to his favorite charity. What was the value of his eastate?1 solutions Answer 307869 by ankor@dixie-net.com(15645)   on 2011-05-09 17:23:01 (Show Source): You can put this solution on YOUR website!Upon his death Mr. Money Bags left 1/2 of his eastate to his wife, 1/8 to each of his two children, 1/10 to each of his two grandchildren and \$10,000 to his favorite charity. What was the value of his estate? : Let x = the value of his estate : x - x - x - x = 10000 Reduce fractions x - x - x - x = 10000 multiply by 20 to get rid of those annoying fractions 20x - 10x - 5x - 4x = 20(10000) 20x - 19x = 200000 x = \$200,000