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 'mananth'

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, >>Next

 Problems-with-consecutive-odd-even-integers/681778: The product of two consecutive even integers is 12 less than 6 times their sum.1 solutions Answer 422779 by mananth(12270)   on 2012-11-16 20:07:08 (Show Source): You can put this solution on YOUR website!let the integerrs be x & x+2 Product = x(x+2) 12 less than 6 times the sum 6(x+x+2)-12 6(2x+2)-12 x(x+2)=6(2x+2)-12 x^2+2x=12x+12-12 x^2+2x-12x=0 x^2-10x=0 x(x-10)=0 x=0 OR 10 10,12
 Mixture_Word_Problems/681775: An airplane, flying with a tail wind, travels 1380 miles in 2 hours. The return trip, against the wind, takes 2.5 hours. Find the cruising speed of the plane and the speed of the wind (assume that both rates are constant). 1 solutions Answer 422778 by mananth(12270)   on 2012-11-16 20:02:19 (Show Source): You can put this solution on YOUR website!Plane speed =x mph wind speed =y mph Against windx-y 2.5 hours with wind x+y 2 hours Distance = 1380 miles distance= 1380 t=d/r against wind 1380.00 / ( x - y )= 2.50 2.50 x - -2.50 y = 1380.00 ....................1 with wind x+y 1380.00 / ( x + y )= 2.00 2.00 ( x + y ) = 1380.00 2.00 x + 2.00 y = 1380.00 ...............2 Eliminate y in the linear system Multiply (1) by 2.00 Multiply (2) by 2.50 we get y 5.00 x + -5.00 y = 2760.00 5.00 x + 5.00 = 3450.00 10.00 x = 6210.00 / 10.00 x = 621 mph plug value of x in (1) y 2.5 x -2.5 y = 1380 1552.5 -2.5 -1552.5 = 1380 -2.5 y = 1380 -2.5 y = -172.5 mph y = 69 Plane 621 mph wind 69 mph CHECK x+y= 690 X-y= 552 + 1380.00 / ( 690.00 )= 2 1380 / ( 552 ) = 2.5
 Polynomials-and-rational-expressions/681763: A right angled triangle has a height of 2x + 3 centimeters, and a hypotenuse of length 4x - 1 centimeters. Find and expression for the base of the triangle. 1 solutions Answer 422776 by mananth(12270)   on 2012-11-16 19:54:10 (Show Source): You can put this solution on YOUR website!height of 2x + 3 centimeters, and a hypotenuse of length 4x - 1 Pythagoras theorem hypotenuse^2= base^2+height^2 base^2= hypotenuse^2-height^2 =(4x-1)^2-(2x+3)^2 =16x^2-8x+1-(4x^2+12x+9) =16x^2-8x+1-4x^2-12x-9 =12x^2-20x-8 =4(3x^2-5x-2) =4(3x^2-6x+x-2) =4(3x(x-2)+1(x-2)) =4(3x+1)(x-2) base = cm
 Polynomials-and-rational-expressions/681764: perform the operation and simplify 1/x-y - 2/x^2-y^2 + 1/x+y1 solutions Answer 422775 by mananth(12270)   on 2012-11-16 19:42:42 (Show Source): You can put this solution on YOUR website! LCD = x^2-y^2
 Travel_Word_Problems/681759: A silversmith has two alloys, one containing 60% silver and the other 40% silver. How much of each should be melted and combined to obtain 800 grams of an alloy containing 54% silver?1 solutions Answer 422774 by mananth(12270)   on 2012-11-16 19:36:50 (Show Source): You can put this solution on YOUR website! Silver percent ---------------- quantity Metal alloy I 60 ---------------- x grams Metal alloy II 40 ------ 800 - x grams Mixture 54 ---------------- 800 60x+ 40(800 -x)=54 * 800 6000x +4000(800-x) = 4320000 6000x+ 3200000 -4000x = 4320000 6000x- 4000x= 4320000 - -3200000 2000 x = 1120000 / 2000 x = 560 grams 60.00% Metal alloy I 240 grams 40.00% Metal alloy II m.ananth@hotmail.ca
 Percentage-and-ratio-word-problems/681755: A large corporation wants to invest 1,200000.00. Part of this amount is invested at 12.5 percent and part at 15%. If the total interest earnings should be 155 000.00 per year, how much should be invested at 15% and how much as 12.5%1 solutions Answer 422773 by mananth(12270)   on 2012-11-16 19:31:21 (Show Source): You can put this solution on YOUR website!Part I 15.00% per annum ------------- Amount invested =x Part II 12.50% per annum ------------ Amount invested = y 1200000 Interest----- 155000 Part I 15.00% per annum ---x Part II 12.50% per annum ---y Total investment x + 1 y= 1200000 -------------1 Interest on both investments 15.00% x + 12.50% y= 155000 Multiply by 100 15 x + 12.5 y= 15500000.00 --------2 Multiply (1) by -15 we get -15 x -15 y= -18000000.00 Add this to (2) 0 x -2.5 y= -2500000 divide by -2.5 y = 1000000 Part I 15.00% \$ 200000 Part II 12.50% \$ 1000000 CHECK 200000 --------- 15.00% ------- 30000.00 1000000 ------------- 12.50% ------- 125000.00 Total -------------------- 155000.00 m.ananth@hotmail.ca
 Linear-equations/681403: My math problem is this: Tell whether the graphs of the two equations are parallel lines. Explain your reasoning. y=5x-7, 5x+y=71 solutions Answer 422666 by mananth(12270)   on 2012-11-15 22:17:06 (Show Source): You can put this solution on YOUR website!y=5x-7, . . 5x+y=7 re write in slope intercept form y=-5x+7 compare the equations with the equation y=mx+b where m is the slope. The slopes of the two lines are 5 & -5. They are not equal. Hence the lines are not parallel. Parallel lines have equal slopes.
 Money_Word_Problems/681439: Fres Calibig invests a part of \$17000 at 8% and the rest 9%. If the annual incomes from the two investments are equal, how much has he invested at each rate?1 solutions Answer 422665 by mananth(12270)   on 2012-11-15 22:11:51 (Show Source): You can put this solution on YOUR website!Part I 8.00% per annum ------------- Amount invested =x Part II 9.00% per annum ------------ Amount invested = y Total= 17000 Part I 8.00% per annum ---x Part II 9.00% per annum ---y Total investment x+y= 17000 -------------1 Interest on both investments 8.00% x = 9.00% Multiply by 100 8 x = 9 y 8x-9y=0 --------2 1 x + 1 y = 17000 .............1 8 x -9 y = 0 .............2 Eliminate y multiply (1)by 9 Multiply (2) by 1 9 x 9 y = 153000 8 x -9 y = 0 Add the two equations 17 x = 153000 / 17 x = 9000 plug value of x in (1) 1 x + 1 y = 17000 9000 + y = 17000 y = 17000 -9000 y = 8000 y = 8000 x= 9000 Part I y= 8000 Part II m.ananth@hotmail.ca
 test/681449: write an equation of the line that is perpendicular to the given line and passes through the given point. y=x-7(0,-5)1 solutions Answer 422662 by mananth(12270)   on 2012-11-15 22:02:14 (Show Source): You can put this solution on YOUR website!y=x-7 and (0,-5) y=x-7 compare with the equation y = mx+b m=1 so the slope is 1 the slope of line perpendicular to this line will be -1 (negative reciprocal) using the equation y-y1=m(x-x1) where m is the slope and (x1,y1) are the co ordibnates of the point on the line. y-(-5)=-1(x-0) y+5=-x y=-x-5 is the equation
 logarithm/681441: The formula below can be used to find the number of milligrams D of a certain drug that is in a patients bloodstream h hours after the drug has been administered. D = 5e-0.38h When the number of milligrams reaches 2, the drug is to be administered again. What is the time between injections?1 solutions Answer 422659 by mananth(12270)   on 2012-11-15 21:53:40 (Show Source): You can put this solution on YOUR website!Generally it is an exponential function. It may be D= 5e^(-0.37h) I assume the above here D = 2 2= 5e^(-0.37h) /5 0.4=e^(-0.37h) taking the natural log ln(0.4)=-0.37h (ln(0.4))/(-0.37)=h h is the time in hours
 Radicals/681437: x + 2y = 3 3x - 2y = 5 What is the solution to the system of equations?1 solutions Answer 422650 by mananth(12270)   on 2012-11-15 21:39:18 (Show Source): You can put this solution on YOUR website!1 x + 2 y = 3................(1) 3 x + 2 y = 5................(2) Eliminate y multiply (1)by -1 Multiply (2) by 1 -1 x -2 y = -3 3 x + 2 y = 5 Add the two equations 2 x = 2 / 2 x = 1 plug value of x in (1) 1 x + 2 y = 3 1 + 2 y = 3 2 y = 3 2 y = 2 y = 1 x= 1 y= 1 The solution (1,1) m.ananth@hotmail.ca
 Travel_Word_Problems/680833: Walter and John leave in their cars at the same time. Walter drives 252 miles. John drives 10 miles per hours faster than Walter and travels 312 miles. If Walter and John arrive at their destinations at the same time, determine how fast Walter is driving.1 solutions Answer 422479 by mananth(12270)   on 2012-11-14 21:55:17 (Show Source): You can put this solution on YOUR website!Walter x mph John 10 faster x + 10 mph Walter 252 miles John 312 miles Walter time = John time t=d/r 252 / x = 312 /( x + 10 ) cross multiply 252 ( x + 10 ) = 312 x 252 x + 2520 = 312 x 252 x - 312 x = -2520 -60 x = -2520 / -60 x = 42 mph Walter speed = 42 mph John speed = 52 mph
 Numbers_Word_Problems/680831: the product of two positive numbers is 32 determine the two numbers if one is four more then the other?1 solutions Answer 422477 by mananth(12270)   on 2012-11-14 21:51:38 (Show Source): You can put this solution on YOUR website!let numbers be x&y xy=32 x=y+4 y(y+4)=32 y^2+4y=32 y^2+4y-32=0 y^2+8y-4y-32=0 y(y+8)-4(y+8)=0 (y+8)(y-4)=0 y=-8 OR 4 The number is positive xy=32 4*x=32 x=8 8,4 are the numbers
 Linear_Equations_And_Systems_Word_Problems/680775: A man has Rs.8000 which he wishes to invest in two enterprises so that his total income per year will be Rs.425. if one enterprise pays 5.5% annually and the other 5% annually, how much must be invested in each. 1 solutions Answer 422473 by mananth(12270)   on 2012-11-14 21:46:52 (Show Source): You can put this solution on YOUR website!Part I 5.50% per annum ------------- Amount invested =x Part II 5.00% per annum ------------ Amount invested = y 8000 Interest----- 425 Part I 5.50% per annum ---x Part II 5.00% per annum ---y Total investment x + 1 y= 8000 -------------1 Interest on both investments 5.50% x + 5.00% y= 425 Multiply by 100 5.5 x + 5 y= 42500.00 --------2 Multiply (1) by -5.5 we get -5.5 x -5.5 y= -44000.00 Add this to (2) 0 x -0.5 y= -1500 divide by -0.5 y = 3000 Part I 5.50% \$ 5000 Part II 5.00% \$ 3000 CHECK 5000 --------- 5.50% ------- 275.00 3000 ------------- 5.00% ------- 150.00 Total -------------------- 425.00 m.ananth@hotmail.ca
 test/680809: Identify the slope and y- intercept of the line with the equation. 2x-3y=01 solutions Answer 422471 by mananth(12270)   on 2012-11-14 21:42:16 (Show Source): You can put this solution on YOUR website!2x-3y=0 2x=3y y=2x/3 y/x= 2/3 slope = 2/3 Here b = 0 in the equation y=2x/3 when comparing with y= mx+b the line passes through the origin. No intercept
 Money_Word_Problems/680811: you inherit \$16,000 and invest it in two bonds that pay 6% and 8% annual interest. At the end of one year the interest from the 8% bond is \$580 greater than the interest from the 6% bond. How much was invested in each bond?1 solutions Answer 422470 by mananth(12270)   on 2012-11-14 21:38:38 (Show Source): You can put this solution on YOUR website!6% bond investment be x 8% bond investment be y x+y = 16000.................(1) 6%x+580=8%y multiply by 100 6x+58000=8y 6x-8y=-58000................(2) solve simultaneously 1 x + 1 y = 16000 .............1 6 x -8 y = -58000 .............2 Eliminate y multiply (1)by 8 Multiply (2) by 1 8 x 8 y = 128000 6 x -8 y = -58000 Add the two equations 14 x = 70000 / 14 x = 5000 plug value of x in (1) 1 x + 1 y = 16000 5000 + y = 16000 y = 16000 -5000 y = 11000 y = 11000 x= 5000 y= 11000 \$ 5000 @ 6% \$ 11000 @8% m.ananth@hotmail.ca
 Equations/680818: I have to write out the answer for 72/n=9. How do I go about this.1 solutions Answer 422468 by mananth(12270)   on 2012-11-14 21:30:57 (Show Source): You can put this solution on YOUR website!72/n=9. In all fractions in equations first you have to eliminate the denominator we can eliminate the denominator by multiplying by n multiply equation by n 72=9n /9 72/9 = 9n/9 n=8
 Equations/680803: find the vertex, any intercepts &the symmetric line? 1. f(x)=x^2+10x+91 solutions Answer 422467 by mananth(12270)   on 2012-11-14 21:28:03 (Show Source): You can put this solution on YOUR website!f(x)=x^2+10x+9 y= x^2+10x+9 x coordinate of vertex = -b/2a= -10/2= -5 plug x= 5 in the equation x^2+10x+9=y (-5)^2+10(-5)+9=y y=-16 Vertex(-5,-16) The x intercept occurs when y=0, make the equation = 0 and solve for x x^2 +10x+9 = 0 Factor (x+9)(x+1) = 0 x = -9 and x = -1, these are the x intercepts : y intercept occurs when x=0, substitute 0 for x in the equation, and find y y = 0^2 - 10(0) + 9 y = 9; : Axis of symmetry x = -b/2a= -10/2=-5 x=-5 is the axis of symmetry.
 Equations/680805: Hi i just want to say thanks alot and if you can break this problem down step by step for me x/2+x/3=401 solutions Answer 422466 by mananth(12270)   on 2012-11-14 21:12:35 (Show Source): You can put this solution on YOUR website! we have to eliminate the denominator LCD = 6 myltiply equation by 6 3x+2x=240 5x=240 /5 x=48
 Complex_Numbers/680802: solve(3-i)/(-4+2i)1 solutions Answer 422464 by mananth(12270)   on 2012-11-14 21:09:49 (Show Source): You can put this solution on YOUR website! -0.7-0.1i
 Trigonometry-basics/680801: What is the x-intercept of 3x + 2y = -6?1 solutions Answer 422463 by mananth(12270)   on 2012-11-14 21:02:08 (Show Source): You can put this solution on YOUR website!3x + 2y = -6? For X intercept plug y =0 3x+2(0) =-6 3x=-6 x=-2 X intercept = -2
 Quadratic_Equations/680795: use the quadratic formula for : 4x^2+4=17x my answer: 4x^2+4=17x 4x^2+4-17=0 (-17)^2-4(4)(4)=225 ___ 17(+/-) /225 ___________ = 17(+/-)15 /8 8 root: 4, (1/4) is this right? 1 solutions Answer 422462 by mananth(12270)   on 2012-11-14 21:00:35 (Show Source): You can put this solution on YOUR website!yes you are right. a= 4 b= -17 c= 4 b^2-4ac= 289 - 64 b^2-4ac= 225 = 15 x1=( 17 + 15 )/ 8 x1= 4 x2=( 17 -15 ) / 8 x2= 0.25 (4,0.25)
 Percentage-and-ratio-word-problems/680793: Anne and Nancy use a metal alloy that is 15.6% copper to make jewelry. How many ounces of an alloy that is 14% copper must be mixed with an alloy that is 16% copper to form 100 ounces of the desired alloy? 1 solutions Answer 422460 by mananth(12270)   on 2012-11-14 20:57:07 (Show Source): You can put this solution on YOUR website! percent ---------------- quantity Metal alloy I 14 ---------------- x ounces Metal alloy II 16 ------ 100 - x ounces Mixture 16 ---------------- 100 14x+16(100-x)=15.6*100 1400x+1600(100- x)=156000 1400x+160000-1600x=156000 1400x-1600x= 156000 -160000 -200 x = -4000 / -200 x=20ounces 14.00% Metal alloy I 80 ounces 16.00% Metal alloy II m.ananth@hotmail.ca
 Quadratic_Equations/680789: use the quadrtic formula for: 4x^2+x-3=01 solutions Answer 422458 by mananth(12270)   on 2012-11-14 20:51:59 (Show Source): You can put this solution on YOUR website!4x^2+x-3=0 compare with ax^2+bx+c=0 Find the roots of the equation by quadratic formula a= 4 b= 1 c= -3 b^2-4ac= 1 - -48 b^2-4ac= 49 = 7 x1=( -1 + 7 )/ 8 x1= 0.75 x2=( -1 -7 ) / 8 x2= -1 The roots are 0.75,-1
 Linear-systems/680783: The question is: Solve each system algebraically. Write the solution as an ordered pair. Problem: {x+ y= 7 {y = 2x -2 I have to find the solution but I am confused on where to begin. Thanks for the help1 solutions Answer 422457 by mananth(12270)   on 2012-11-14 20:47:57 (Show Source): You can put this solution on YOUR website!1 x + 1 y = 7 .............1 y=2x-2 2x-y=2 2 x - y = 2 .............2 Eliminate y multiply (1)by 1 Multiply (2) by 1 1 x 1 y = 7 2 x -1 y = 2 Add the two equations 3 x = 9 / 3 x = 3 plug value of x in (1) 1 x + 1 y = 7 3 + y = 7 y = 7 -3 y = 4 y = 4 x= 3 y= 4 (3,4) is the solution m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/680782: A father is six times as old as the son. Four years ago the father was ten times as old as his son. Find the 1. son's age 2. Father's age 3. Son's age in 3yrs times. 1 solutions Answer 422456 by mananth(12270)   on 2012-11-14 20:43:36 (Show Source): You can put this solution on YOUR website!son's age =x father's age =6x 4 years ago son's age = x-4 father's age =6x-4 conditon 6x-4=10(x-4) 6x-4=10x-40 6x-10x=-40+4 -4x=-36 /-4 x=9 son's age = 9 years father's age = 6x= 54 son's age 3 years later --> x+3= 9+3=12
 Linear_Algebra/680747: Solve Linear Systems Algebraically. x+ 4y = 1 3x + 2y = -12 and 3x + 2y = 6 x-4y = -6 Pleas help, Clari1 solutions Answer 422453 by mananth(12270)   on 2012-11-14 20:05:36 (Show Source): You can put this solution on YOUR website!1 x + 4 y = 1 .............1 3 x + 2 y = -12 .............2 Eliminate y multiply (1)by 1 Multiply (2) by -2 1 x 4 y = 1 -6 x -4 y = 24 Add the two equations -5 x = 25 / -5 x = -5 plug value of x in (1) 1 x + 4 y = 1 -5 + 4 y = 1 4 y = 1 + 5 4 y = 6 y = 2 x= -5 y= 2 --------------- 3 x + 2 y = 6 .............1 1 x -4 y = -6 .............2 Eliminate y multiply (1)by 2 Multiply (2) by 1 6 x 4 y = 12 1 x -4 y = -6 Add the two equations 7 x = 6 / 7 x = 1 plug value of x in (1) 3 x + 2 y = 6 3 + 2 y = 6 2 y = 6 -3 2 y = 3 y = 2 x= 1 y= 2 m.ananth@hotmail.ca
 Rectangles/679545: The three dimensions of a rectangular box are height, length, and width. The us of the dimensions is 18 feet. The height equals four fifths the sum of the length and the width. It also equals four times the difference of the length and the width. What are the dimensions of the box?1 solutions Answer 421973 by mananth(12270)   on 2012-11-12 21:23:06 (Show Source): You can put this solution on YOUR website!sum of dimensions = 18 feet l+w+h=18 (l+w)=18-h . . second condition h= 4/5(l+w) replace l+w by (18-h) h=4/5(18-h) multiply equation by 5 5h= 4(18-h) 5h=72-4h 5h+4h=72 9h=72 h=8 h=4(l-w) 8=l-w l=8+w l+w+h=18 8+w+w+8=18 2w+16=18 2w=18-16 2w=2 w=1 so Length =8+w= 9 feet (w=1) the dimensions are 9 by 8 by 1 feet
 Angles/679542: Please help me to solve the following; The complement of an angle measures 10(degrees) less than one-fifth of its supplement. Find the measure of the angle. I started out by writing: 90-x = 10 -1/5(90 - x) I"m not sure how to handle the fraction (one-fifth). The answer is x=80. Everything I've tried did not work. Your help is appreciated. Thanks Joshua1 solutions Answer 421969 by mananth(12270)   on 2012-11-12 21:13:26 (Show Source): You can put this solution on YOUR website!angle =x complement= (90-x) supplement = 180-x (90-x)= 1/5(180-x)-10 multiply the equation by 5 5(90-x)= (180-x)-50 450-5x=180-x-50 5x-x= 450-180+50 4x=320 /4 x=80 deg
 Linear-systems/679515: 1.find the equation of a line that passes through the point (0,2)and (4,-1) 2.find the equation of a line that passes through the points (-2,0)and (0,1) 1 solutions Answer 421968 by mananth(12270)   on 2012-11-12 21:07:14 (Show Source): You can put this solution on YOUR website!(x1,y1)(0,2)and (x2,y2)(4,-1) The equation of line when coordinates of two pointsa are given plug the values of (x1,y1)(0,2)and (x2,y2)(4,-1) y-2=3(x-4) y-2=3x-12 3x-y-10=0
 Linear-systems/679506: Solving Linear Systems of equations The problem: one is 5% acid and one is 6.5% acid . You want to make 200ml of vinegar,with 6% acid. How many ml of each vinegar do you need to mix together? My question: With percents I get confused, and I am not sure which variables you would use to set this up into two equations? 1 solutions Answer 421967 by mananth(12270)   on 2012-11-12 20:58:17 (Show Source): You can put this solution on YOUR website!Let quantity of 5% acid required be x Let quantity of 6.5% acid required be y Mixture = 6% Equate percentages 5%x+6.5%y=6%*200 multiply by 100 5x+6.5y=1200................(1) Quantity x+y=200.....................(2) multiply equation (2) by -5 we get -5x-5y=-1000 Add this equation to (1) we get 1.5y=200 y= 200/1.5 y=133.3 ml x= balance amount= 66.67ml