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 logarithm/45116: This question is from textbook INTERMEDIATE ALGEBRA Exponential and Logarithmic Functions. Compound Interest. If \$500 is deposited in an account paying 8.5% annual interest, compounded semiannually, how long will it take for ethe account to increase to \$800?1 solutions Answer 29938 by venugopalramana(3286)   on 2006-07-08 22:28:21 (Show Source): You can put this solution on YOUR website!Exponential and Logarithmic Functions. Compound Interest. If \$500 is deposited in an account paying 8.5% annual interest, compounded semiannually, how long will it take for ethe account to increase to \$800? A=P(1+R/100)^N 800=500*(1+8.5/100)^N (1.085)^N=800/500=1.6 NLOG(1.085)=LOG(1.6) N=LOG(1.6)/LOG(1.085)=0.2041/0.0354=5.76 YRS...ROUNDED ...6 YEARS
 Radicals/44929: I am required to solve using the quadratic formula, if there are no real roots, then that can be an answer too. Thank you. 3=7x-4x(2) the two in parentheses is a power.1 solutions Answer 29769 by venugopalramana(3286)   on 2006-07-06 12:34:59 (Show Source): You can put this solution on YOUR website!I am required to solve using the quadratic formula, if there are no real roots, then that can be an answer too. Thank you. 3=7x-4x(2) the two in parentheses is a power. 4X^2-7X+3=0...IF AX^2+BX+C=0...THEN A=4...B=-7...C=3 x=(7+1)/6=8/8=1.....and x=(7-1)/8=6/8=3/4
 Exponential-and-logarithmic-functions/44930: This question is from textbook Algebra and Trigonometry with Analytic geometry The amount A in account after t years of an initial principle P invested at an annual rate r compounded continuiusly is given by A = Pe^rt where r is expressed as a decimal. What is the amount in the account if \$500 is invested for 10 years at the rate of 5% compounded continuously? My answer is \$750.00, thanks for checking my answer.1 solutions Answer 29767 by venugopalramana(3286)   on 2006-07-06 12:28:13 (Show Source): You can put this solution on YOUR website!The amount A in account after t years of an initial principle P invested at an annual rate r compounded continuiusly is given by A = Pe^rt where r is expressed as a decimal. What is the amount in the account if \$500 is invested for 10 years at the rate of 5% compounded continuously? My answer is \$750.00, thanks for checking my answer. P=500 \$ R=5%=5/100=0.05 T=10 YRS. A=500*E^10*0.05=500*E^0.5=824.36
 Exponential-and-logarithmic-functions/44931: This question is from textbook Algebra and Trigonometry with Analytic geometry Find the number log5(1/5). my answer is -1 but not sure. thanks for checking.1 solutions Answer 29765 by venugopalramana(3286)   on 2006-07-06 12:24:52 (Show Source): You can put this solution on YOUR website!Find the number let x = log5(1/5). hence 5^x=1/5=5^-1 hence x=-1 my answer is -1 but not sure...PERFECT 100% OK. thanks for checking.
 Exponential-and-logarithmic-functions/44932: This question is from textbook Algebra and Trigonometry with Analytic geometry solve log a (8x+5)=log a (4x+29) My answer is 6, is that right. thanks for checking.1 solutions Answer 29763 by venugopalramana(3286)   on 2006-07-06 12:07:47 (Show Source): You can put this solution on YOUR website!solve log a (8x+5)=log a (4x+29) 8x+5=4x+29 8x-4x=29-5=24 4x=24 x=6 My answer is 6, is that right. thanks for checking
 Exponential-and-logarithmic-functions/44935: This question is from textbook Algebra and Trigonometry with Analytic geometry Given that log a (x)=3.58 and log a (y)=4.79. find loga(y/x). My answer is 8.37, is this right. thanks for looking at answer.1 solutions Answer 29762 by venugopalramana(3286)   on 2006-07-06 12:03:21 (Show Source): You can put this solution on YOUR website!Given that log a (x)=3.58 and log a (y)=4.79. find loga(y/x). log(y/x)=log(y)-log(x)=4.79-3.58=1.21 My answer is 8.37, is this right. ...no you did log(xy)which is log(x)+log(y)=8.37 thanks for looking at answer.
 Polynomials-and-rational-expressions/44913: DIVIDE X^3-64 BY (X-4)1 solutions Answer 29761 by venugopalramana(3286)   on 2006-07-06 11:51:32 (Show Source): You can put this solution on YOUR website!DIVIDE X^3-64 =(x)^3-(4)^3=(x-4)(x^2+4x+16)...hence this divided by x-4 gives x^2+4x+16
 Functions/44923: This question is from textbook College Algebra Determine the average rate of change of the function between the given values of the variable. f(t) = Sqrt(t); t = a, t= a+h I came out with 1/sqrt(a+h) + Sqrt (a) Thank you so much!1 solutions Answer 29760 by venugopalramana(3286)   on 2006-07-06 10:26:16 (Show Source): You can put this solution on YOUR website!Determine the average rate of change of the function between the given values of the variable. f(t) = Sqrt(t); t = a, t= a+h I came out with f(a+h)= sqrt(a+h) f(a)= Sqrt (a) f(a+h)-f(a)=sqrt(a+h)-sqrt(a) avg rate of change={f(a+h)-f(a)}/(a+h-a)={sqrt(a+h)-sqrt(a)}/h
 Graphs/44926: ok here is a problem that is driving me nuts i can't understand what to do. the question says " for the given functions f and g, find the indicated composition." and here is the problem f(x)=x^2+2x+3, g(x)=x^2+2x+2 (f of g)(-5)1 solutions Answer 29759 by venugopalramana(3286)   on 2006-07-06 09:56:03 (Show Source): You can put this solution on YOUR website!ok here is a problem that is driving me nuts i can't understand what to do. the question says " for the given functions f and g, find the indicated composition." and here is the problem f(x)=x^2+2x+3 g(x)=x^2+2x+2 f of g(-5)=f{g(-5)} g(-5)=(-5)^2+2(-5)+2=25-10+2=17 f{g(-5)}=f(17)=17^2+2*17+3=289+34+3=326
 Functions/44924: This question is from textbook College Algebra A linear function is given. (a) Find the average rate of change of the function between x = a and x = a + h. (b). Show that the average rate of change is the same as the slope of the line. g(x) = -4x + 2 I came out with 4 for both answers. Thank you so much!1 solutions Answer 29758 by venugopalramana(3286)   on 2006-07-06 09:52:26 (Show Source): You can put this solution on YOUR website!A linear function is given. (a) Find the average rate of change of the function between x = a and x = a + h. (b). Show that the average rate of change is the same as the slope of the line. g(x) = -4x + 2 g(a+h)=-4(a+h)+2=-4a-4h+2 g(a)=-4a+2 g(a+h)-g(a)=-4h avg.rate of change = {g(a+h)-g(a)}/(a+h-a)=-4h/h=-4 slope of the given line =-4 I came out with 4 for both answers....no -4 is the answer Thank you so much!
 Exponential-and-logarithmic-functions/44727: This question is from textbook Algebra and Trigonometry with Analytic geometry Find an exponential function of the form f(x)= ba^x+c with y intercept 2, horizontal asymptote=-2, that passes through the point P(1,4). My answer is f(x)= 2(1.5^x)-2. Thanks for the help.1 solutions Answer 29615 by venugopalramana(3286)   on 2006-07-04 12:40:05 (Show Source): You can put this solution on YOUR website!Find an exponential function of the form f(x)=Y= ba^x+c with y intercept 2, THAT FOR X=0...Y=2 Y=2=B*A^0+C=B+C...............................I horizontal asymptote=-2, THAT IS AS X TENDS TO + OR - INFINITY Y TENDS TO -2 A^X WILL TEND TO ZERO AS X TENDS TO +INFINITY IF A<1 AND A^X WILL TEND TO ZERO AS X TENDS TO -INFINITY IF A>1..HENCE WE TAKE THAT A^X WILL TEND TO ZERO AS X TENDS TO + OR - INFINITY TO GET Y=-2=B*0+C...............................II C=-2 FROM EQN.I....B-2=2.. B=4 that passes through the point P(1,4). My answer is f(x)= 2(1.5^x)-2. Thanks for the help. Y=4=4*A^1-2..................III 4A=4+2=6 A=6/4=1.5 ANSWER IS F(X)=Y=4*1.5^X-2...GRAPH IS GIVEN BELOW
 Matrices-and-determiminant/44740: This question is from textbook College Algebra Solve each system using Gaussian elimination. State whether each system is independent, dependent, or inconsistent. x - y = 2 3x - y =121 solutions Answer 29607 by venugopalramana(3286)   on 2006-07-04 12:15:31 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK ----------------------- x - y + z = 2 -x + y + z = 4 -x + z = 2 augmented matrix is 1.....................-1.......................1.............................2 -1.....................1.......................1.............................4 -1.....................0.......................1.............................2 nr2=r2+r1 and nr3=r3+r1 1..................-1.................1.............2 1-1=0............1-1=0............1+1=2..........2+4=6 1-1=0...........-1+0=-1...........1+1=2..........2+2=4 nr2=r2/2....nr3=r3-r2 1....................-1...............1..............2 0/2=0.............0/2=0..............2/2=1........6/2=3 0-0=0............-1-0=-1..............2-2=0.......4-6=-2 nr1=r1-r3-r2.......nr2=2r2........nr3=-r3 1-0-0=1............-1+1-0=0.........1-0-1=0.......2+2-3=1 0.....................0...................1............3 0.....................1...................0.............2 exchange r2 and r3 1....0........0.......1 0....1........0.......2 0....0........1.......3 hence x=1......y=2.....z=3
 Volume/44741: My Question A trough, in the form of an open rectangular box, is 1.85 m long, 45 cm wide and 28 cm deep externally. If the trough is made of wood 2.5 cm thick, find, in cubic centimetres, the volume of wood used. Thank you in anticipation.1 solutions Answer 29605 by venugopalramana(3286)   on 2006-07-04 12:13:49 (Show Source): You can put this solution on YOUR website!A trough, in the form of an open rectangular box, is 1.85 m long, 45 cm wide and 28 cm deep externally. If the trough is made of wood 2.5 cm thick, find, in cubic centimetres, the volume of wood used. EXTERNAL DIMENSIONS L=1.85 M =185 CM. B=45 CM H=28 CM OPEN AT TOP. EXTERNAL VOLUME OF BOX =LBH=185*45*28=233100 CC INTERNAL DIMENSIONS WOOD THICKNESS=2.5 CM L'=185-2*2.5=180 CM B'=45-2*2.5=40 CM H'=28-1*2.5=25.5 CM...SINCE THE BOX IS OPEN AT TOP INTERNAL VOLUME OF BOX =L'*B'*H'=180*40*25.5=183600 CC HENCE VOLUME OF WOOD =233100-183600=49500 CC
 Linear-equations/44749: Im not sure what topic it would fall under. But here is my questions the variable x is 4 less than the variable y? answer I think it is, x - 4 = y next question if the variable t is multiplied by 5, the result is equal to the variable r. answer I think it is, t * 5 = r next question if 3 is subtracted from the product of the variables x and y the result is equal to 4 time the variable z this one I really couldn't understand next question the quotient of the variable x with the variable y is 2 more than o.7 of the variable z. this is another one I don't understand. If there is a way to explain the answer to me and how you get the answer I would appreciate it.1 solutions Answer 29603 by venugopalramana(3286)   on 2006-07-04 12:04:22 (Show Source): You can put this solution on YOUR website!Im not sure what topic it would fall under. But here is my questions the variable x is 4 less than the variable y? THINK THIS WAY..WHICH IS LESS OR MORE..X IS LESS..Y IS MORE..SO TO GET SMALLER NUMBER X FROM A BIGGER NUMBER Y YOU NEED TO SUBTRACT 4 FROM BIGGER NUMBER.HENCE ANSWER IS X=Y-4 answer I think it is, x - 4 = y...NO...Y-4=X next question if the variable t is multiplied by 5, the result is equal to the variable r. answer I think it is, t * 5 = r...OK..GOOD next question if 3 is subtracted from the product of the variables x and y the result is equal to 4 time the variable z GO STEP BY STEP PRODUCT OF X AND Y =XY 3 IS SUBTRACTE..FROM THE PRODUCT ..SO WE GET XY-3 4 TIMES Z =4Z BOTH ARE SAME..SO XY-3=4Z this one I really couldn't understand next question the quotient of the variable x with the variable y is 2 more than o.7 of the variable z. this is another one I don't understand.
 Length-and-distance/44743: My Question A tin which is 12 cm long, 9 cm wide and 4 cm deep holds 120 g of tea. If 1 kg of the same tea is packed into a tin which has a 12 cm square base, how tall will the tin have to be ? Please help me to solve this. Thanks.1 solutions Answer 29602 by venugopalramana(3286)   on 2006-07-04 11:57:26 (Show Source): You can put this solution on YOUR website!A tin which is 12 cm long, 9 cm wide and 4 cm deep holds 120 g of tea. If 1 kg of the same tea is packed into a tin which has a 12 cm square base, how tall will the tin have to be ? VOLUME OF TIN =L*B*H=12*9*4=432 CC IT HOLDS 120 GM.OF TEA TO HOLD 1 KG=1000 GMS..WE NEED 1000*432/120 =36000 CC BASE AREA OF NEW TIN =A=12*12=144 SQ.CM. HENCE HT NEEDED =V/A=36000/144=250 CM Please help me to solve this. Thanks.
 Linear-systems/44751: equations with 3 linear variables 6x-4y+5z=31 5x+2y+2z=13 x+y+z=2 should you multiply the 2nd equation by 2? show work1 solutions Answer 29601 by venugopalramana(3286)   on 2006-07-04 11:53:09 (Show Source): You can put this solution on YOUR website!OK..THE PROBLEM,WE FACE IN ANSWERING IS THAT WE ARE NOT AWARE OF YOUR COURSE OF STUDY AND BACKGROUND.THE SOLUTION I GAVE IS BY GAUSS JORDAN ELIMINATION METHOD USED IN MATRICES AS WANTED BY SOME STUDENTS.IF YOU ARE NOT TAUGHT THAT ,WE SHALL DO BY NORMAL ELIMINATION. equations with 3 linear variables 6x-4y+5z=31.......................................I 5x+2y+2z=13...........................II x+y+z=2.......................III EQN.II - 2*EQN.III 5X+2Y+2Z-2X-2Y-2Z=13-2*2=9 3X=9 X=9/3=3 EQN.I+4*EQN.III 6X-4Y+5Z+4X+4Y+4Z=31+4*2=39 10X+9Z=39...BUT...X=3..SO 10*3+9Z=39 9Z=39-30=9 Z=9/9=1 PUTTING IN EQN.III 3+Y+1=2 Y=2-4=-2 HOPE YOU UNDERSTOOD. ------------------------------------------------------------------------ SEE THE FOLLOWING AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK YOU MAY MULTIPLY EQN.II WITH 2 AND ADD TO EQN.I TO ELIMINATE Y x - y + z = 2 -x + y + z = 4 -x + z = 2 augmented matrix is 1.....................-1.......................1.............................2 -1.....................1.......................1.............................4 -1.....................0.......................1.............................2 nr2=r2+r1 and nr3=r3+r1 1..................-1.................1.............2 1-1=0............1-1=0............1+1=2..........2+4=6 1-1=0...........-1+0=-1...........1+1=2..........2+2=4 nr2=r2/2....nr3=r3-r2 1....................-1...............1..............2 0/2=0.............0/2=0..............2/2=1........6/2=3 0-0=0............-1-0=-1..............2-2=0.......4-6=-2 nr1=r1-r3-r2.......nr2=2r2........nr3=-r3 1-0-0=1............-1+1-0=0.........1-0-1=0.......2+2-3=1 0.....................0...................1............3 0.....................1...................0.............2 exchange r2 and r3 1....0........0.......1 0....1........0.......2 0....0........1.......3 he nce x=1......y=2.....z=3
 Linear-systems/44750: equation with 3 linear variables 2x-y+z=10 4x+2y-3z=10 x-3y+2z=8 wouldn't you divide the first equation by 2?1 solutions Answer 29600 by venugopalramana(3286)   on 2006-07-04 11:41:13 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING AND TRY.IF TILL IN DIFFICULTY PLEASE COME BACK YOU CAN DIVIDE EQN.I WITH 2 AND ADD TO EQN.III TO ELIMINATE X ------------------------------------------------------------------- x - y + z = 2 -x + y + z = 4 -x + z = 2 augmented matrix is 1.....................-1.......................1.............................2 -1.....................1.......................1.............................4 -1.....................0.......................1.............................2 nr2=r2+r1 and nr3=r3+r1 1..................-1.................1.............2 1-1=0............1-1=0............1+1=2..........2+4=6 1-1=0...........-1+0=-1...........1+1=2..........2+2=4 nr2=r2/2....nr3=r3-r2 1....................-1...............1..............2 0/2=0.............0/2=0..............2/2=1........6/2=3 0-0=0............-1-0=-1..............2-2=0.......4-6=-2 nr1=r1-r3-r2.......nr2=2r2........nr3=-r3 1-0-0=1............-1+1-0=0.........1-0-1=0.......2+2-3=1 0.....................0...................1............3 0.....................1...................0.............2 exchange r2 and r3 1....0........0.......1 0....1........0.......2 0....0........1.......3 hence x=1......y=2.....z=3
 Matrices-and-determiminant/44744: This question is from textbook College algebra Solve each system using Gaussian elimination. State whether each system is independent, dependent, or inconsistent. 2x - 3y = -1 3x - 2y = 11 solutions Answer 29599 by venugopalramana(3286)   on 2006-07-04 11:31:24 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING AND TRY.IF STILL IN DIFFICULTY PLEASE COME BACK x - y + z = 2 -x + y + z = 4 -x + z = 2 augmented matrix is 1.....................-1.......................1.............................2 -1.....................1.......................1.............................4 -1.....................0.......................1.............................2 nr2=r2+r1 and nr3=r3+r1 1..................-1.................1.............2 1-1=0............1-1=0............1+1=2..........2+4=6 1-1=0...........-1+0=-1...........1+1=2..........2+2=4 nr2=r2/2....nr3=r3-r2 1....................-1...............1..............2 0/2=0.............0/2=0..............2/2=1........6/2=3 0-0=0............-1-0=-1..............2-2=0.......4-6=-2 nr1=r1-r3-r2.......nr2=2r2........nr3=-r3 1-0-0=1............-1+1-0=0.........1-0-1=0.......2+2-3=1 0.....................0...................1............3 0.....................1...................0.............2 exchange r2 and r3 1....0........0.......1 0....1........0.......2 0....0........1.......3 hence x=1......y=2.....z=3
 Matrices-and-determiminant/44742: This question is from textbook College Algebra Solve each system using Gaussian elimination. State whether each system is independent, inconsistent, or dependent.1 solutions Answer 29598 by venugopalramana(3286)   on 2006-07-04 11:28:59 (Show Source): You can put this solution on YOUR website!SEE THE FOLLOWING EXAMPLE AND TRY.COME BACK IF STILL IN DIFFICULTY -------------------------------------------------------------------------------- x - y + z = 2 -x + y + z = 4 -x + z = 2 augmented matrix is 1.....................-1.......................1.............................2 -1.....................1.......................1.............................4 -1.....................0.......................1.............................2 nr2=r2+r1 and nr3=r3+r1 1..................-1.................1.............2 1-1=0............1-1=0............1+1=2..........2+4=6 1-1=0...........-1+0=-1...........1+1=2..........2+2=4 nr2=r2/2....nr3=r3-r2 1....................-1...............1..............2 0/2=0.............0/2=0..............2/2=1........6/2=3 0-0=0............-1-0=-1..............2-2=0.......4-6=-2 nr1=r1-r3-r2.......nr2=2r2........nr3=-r3 1-0-0=1............-1+1-0=0.........1-0-1=0.......2+2-3=1 0.....................0...................1............3 0.....................1...................0.............2 exchange r2 and r3 1....0........0.......1 0....1........0.......2 0....0........1.......3 hence x=1......y=2.....z=3
 Matrices-and-determiminant/44746: This question is from textbook College Algebra Solve each system in three variables using Gaussian elimination. State whether each system is independent, dependent, or inconsistent. x - y + z = 2 -x + y + z = 4 -x + z = 21 solutions Answer 29594 by venugopalramana(3286)   on 2006-07-04 10:27:39 (Show Source): You can put this solution on YOUR website!x - y + z = 2 -x + y + z = 4 -x + z = 2 augmented matrix is 1.....................-1.......................1.............................2 -1.....................1.......................1.............................4 -1.....................0.......................1.............................2 nr2=r2+r1 and nr3=r3+r1 1..................-1.................1.............2 1-1=0............1-1=0............1+1=2..........2+4=6 1-1=0...........-1+0=-1...........1+1=2..........2+2=4 nr2=r2/2....nr3=r3-r2 1....................-1...............1..............2 0/2=0.............0/2=0..............2/2=1........6/2=3 0-0=0............-1-0=-1..............2-2=0.......4-6=-2 nr1=r1-r3-r2.......nr2=2r2........nr3=-r3 1-0-0=1............-1+1-0=0.........1-0-1=0.......2+2-3=1 0.....................0...................1............3 0.....................1...................0.............2 exchange r2 and r3 1....0........0.......1 0....1........0.......2 0....0........1.......3 hence x=1......y=2.....z=3
 Miscellaneous_Word_Problems/44451: This question is from textbook for sets H and K, we define the inersection H intersect k by H intersect k = {x|x in H and x in k} show that if H <= G and k <= G, then H intersect K <= g. ( remember: <= denotes "is a sub group of," not "is a subgroup of.")1 solutions Answer 29546 by venugopalramana(3286)   on 2006-07-03 12:09:10 (Show Source): You can put this solution on YOUR website!or sets H and K, we define the inersection H intersect k by H intersect k = {x|x in H and x in k} show that if H <= G and k <= G, then H intersect K <= g. ( remember: <= denotes "is a sub group of," not "is a subgroup of.") CASE 1....H=G AND K=G.... THEN IT IMPLIES THAT IF H1 IS ANY ELEMENT OF H THEN IT IS ALSO AN ELEMENT OF G AND HENCE K. SO H1 WILL BE AN ELEMENT OF H INTERSECTION K SO H I.S. K IS A SUBSET OF G.................I SIMILARLY ,WE CAN PROVE THAT IF G1 IS ANY ELEMENT OF G THEN IT IMPLIES IT IS ALSO AN ELEMENT OF H ,K AND HENCE H I.S. K SO G IS A SUB SET OF H I.S. K.............II FROM I AND II H I.S. K=G CASE 2 .....H < G......AND K < G HENCE IF H1 IS AN ELEMENT OF H IT IMPLIES IT IS AN ELEMENT OF G. BUT IT MAY OR MAY NOT BE AN ELEMENT OF K IF IT IS THEN H1 IS AN ELEMENT OF H I.S.K...HENCE H I.S.K IS A SUB SET OF G IF IT IS NOT THEN IT IS NOT AN ELEMENT OF H I.S.K..SO OK. NOW THE OTHER WAY ROUND.. SINCE H THERE WILL BE AT LEAST ONE ELEMENT OF G SAY G1 WHICH IS NOT AN ELEMENT OF H. HENCE G1 WILL NOT BE AN ELEMENT OF H I.S. K HENCE H I.S.K IS A SUBSET OF G SIMILARLY WE CAN ARGUE FOR K....TO SHOW H I.S.K IS A SUBSET OF G
 Equations/44653: elimination method 2x/3 + 3y/4 =11/12 x/3 + 7y/18 =1/2 wouldn't 12 be the common denominator in the first equation help1 solutions Answer 29541 by venugopalramana(3286)   on 2006-07-03 11:45:54 (Show Source): You can put this solution on YOUR website!elimination method 2x/3 + 3y/4 =11/12..........I x/3 + 7y/18 =1/2..........II wouldn't 12 be the common denominator in the first equation YES SO MULTIPLY WITH 12...EQN.I 8X+9Y=11...............III SIMILARLY MULTIPLY EQN.II WITH 18 6X+7Y=9..............IV 7*EQNIII-9*EQN.IV 56X+63Y-72X-63Y=77-81 -16X=-4 X=1/4...PUT IN EQN.III 8*1/4+9Y=11 9Y=11-2=9 Y=1
 Equations/44568: Write the equation of the line that passes through point (-2,3) with a slope of -4.1 solutions Answer 29531 by venugopalramana(3286)   on 2006-07-03 07:19:10 (Show Source): You can put this solution on YOUR website!Write the equation of the line that passes through point A..(X1,Y1).. (-2,3) with a slope of ...M=-4. EQN IS Y-Y1=M(X-X1) Y-3=-4(X+2) Y+4X=3-8=-5 Y+4X+5=0
 Equations/44575: Solve the system by addition 2x-4y=7 4x+2y=91 solutions Answer 29530 by venugopalramana(3286)   on 2006-07-03 07:16:29 (Show Source): You can put this solution on YOUR website!2x-4y=7......................I 4x+2y=9.................II EQN.I+EQN.II*2 2X-4Y+8X+4Y=7+18=25 10X=25 X=25/10=2.5 4*2.5+2Y=9 2Y=9-10=-1 Y=-1/2=-0.5
 Equations/44579: Solve the system by graphing. 3x+y=6 3x-y=01 solutions Answer 29529 by venugopalramana(3286)   on 2006-07-03 06:33:48 (Show Source): You can put this solution on YOUR website!Solve the system by graphing. 3x+y=6 3x-y=0 X.................0..............1...........................5........................ Y=6-3X..........=6-3**0=3.....=6-3*1=3....................=6-3*5=-9................. Y=3X............=3*0=0........=3*1=3......................=3*5=15 WE SEE THAT THE 2 LINES INTERSECT AT X=1 AND Y=3 WHICH IS THE ANSWER
 Expressions-with-variables/44598: Fact: 1 a divided by c = a Fact: 2 a plus b = a Fact: 3 abc = 1 If fact 1 and 2 are correct why is fact 3 wrong? What are the value of each of the variables in fact 1 and 2? 1 solutions Answer 29528 by venugopalramana(3286)   on 2006-07-03 06:26:45 (Show Source): You can put this solution on YOUR website!Fact: 1 a divided by c = a A/C=A.... CASE 1.A=0 CASE 2.IF A IS NOT ZERO THEN C=A/A=1 Fact: 2 a plus b = a A+B=A.......B=0 Fact: 3 abc = 1 CASE 1. ABC=0*0*C=0..WHATEVER MAY BE C HENCE ABC CANNOT EQUAL 1 CASE 2. IF A IS NOT EQUAL TO ZERO THEN ABC=A*0*1=0...WHATEVER MAY BE A HENCE ABC CANNOT EQUAL 1 If fact 1 and 2 are correct why is fact 3 wrong? What are the value of each of the variables in fact 1 and 2?
 Proportions/44593: IF a+b=1,a>0,b>0,then show 1/a+1/b>=41 solutions Answer 29527 by venugopalramana(3286)   on 2006-07-03 06:19:47 (Show Source): You can put this solution on YOUR website!IF a+b=1,a>0,b>0,then show 1/a+1/b>=4 1/A + 1/B = (A+B)/AB TST (A+B)/AB>=4 SINCE A>0 AND B>0 ,AB>0..SO WE CAN MULTIPLY BOTH SIDES WITH AB TST A+B>=4AB TST A+B-4AB>=0 A+B=1 B=1-A A+B-4AB=1-4A(1-A)=1-4A+4A^2=(2A-1)^2..THIS BEING A PERFECT SQUARE IS ALWAYS >=0... PROVED