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'

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 , 15660..15689 , 15690..15719 , 15720..15749, >>Next

 Percentage-and-ratio-word-problems/191841: this year, 75 percent of the graduating class of harriet high school had taken at least 8 math courses. of the remaining class members, 60 percent had taken 6 or 7 courses. what percent of the graduating class has taken fewer than 6 math courses? this question is from the ace practice test online by going to deltacollege.edu then clicking on assessment test then ace sample questions1 solutions Answer 143971 by ankor@dixie-net.com(15746)   on 2009-04-18 20:52:43 (Show Source): You can put this solution on YOUR website!this year, 75 percent of the graduating class of harriet high school had taken at least 8 math courses. of the remaining class members, 60 percent had taken 6 or 7 courses. what percent of the graduating class has taken fewer than 6 math courses? : Use a convenient total number of students, 100 students then 75 students took at least 8 math courses and 25 students did not, of these 60% took 6 or 7 math courses. therefore .6 * 25 = 15 students took 6 or 7 math courses : That leaves, 100 - 75 - 15 = 10 students took fewer than 6 math courses : Obviously then; 10% of the total class (of 100) took less than 6 math courses
 Volume/191520: Given the surface area of a sphere is 40 pi cm^2, find its volume. And given that the area of an equilateral triangle is 67 cm^2, find its perimeter. 1 solutions Answer 143943 by ankor@dixie-net.com(15746)   on 2009-04-18 13:32:37 (Show Source): You can put this solution on YOUR website!Given the surface area of a sphere is 40 pi cm^2, find its volume. : Two formulas: V = & SA = : = 40*pi Divide both sides by 4pi r^2 = 10 r = Find the Volume V = V = 132.46 cu/cm : : And given that the area of an equilateral triangle is 67 cm^2, find its perimeter. ; Let x = the side of the triangle; Find the height: h = h = Find x using the area: = 67 Multiply both sides by 2 = 134 = 134 = 134 = x^2 = 154.73 x = x = 12.44 : P = 3(12.44) P = 37.3 cm
 Polynomials-and-rational-expressions/191744: help me please???!!!(7a^2+50ab+7b^2) i tried to factot it out but i didn't know what to do with the 50ab in this equation because the first and last terms do not add up to be fifty, aren't they supposed to????1 solutions Answer 143857 by ankor@dixie-net.com(15746)   on 2009-04-17 21:28:17 (Show Source): You can put this solution on YOUR website!(7a^2+50ab+7b^2) actually this will factor: : (7a + b)(a + 7b) If you FOIL this 7a^2 + 49ab + ab + 7b^2 which is 7a^2 + 50ab + 7b^2, right?
 Linear-systems/191711: Good afternoon, I have a problem I really need some help with. The directions say "Solve the systems of equations by graphing. Then classify the system." The problem has 4 graphs to choose from(they won't let me copy so I can't paste,lol). I think if you could give me the coordinates I could figure out which graph they go to. Than-x in advance,you've saved a lot of grey hairs:-) The equations are: 7u+v=47 7u=v+571 solutions Answer 143853 by ankor@dixie-net.com(15746)   on 2009-04-17 21:05:18 (Show Source): You can put this solution on YOUR website!7u+v=47 7u=v+57 : If we solve it, you will know at which coordinates they intersect; Put the 2nd equation in the standard form also, then add, eliminating v, find u 7u + v = 47 7u - v = 57 ------------- 14u = 104 u = u = : Find v using the 1st equation 7) + v = 47 52 + v = 47 v = 47 - 52 v = -5 : The coordinates are , -5
 Polynomials-and-rational-expressions/191725: This question is from textbook Elementary and Intermediate Algebra A red ball and a green ball are simultaneously 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 _16t2 _ 96t feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tossed is _16t2 _ 80t feet. a) Find a polynomial D(t) that represents the difference in the heights of the two balls. b) How much higher is the red ball 2 seconds after the balls are tossed? c) In reality, when does the difference in the heights stop increasing? 1 solutions Answer 143851 by ankor@dixie-net.com(15746)   on 2009-04-17 20:48:54 (Show Source): You can put this solution on YOUR website!A red ball and a green ball are simultaneously 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 -16t2 + 96t feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tossed is -16t2 + 80t feet. ; -16t^2 + 96t = h (redball) and -16t^2 + 80t = h (greenball) a) 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 D(t) = 16t : b) How much higher is the red ball 2 seconds after the balls are tossed? D(t) = 16(2) D(t) = 32 ft after 2 sec : c) In reality, when does the difference in the heights stop increasing? When the green ball hits the ground. h = 0 If you solve -16t^2 + 80t = 0, you will find that will occur in 5 sec ; Seen graphically; x axis is time in seconds, y axis is height in feet
 Equations/191731: This question is from textbook Three consecutive even integers are such that the square of the third is 100 more than the square of the second. Find 3 integers. I am sooo lost. Thank You1 solutions Answer 143836 by ankor@dixie-net.com(15746)   on 2009-04-17 19:23:47 (Show Source): You can put this solution on YOUR website!Three consecutive even integers: x, (x+2), (x+4) : the square of the third is 100 more than the square of the second. (x+4)^2 = (x+2)^2 + 100 FOIL x^2 + 8x + 16 = x^2 + 4x + 4 + 100 : x^2 + 8x + 16 = x^2 + 4x + 104 : Arrange the x's on the left, numbers on the right: x^2 - x^2 + 8x - 4x = 104 - 16 : 4x = 88 x = x = 22, 24, 26; are the numbers : : Check solution in the statement: "the square of the third is 100 more than the square of the second." 26^2 = 24^2 + 100 676 = 576 + 100
 Miscellaneous_Word_Problems/191499: A digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a 1, it mistakenly displays a 9. What fraction of the day will the clock show the correct time? 1 solutions Answer 143832 by ankor@dixie-net.com(15746)   on 2009-04-17 18:04:28 (Show Source): You can put this solution on YOUR website!A digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a 1, it mistakenly displays a 9. What fraction of the day will the clock show the correct time? ; Find the no of minutes that it will display the incorrect time: Total min in 12 hrs. 12 * 60 = 720 minutes : The hrs that use 1: 01, 10, 11, 12, wrong for 4 hrs, 4 * 60 = 240 minutes : the minutes digits that will be wrong for each hr: 01, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51. Total of 15 min each hr : 4 hrs are completely wrong, the remaining 8 hrs are only wrong for 15 min each; 8 * 15 = 120 min : Total wrong minutes, 240 + 120 = 360 min. = the time it is correct.
 Travel_Word_Problems/191682: A diesel train traveled to Johannesburg and back. It took 9 hours longer to go there than it did to come back. The average speed on the trip there was 10 km/h. The average speed on the way back was 55 km/h. How many hours did trip there take. Manish1 solutions Answer 143819 by ankor@dixie-net.com(15746)   on 2009-04-17 16:24:38 (Show Source): You can put this solution on YOUR website! It took 9 hours longer to go there than it did to come back. The average speed on the trip there was 10 km/h. The average speed on the way back was 55 km/h. How many hours did trip there take. : Let t = time to come back then (t+9) = time to got there : The two trip were the same distance, write a distance equation from this fact: Dist = speed * time : to dist = from dist 10(t+9) = 55t 10t + 90 = 55t 90 = 55t - 10t 90 = 45t t = t = 2 hrs to return, and 11 hrs to go ; ; Check solution, find the distances 11*10 = 110 km 2*55 = 110 km
 Square-cubic-other-roots/191442: Please help! 4th sqrt of 48 plus 4th sqrt of 3 equals what?1 solutions Answer 143807 by ankor@dixie-net.com(15746)   on 2009-04-17 14:35:38 (Show Source): You can put this solution on YOUR website!4th sqrt of 48 plus 4th sqrt of 3 equals what? : 4thRoot(48) + 4thRoot(3) = : Factor to reveal the 4th power of 2 which is 16 4thRoot(16*3) + 4thRoot(3) = : Extract the 4th root of 16 2*4thRoot(3) + 4thRoot(3) = 3*4thRoot(3) : These are like terms, so just add them : " Check using a calc; enter: 48^(1/4) + 3^(1/4) = 3.94382.. Enter our solution 3 * 3^(1/4) = 3.94382...; confirms our solution
 Travel_Word_Problems/191436: A 100-foot vertical tower is to be erected on the side of a hill that makes a 6* angle with the horizontal. Find the length of each of the two guy wires that will be anchored 75 feet uphill and downhill from the base of the tower.1 solutions Answer 143730 by ankor@dixie-net.com(15746)   on 2009-04-16 19:01:28 (Show Source): You can put this solution on YOUR website!A 100-foot vertical tower is to be erected on the side of a hill that makes a 6* angle with the horizontal. Find the length of each of the two guy wires that will be anchored 75 feet uphill and downhill from the base of the tower. : Treat this as two different triangles; The uphill triangle: A= 90-6 = 84 degrees Use the law of cosines: a^2 = b^2 + c^2 - 2(a*b)cos(A) A = 84 degrees a = guy wire length b = 75' c = 100' : a^2 = 75^2 + 100^2 - 2(75*100)cos(84) a^2 = 5625 + 10000 - 2(7500)*.104528 a^2 = 15625 - 1567.9 a = a = 118.56' length of the up-hill guy wire : : The down-hill triangle A = 90+6 = 96 degrees A = 96 degrees a = guy wire length b = 75' c = 100' : a^2 = 75^2 + 100^2 - 2(75*100)cos(96) a^2 = 5625 + 10000 - 2(7500)*-.1045 a^2 = 15625 - (-1567.9) a^2 = 15625 + 1567.9 a = a = 131.12' length of the down-hill guy wire ; I'll leave it up to you to check my math here.
 Equations/191325: The denominator of fraction is 4 more than its numenator . Taking square of this fraction we get a new fraction .The difference between the denominator and numenator of the new fraction is 40. Find the fraction.1 solutions Answer 143634 by ankor@dixie-net.com(15746)   on 2009-04-15 21:56:43 (Show Source): You can put this solution on YOUR website!Just write what it says: : The denominator of fraction is 4 more than its numerator. d = n + 4 : Taking square of this fraction we get a new fraction. n^2/d^2 : The difference between the denominator and numerator of the new fraction is 40. d^2 - n^2 = 40 : Find the fraction. Substitute (n+4) for d in the above equation (n+4)^2 - n^2 = 40 FOIL n^2 + 8n + 16 - n^2 = 40 : 8n = 40 - 16 : 8n = 24 n = n = 3 then d = 3 + 4 d = 7 : is the fraction : : Check: 9/49 is the new fraction, difference of 40
 Equations/191320: A man bought some chairs for Rs 200/- .Five chairs were stolen from the total. He sold the remaining chairs for a profit of Rs 40 The selling price of chair was Rs 4 more than its cost price. How many chairs did he buy and how much was the cost price of each chair?1 solutions Answer 143627 by ankor@dixie-net.com(15746)   on 2009-04-15 21:44:01 (Show Source): You can put this solution on YOUR website!A man bought some chairs for Rs 200/- .Five chairs were stolen from the total. He sold the remaining chairs for a profit of Rs 40. The selling price of chair was Rs 4 more than its cost price. How many chairs did he buy and how much was the cost price of each chair? : Let x = no. of chairs bought originally then = cost of each chair he bought : (x-5) = no. of chairs sold ; Since he made \$40 profit, selling price must be: : Selling price - unit cost = 4 - = 4 Multiply equation by x(x-5), results: 240x - 200(x-5) = 4x(x-5) ; 240x - 200x + 1000 = 4x^2 - 20x : 40x + 1000 = 4x^2 - 20x : 0 = 4x^2 - 20x - 40x - 1000 A quadratic equation: 4x^2 - 60x - 1000 = 0 Simplify, divide by 4 x^2 - 15x - 250 = 0 Factor (x-25)(x+10) = 0 The positive solution x = 25 chairs originally purchased ; Find original cost: = \$8 per chair : Selling price (5 fewer chairs sold): = \$12 per chair (which is a \$4 profit on ea chair)
 logarithm/191308: Radium-226 is a radioactive element with a half-life of 1600 years. How much of a 1000 g sample of the element will be present after 6400 years? How long will it take for the 1000 gram sample to decay to 1 gram? 1 solutions Answer 143605 by ankor@dixie-net.com(15746)   on 2009-04-15 19:45:04 (Show Source): You can put this solution on YOUR website!Radium-226 is a radioactive element with a half-life of 1600 years. How much of a 1000 g sample of the element will be present after 6400 years? : The half-life decay formula: A = Ao(2^(-t/h)) where: Ao = initial amt A = resulting amt after t years h = half-life of substance t = time in years : A = 1000(2^(-6400/1600)) A = 1000(2^-4) A = 1000 * .0625 A = 62.5 grams after 6400 yrs : : How long will it take for the 1000 gram sample to decay to 1 gram? 1 = 1000(2^(-t/1600)) Divide both sides by 1000 and we can write this: 2^(-t/1600) = 2^(-t/1600) = .001 log(2^(-t/1600)) = log(.001) *log(2) = log(.001) *.30103 = -3 Multiply both sides by 1600, results -.30103t = -4800 t = t = 15,945.25 yrs for 1000 g to decay to 1 g ; : Check by using this in the following equation with a calc A = 1000(2^(-15945.25/1600)) A = 1.000; confirms our solution
 Surface-area/191162: Tony and Edwin each built a rectangular garden. Tony's garden is twice as long and twice as wide as Edwin's garden. If the area of Edwin's garden is 600 square feet, what is the area of Tony's garden?1 solutions Answer 143489 by ankor@dixie-net.com(15746)   on 2009-04-14 21:48:09 (Show Source): You can put this solution on YOUR website!Tony and Edwin each built a rectangular garden. Tony's garden is twice as long and twice as wide as Edwin's garden. If the area of Edwin's garden is 600 square feet, what is the area of Tony's garden? : Let dimensions of E's garden be L x W then LW = 600 : The dimensions of T's garden is 2L x 2W then 2L*2W = 4LW = area of T's garden : Replace LW with 600; 4*600 = 2400 sq ft area of T's garden
 Graphs/191131: Solve for x. Collect x's on the LEFT side of the inequality. The solution must be presented with x first, the correct inequality symbol, then the number. 2(x - 3) ≤ -12 1 solutions Answer 143488 by ankor@dixie-net.com(15746)   on 2009-04-14 21:26:01 (Show Source): You can put this solution on YOUR website!2(x - 3) ≤ -12 : 2x - 6 <= -12 : 2x <= -12 + 6 : 2x <= -6 x <= x <= -3
 Exponential-and-logarithmic-functions/191083: Please help me solve this equation 5-5 Completing the Square Solving a quadratic equation if the coefficient of x^2 is NOT 1 3x^2+12x-9=01 solutions Answer 143452 by ankor@dixie-net.com(15746)   on 2009-04-14 16:03:11 (Show Source): You can put this solution on YOUR website!3x^2 + 12x - 9 = 0 : 3x^2 + 12x + ___ = 9 Divide both sides by 3, makes the coefficient of x^2 to be 1 x^2 + 4x + ___ = 3 Complete the square, divide the coefficient of x by 2 and square it: x^2 + 4x + 4 = 3 + 4 : (x + 2)^2 = 7 : x + 2 = +/- x = -2 + and x = -2 -
 Linear-equations/191000: A united airline jet leaves new york's kennedy airport headed to los angeles international airport, a distance of 2700 miles. at the same time, a delta airline jet leaves the los angeles airport headed for kennedy airport. due to headwinds and tailwinds, the united jet average speed is 100 miles per hour greater than that of the delta jet. if the two jets pass one another after 3 hours, find the speed of each plane?1 solutions Answer 143431 by ankor@dixie-net.com(15746)   on 2009-04-14 14:07:30 (Show Source): You can put this solution on YOUR website!A united airline jet leaves new york's kennedy airport headed to los angeles international airport, a distance of 2700 miles. at the same time, a delta airline jet leaves the los angeles airport headed for kennedy airport. due to headwinds and tailwinds, the united jet average speed is 100 miles per hour greater than that of the delta jet. if the two jets pass one another after 3 hours, find the speed of each plane? : Let s = speed of Delta jet then (s+100) = speed of UA jet : We know when the jets meet they will have traveled a total of 2700 mi Use this fact to write a distance equation: Dist = time * speed : Delta dist + UA dist = 2700 mi 3s + 3(s+100) = 2700 : 3s + 3s + 300 = 2700 : 6s = 2700 - 300 : 6s = 2400 s = s = 400 mph is the Delta and 400 + 100 = 500 mph is the UA jet : : Check solutions 3(400) + 3(500) = 2700 mi
 Linear-equations/190998: Zoha jogs 3 miles per hour faster than she walks. She jogs for 2 miles and then walks for 2 miles. If the total time of her outing is one hour, find the rate at which she walks and jogs?1 solutions Answer 143410 by ankor@dixie-net.com(15746)   on 2009-04-14 09:40:14 (Show Source): You can put this solution on YOUR website!Zoha jogs 3 miles per hour faster than she walks. She jogs for 2 miles and then walks for 2 miles. If the total time of her outing is one hour, find the rate at which she walks and jogs? : Let x = walking speed then (x+3) = jogging speed : Write a time equation; Time = : walk time + jog time = 1 hr + = 1 : Multiply equation by x(x+3), results: 2(x+3) + 2x = x(x+3) 2x + 6 + 2x = x^2 + 3x 4x + 6 = x^2 + 3x 0 = x^2 + 3x - 4x - 6 a quadratic equation: x^2 - x - 6 = 0 Factors to (x-3)(x+2) = 0 Positive solution x = 3 mph is the walking speed then 3 + 3 = 6 mph is the jogging speed : : Check solution: 2/3 + 2/6 = 1
 Linear-systems/190977: Hi, was wondering if anyone could help me with the following system of equations problem. Steps on how to solve fully would be ideal also. A-B+C=1 2A-2B=0 3A+B-3C=2 Any help would be most appreciated, -Thanks, -Nick.1 solutions Answer 143384 by ankor@dixie-net.com(15746)   on 2009-04-13 21:58:13 (Show Source): You can put this solution on YOUR website!A - B + C = 1 2A -2B = 0 3A + B -3C = 2 : multiply the 1st equation by 2, subtract the 2nd equation 2A - 2B + 2C = 2 2A - 2B + 0C = 0 ------------------ subtraction eliminates A & B, find C 2C = 2 C = 1 : Substitute 1 for C in the 1st and 3rd equations A - B + 1 = 1 3A +B -3(1) = 2 : A - B = 1 - 1 3A +B = 2 + 3 : A - B = 0 3A +B = 5 ------------Adding eliminates B 4A = 5 A = : Find B using 2A - 2B = 0; therefore: B = A B = : Solution: A = , B = , C = 1 ; : Check solution in the 3rd equation: 3A + B -3C = 2 3() + - 3(1) = 2 + - 3 = 2 - 3 = 2 5 - 3 = 2
 Complex_Numbers/190905: Hello. I am not positive I put in the right topic. We are learning complex algebraic fractions. I solved a problem, and I am not sure if i solved it correctly, and if I did I am not sure how to show the work for the check. the problem is x-1/x + 7/3x = 9/4x we have to cancel the denominators by finding an LCD and multiplying by that. EX: LCD for the above problem is 12x, so i would x x-1 x 12x and the x and 12 x simplify it to 12x-12. The answer i got is 11/12, but I am not sure if it is correct. If not, please provide help on solving it because I am quite confused, and if you don't mind please assist me in the check (if the correct solution is a fraction because my teacher goes too fast and never stops so I am not able to ask for help) thank you so much for your help :) ~Katie 1 solutions Answer 143350 by ankor@dixie-net.com(15746)   on 2009-04-13 18:39:29 (Show Source): You can put this solution on YOUR website! the problem is + = I think you are right but let's just go thru it and check the solution 12x* + 12x* = 12x* Cancel out the denominators and you have: 12(x-1) + 4(7) = 3(9) 12x - 12 + 28 = 27 12x + 16 = 27 12x = 27 - 16 12x = 11 x = just as you said : : But you can be sure by substituting 11/12 for x in the original problem: + = Remember when you have a fraction in the denominator, you invert it and mult the numerator: ((11/12) - 1)*(12/11)) + 7(12/33) = 9(12/44) : ((-1/12)*(12/11)) + 7(12/33) = 9(12/44) ; (-1/11) + (84/33) = (108/44) ; Reduce the fractions (-1/11) + (28/11) = (27/11); confirms our solution
 Travel_Word_Problems/190828: A cyclist bikes at a constant speed for 17 miles. He then returns home at the same speed but takes a different route. His return trip takes one hour longer and is 22 miles. Find his speed. I was trying to do this problem this way: Distance Rate Time = Distance/Rate cyclist travels away from home 17 x = speed? 17/x cyclist returns home different route 22 x + 1 22/x+1 I know this is not correct and that I have to find the average rate. I also don't know the time. Thank you in advance! 1 solutions Answer 143337 by ankor@dixie-net.com(15746)   on 2009-04-13 17:13:14 (Show Source): You can put this solution on YOUR website!A cyclist bikes at a constant speed for 17 miles. He then returns home at the same speed but takes a different route. His return trip takes one hour longer and is 22 miles. Find his speed. : I would do it this way; : Let s = the constant speed Then = initial time out and = time to return : Write a time equation: Time to return = initial time + 1 hr = + 1 Multiply equation by s 22 = 17 + s : 22 - 17 = s : s = 5 mph : Check solution by finding the times of each trip 22/5 = 4.4 hrs 17/5 = 3.4 hrs ------------- diff = 1 hr
 Linear-systems/190869: This question is from textbook Alegbra Structure and Method When the digits of a two-digits number are reversed, the new number is 36 more than the original number. The units digits is twice the tens digit. What is the original number?1 solutions Answer 143335 by ankor@dixie-net.com(15746)   on 2009-04-13 16:08:37 (Show Source): You can put this solution on YOUR website!When the digits of a two-digits number are reversed, the new number is 36 more than the original number. The units digits is twice the tens digit. What is the original number? : Let x = original 10's digit Let y = original units 10x + y = original number : "When the digits of a two-digits number are reversed, the new number is 36 more than the original number." 10y + x = 10x + y + 36 10y - y = 10x - x = 36 9y = 9x + 36 Simplify divide by 9 y = x + 4 : " The units digits is twice the tens digit." y = 2x : Substitute; 2x = x + 4 x = 4, then y = 8 ; What is the original number? It's 48 ; ; Check solution 84 = 48 + 36
 Complex_Numbers/190881: This question is from textbook algebra and trigonometry structure and method book 2 Please help i am so confused and i keep coming up with these horrible fractions. this is supposed to be synthetic division. 6t^4+5t^3-10t+4/3t-21 solutions Answer 143330 by ankor@dixie-net.com(15746)   on 2009-04-13 15:55:53 (Show Source): You can put this solution on YOUR website!synthetic division. (6t^4 + 5t^3 - 10t + 4)/(3t-2) : Note that the t^2 is not represented so we have to write it: 6t^2 + 5t^3 + 0t^2 - 10t + 4 divided by 3t-2 : Find the divisor 3t = +2 t = : Synthetic division: : ............____________________ (2/3)| 6 + 5 + 0 - 10 + 4 ......................4 + 6 + 4 - 4 .............------------------- ..............6 + 9 + 6 - 6 + 0 (no remainder) : Quotient; 6t^3 + 9t^2 + 6t - 6
 Radicals/190845: Initial speed (velocity) of Vo will travel a distance of (s) meters, where s=4.9t^2 + Vot and t is measured in seconds. Solve for t. Use 4.9t^2 + Vot=s Downward speed: An object thrown downward from 200-m cliff travels 91.2m in 4 sec. What was the initial velocity of the object.1 solutions Answer 143318 by ankor@dixie-net.com(15746)   on 2009-04-13 15:29:24 (Show Source): You can put this solution on YOUR website!Initial speed (velocity) of Vo will travel a distance of (s) meters, where s=4.9t^2 + Vot and t is measured in seconds. Solve for t. Use 4.9t^2 + Vot = s : 4.9t^2 + Vot - s = 0 : Treat it as a quadratic equation, use the quadratic formula: In this equation: x = t ; a = 4.9, b = Vo, c = -s : : : : ; Downward speed: An object thrown downward from 200-m cliff travels 91.2m in 4 sec. What was the initial velocity of the object. : 4.9t^2 + Vot = s Substitute 4 for t and 91.2 for s 4.9(4^2) + 4Vo = 91.2 4.9(16) + 4Vo = 91.2 78.4 + 4Vo = 91.2 4Vo = 91.2 - 78.4 4Vo = 12.8 Vo = Vo = 3.2 m/sec : : Check solution using Vo = 3.2 & s = 91.2 m ; : : : Positive solution t = t = 4 sec as given above
 Mixture_Word_Problems/190731: Adjusting Antifreeze: Angela needs 20 quarts of 50% antifreeze solution in her radiator. She plans to obtain this by mixing some pure antifreeze with an appropriate amount of a 40% antifreeze solution. How many quarts of each should she use?1 solutions Answer 143216 by ankor@dixie-net.com(15746)   on 2009-04-12 19:25:02 (Show Source): You can put this solution on YOUR website!Adjusting Antifreeze: Angela needs 20 quarts of 50% antifreeze solution in her radiator. She plans to obtain this by mixing some pure antifreeze with an appropriate amount of a 40% antifreeze solution. How many quarts of each should she use? : Let x = amt of 40% solution to be removed and Let x = amt of pure antifreeze to be added : .4(20-x) + 1.0x = .50(20) : 8 - .4x + 1x = 10 : -.4x + 1x = 10 - 8 : .6x = 2 x = x = 3 qts removed and added ; : Check: .4(16.67) + 1(3.33) = .5(20) 6.67 + 3.33 = 10
 Polynomials-and-rational-expressions/190373: can you please help me? Solve the equation by graphing. Find the solution algebraically to verify your graph. Are there any values for x that are not found in the domain? In other words, are there any values for x that make the equation undefined? What are they? 1 solutions Answer 143175 by ankor@dixie-net.com(15746)   on 2009-04-12 13:07:20 (Show Source): You can put this solution on YOUR website!Right off you can see that x=0 is not in the domain (division by 0) : Arrange the equation in the general form: y = - - 5 y = - 5 : Plot the graph, skipping x = 0 x | y ------- -4 |-4.75 -2 |-4.5 -1 |-4 +1 |-6 +2 |-5.5 +4 |-5.25 : Looks like this there should be a gap where x=0 : : "Find the solution algebraically to verify your graph." - 5 = 0 = +5 Multiply both sides by x -1 = 5x x = is the solution, (the x intercept on the graph)
 Age_Word_Problems/190312: Ten years ago a father was seven times as old as his son, two years hence twice his age will be equal to five times his son's age. What are their present ages?1 solutions Answer 142924 by ankor@dixie-net.com(15746)   on 2009-04-09 21:45:49 (Show Source): You can put this solution on YOUR website!Ten years ago a father was seven times as old as his son, two years hence twice his age will be equal to five times his son's age. What are their present ages? : Let f = father's present age Let s = son's present age : Write an equation & simplify, for each statement: : "Ten years ago a father was seven times as old as his son," (f-10) = 7(s-10) f - 10 = 7s - 70 f = 7s - 70 + 10 f = 7s - 60 ; " two years hence twice his age will be equal to five times his son's age." 2(f + 2) = 5(s + 2) 2f + 4 = 5s + 10 2f = 5s + 10 - 4 2f = 5s + 6 : What are their present ages? Substitute (7s-60) for f in the above equation: 2(7s - 60) = 5s + 6 14s - 120 = 5s + 6 14s - 5s = 6 + 120 9s = 126 s = s = 14 yr's is son's present age : find f using eq: f = 7s - 60 f = 7(14) - 60 f = 98 - 60 f = 38 yrs is father's present age : : Check solution's in the statement: "two years hence twice his age will be equal to five times his son's age." 2(38+2) = 5(14+2) 2(40) = 5(16)
 Word_Problems_With_Coins/190237: sandy has \$3.25 in change. She has five more dimes than quarters but twice as many nickels as dimes. Express the given information as an algebraic equation and simplify.1 solutions Answer 142792 by ankor@dixie-net.com(15746)   on 2009-04-08 21:52:07 (Show Source): You can put this solution on YOUR website!andy has \$3.25 in change. She has five more dimes than quarters but twice as many nickels as dimes. Express the given information as an algebraic equation and simplify. ; An equation for the total \$ .05n + .10d + .25q = 3.25 : "She has five more dimes than quarters" d = (q + 5) or q = (d-5) : " but twice as many nickels as dimes." n = 2d : Substitute for n and q in the \$\$ equation: .05(2d) + .10d + .25(d-5) = 3.25 : .10d + .10d + .25d - 1.25 = 3.25 Simplify: .45d = 3.25 + 1.25 : .45d = 4.50 : They didn't say anything about solving it, but it's pretty easy now
 Miscellaneous_Word_Problems/190263: The sum of two numbers is 64. Two more than twice the larger number is five less than seven times the smaller. Find the numbers.1 solutions Answer 142790 by ankor@dixie-net.com(15746)   on 2009-04-08 21:32:39 (Show Source): You can put this solution on YOUR website!Two numbers, x & y; (x the largest) : The sum of two numbers is 64. x + y = 64 or x = (64-y) : Two more than twice the larger number is five less than seven times the smaller. 2x + 2 = 7y - 5 2x = 7y - 5 - 2 2x = 7y - 7 : Find the numbers. : Substitute (64-y) for x in the above equation 2(64-y) = 7y - 7 : 128 - 2y = 7y - 7 : 128 + 7 = 7y + 2y : 135 = 9y y = y = 15 : Find x: x = 64 - 15 x = 49 : : Check solution in the statement: "Two more than twice the larger number is five less than seven times the smaller." 2(49) + 2 = 7(15) - 5 98 + 2 = 105 - 5
 Geometry_Word_Problems/190253: a mountain bike tire is typically 26 inches in diameter. How many rotations will the tire make in one mile(5280 feet)?1 solutions Answer 142775 by ankor@dixie-net.com(15746)   on 2009-04-08 20:13:38 (Show Source): You can put this solution on YOUR website!a mountain bike tire is typically 26 inches in diameter. How many rotations will the tire make in one mile(5280 feet)? : Rotations = = 775.7 revolutions
 Length-and-distance/190162: I want to order an object from a brochure, but need to know if it will fit my space. The dimensions are given as: 12x24x36 inches. Is there a RULE about how to write/read dimensions? (similar to" the top of the map is north".) example do I read this size as width, length and depth? or as length, width, height? or .......? HELP and THANKS.1 solutions Answer 142752 by ankor@dixie-net.com(15746)   on 2009-04-08 16:40:08 (Show Source): You can put this solution on YOUR website!Almost always it's: Length x width x height Usually the length is longer than the width, however, but the height is always last.