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 Linear-systems/446133: Solve the system of equations. 2x+8y+z=17 -x+y+4z=-7 x+4y+4z=-2 I would appreciate the help. thank you1 solutions Answer 307194 by mananth(12270)   on 2011-05-06 21:25:25 (Show Source): You can put this solution on YOUR website!2x+8y+1 z=17--------------1 -1x+1y+4z=-7--------------2 1x+4y+4z=-2--------------3 consider equation 1 &2 Eliminate y Multiply 1 by 1 Multiply 2 by -8 we get 2x+8y+z =17 8x-8y-32z=56 Add the two 10x-31z=73 -------------4 consider equation 2 & 3 Eliminate y Multiply 2 by-4 Multiply 3 by 1 we get 4x-4y-16z=28 x+4y+4z=-2 Add the two 5x-12z=26 -------------5 5 Consider (4) & (5) Eliminate x Multiply 4 by 1 Multiply (5) by -2 we get 10x-31z=73 -10x+24z=-52 Add the two -7z=21 / -7 z=-3 Plug the value of z in 5 5x+36=26 5x=-10 x=-2 plug value of x & z in 1 -4+8y-3 =17 8y=4+3+17 y=24 m.ananth@hotmail.ca
 Graphs/446059: Can you help me find the x- and y-intercepts and graph the equation plotting the intercepts? -2x + 3y = -15 Thank you so much! 1 solutions Answer 307192 by mananth(12270)   on 2011-05-06 21:10:03 (Show Source): You can put this solution on YOUR website!-2x + 3y = -15 3y=2x-15 y =2x/3-5 y intercept, x=0 when x=0 y = -5 (0,-5) x Intercept when y=0, x =15/2 ( 15/2,0) Plot the points draw the line
 Travel_Word_Problems/446063: two cars start from the same point and travel in opposite directions. One car goes 15 mph faster than the other. In the 3 hours the cares are 315 miles apart. What is the rate of the faster car?1 solutions Answer 307191 by mananth(12270)   on 2011-05-06 20:59:51 (Show Source): You can put this solution on YOUR website!Car I x mph Car II x+ 15 .. They are going away from each other. So add up their speed. combined speed = x+x+15 (2x+15) Time = 3 hours Distance = 315 miles Distance = speed * time (2x+15)*3=315 6x+45=315 6x=315+-45 6x=270 /6 x=45 mph Car I Car II 45+15=60 mph
 Rational-functions/446074: ok in my book im haven trouble with the problem 3x+x/3=51 solutions Answer 307190 by mananth(12270)   on 2011-05-06 20:53:09 (Show Source): You can put this solution on YOUR website!3x+x/3=5 multiply by 3 9x+x=5*3 10x=15 /10 x=15/10 x=3/2
 Mixture_Word_Problems/446083: how many gallons of 70% antifreeze should be mixed with 10 gallons of 30% antifreeze to obtain 45% antifreeze.1 solutions Answer 307188 by mananth(12270)   on 2011-05-06 20:51:05 (Show Source): You can put this solution on YOUR website!------ percent ---------------- quantity Antifreez1 I 80---------------- 40 gallons Antifreeze II 10----------------x gallons Total 30 ----------------40+x gallons 30*10+70*x=45(10+x) 300+70x=450+45x 70x-45x=450-300 25x=150 /25 x=6 gallons 70 % Antifreeze II
 Travel_Word_Problems/446084: If train a is traveling at 55mph and a second train is traveling at 110mph, how many more miles would the first train travel in 3 hrs?1 solutions Answer 307186 by mananth(12270)   on 2011-05-06 20:44:49 (Show Source): You can put this solution on YOUR website!110-55 = 55 mph is the difference in speed 55*3= 165 miles ahead
 Mixture_Word_Problems/446085: how many gallons 65%antifreeze and how many 20% antifreeze should be mixed up to obtain 50 gallons of 56% mixture of antifreeze?1 solutions Answer 307185 by mananth(12270)   on 2011-05-06 20:42:57 (Show Source): You can put this solution on YOUR website! percent ---------------- quantity Antifreeze I 65----------------x gallons Antifreeze II 20 ----------------50-x gallons Total 56.00% ----------------50 gallons 65x+20(50-x)=56 *50 65x+1000-20x=2800 65x-20x=2800-1000 45x=1800 /45 x=40 gallons 65.00% 10 gallons 20.00%
 Travel_Word_Problems/446098: a person rowed her boat upstream a distance of 5 miles and then back to the starting point. The total time of the trip was 6 hours. If the rate of the current was 2 miles per hour, find the average speed of the boat in still water1 solutions Answer 307184 by mananth(12270)   on 2011-05-06 20:36:32 (Show Source): You can put this solution on YOUR website!Boat speed x current speed 2 against current x-2 mph with current x+ 2 mph Distance= 5 miles Time against + time with = 6 hours t=d/r Find the roots of the equation by quadratic formula a= 6, b= -10, c= -24, b^2-4ac=100+576 b^2-4ac=676 sqrt(676)=26 x1=(10 +26)/12 x1=3 x2=(10-26)/12 x2= -1.33 Ignore negative value 3 mph speed of boat in still water
 Travel_Word_Problems/446104: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9ft. Find the length of the ladder if the length is 3ft more than its distance from the wall.1 solutions Answer 307183 by mananth(12270)   on 2011-05-06 20:29:08 (Show Source): You can put this solution on YOUR website!wall ladder distance =x length of ladder = x+3 height touching the wall = 9 (x+3)^2=x^2+9^2 x^2+6x+9=x^2+81 6x=81-9 6x=72 /6 x=12 feet ladder ===>x+3= 12+3=15 feet m.ananth@hotmail.ca
 Travel_Word_Problems/446106: A boat is 92 feet from the base of a cliff. If the distance from the top of the cliff to the boat is 23 less than twice the height of the cliff to the water, find the height of the cliff. Round to the nearest tenth of afoot if necessary.1 solutions Answer 307182 by mananth(12270)   on 2011-05-06 20:23:55 (Show Source): You can put this solution on YOUR website!let height of cliff be x distance from cliff to boat = 2x-3 distance from boat to cliff on ground = 92 Use Pythagoras theorem (2x-3)^2=x^2+92^2 4x^2-12x+9=x^2+8464 3x^2-12x-8455=0 a= 3, b= -12, c= -8455 b^2-4ac=144+101460 b^2-4ac=101604 sqrt(101604)=318.75 x1=(12+318.75)/6 x1= 55.13 x2=(12-318.75)/6 x2=-51.13 Ignore negative value Height = 55.13 ft m.ananth@hotmail.ca
 Expressions-with-variables/446112: solving systems Using Elimination : 2x-3y=-11 3x+2y=291 solutions Answer 307180 by mananth(12270)   on 2011-05-06 20:12:11 (Show Source): You can put this solution on YOUR website!2x-3y= -11 .............1 3x+2y=29 .............2 Eliminate y multiply (1)by 2 Multiply (2) by 3 4x-6y=-22 9x+6y= 87 Add the two equations 13x=65 /13 x= 5 plug value of x in (1) 2x-3y=-11 10-3y=-11 -3y=-11-10 -3y=-21 y=7
 Word_Problems_With_Coins/445908: a toy savings bank contains \$17.30 consisting of nickels, dimes and quarters. the number of dimes exceeds twice the number of nickels by 3 and the number of quarters is 4 less than 5 times the number of nickels. how many quarters are in the bank?1 solutions Answer 307062 by mananth(12270)   on 2011-05-06 07:28:22 (Show Source): You can put this solution on YOUR website!nickels 5 x dimes 10 (2x+3) quarters 25 (5x-4) Value= 1730 5x+20x+30+125x-100=1730 150x+30 =1830 150x=1830-30 150x=1800 /150 x=12 nickels 15 2x+3 dimes = 27 5x-4 = 56 quarters
 Systems-of-equations/445829: Determine whether the graphs of the two equations are perpendicular. x+2y=7 2x+4Y=3 are the graphs of the given equations perpendicular? Y-N1 solutions Answer 307055 by mananth(12270)   on 2011-05-06 05:52:45 (Show Source): You can put this solution on YOUR website!x+2y=7 2y=-x+7 y=-x/2+7 .. 2x+4y=3 4y=-2x+3 y=-2x/4 +3 y=-x/2+3 The slopes are same. so they are not perpendicular
 Travel_Word_Problems/445844: A boat travels 10 km upstream and 10 km back. The time for the round trip is 10 hours. The speed of the stream is 4 km/hr. What is the speed of the boat in still water? 1 solutions Answer 307054 by mananth(12270)   on 2011-05-06 05:09:54 (Show Source): You can put this solution on YOUR website!Boat speed x current speed 4 against current x-4 mph with current x+ 4 mph Distance= 10 miles Time agianst + time with = 10 hours t=d/r 10/(x +4)+10/(x -4)=10 LCD =(x -4)(x+4) 10*(x-4)+10x+4)=10 10x-40+10x+40=10(x ^2-16) 20x=10x^2-160 10x ^2-20x-160 =0 Find the roots of the equation by quadratic formula a= 10 b= -20 c= -160 b^2-4ac=400+6400 b^2-4ac=6800 sqrt(6800)=82.46 x1=(20+82.46)/20 x1=5.12 x2=(20-82.46)/20 x2= -3.12 Ignore negative value speed = 5.12 mph
 Mixture_Word_Problems/445863: If a merchant has two types of tea, one work \$2.70 per kilogram and the other worth \$3.00 per kilogram, how many kilograms of each type should the merchant use in order to produce 30 kilograms of a blend that is worth \$2.95 per kilogram? 1 solutions Answer 307053 by mananth(12270)   on 2011-05-06 04:59:09 (Show Source): You can put this solution on YOUR website! Price ----------------quantity Tea Type I 2.7----------------x pounds Tea Type II 3----------------30-x pounds Total 2.95----------------30 2.7x+3(30-x)=2.95*30 2.7x+90 -3x=88.5 2.7x-3x=88.5-90 -0.3x=-1.5 /-0.3 x=5 pounds\$ 2.70 25 pounds \$3.00
 Reduction-of-unit-multipliers/445898: Anuranjita is driving at a speed of 74 miles per hour. At this speed, how many inches will Anuranjita travel in 1 second?1 solutions Answer 307052 by mananth(12270)   on 2011-05-06 04:51:08 (Show Source): You can put this solution on YOUR website!Anuranjita 74 mph convert miles to inches and hours to seconds 1760 yards = 1 mile 3feet = 1 yard 12 inches = 1 foot (1760*3*12*74)/3600 =1302.4 in/sec
 Probability-and-statistics/445878: In a recent season, Monique Currie of the Duke Blue Devils scored 635 points. She made a total of 356 shots, including 3 point field goals, 2-point field goals, and 1-point free throws. She made 76 more 2-point field goals than free throws and 77 more free throws than 3-point field goals. Find the number of each type of shot she made. Appreciate if someone can help. 1 solutions Answer 307051 by mananth(12270)   on 2011-05-06 04:45:09 (Show Source): You can put this solution on YOUR website!Free throw goals =x 2pt field goals = x+76 3pt field goals=x-77 x+x+76+x-77=356 3x-1=356 3x=357 x=119 free throw goals x+76 = 2 pt field goals = 119 +76=195 x-77 = 119-77 = 42 -- 3pt goals CHECK 119*1 + 2*195+3*42= 635 points
 Linear_Equations_And_Systems_Word_Problems/445894: a) John is now 3 times as old as his brother Sam. In 5 years, John will be twice as old as Sam will be then. Find their present ages.1 solutions Answer 307048 by mananth(12270)   on 2011-05-06 04:24:14 (Show Source): You can put this solution on YOUR website!Sam's age x John's age 3x 5 years later Sam's age x+5 John's age 3x+5 John's age 2 times older 3x+5=2(x+5) 3x+5=2x+10 x=10-5 x=5 x= 5 Sam's age 3x=15 John's age
 Geometric_formulas/445889: If there were 600 people at a play, the total receipts were 9,800 pesos, and the admission price was 20 pesos for adults and 10 pesos for children, how many adults and how many children were in attendance? .....thank you 1 solutions Answer 307047 by mananth(12270)   on 2011-05-06 04:17:36 (Show Source): You can put this solution on YOUR website!Adult x Numbers Child ------------ y Numbers x+y=600 .............1 20x+10y=9800 .............2 Eliminate y multiply (1)by -10 Multiply (2) by 1 -10x-10y=-6000 20x+10y=9800 Add the two equations 10x= 3800 /10 x=380 plug value of x in (1) x+y=600 380+y=600 y=600 -380 y=220
 Linear_Equations_And_Systems_Word_Problems/445895: 7 audio cassettes and 3 video cassettes cost rs 1110,while 5 audio cassettes and 4 video cassettes cost rs 1350 find the cost of an audio cassette and a video casette1 solutions Answer 307046 by mananth(12270)   on 2011-05-06 04:08:32 (Show Source): You can put this solution on YOUR website!Video--- x Cost Audio=== y Cost 3x+7y=1100 .............1 4x+5y=1350 .............2 Eliminate y multiply (1)by -5 Multiply (2) by 7 -15x-35y=-5500 28x+35y =9450 Add the two equations 13x=3950 /13 x= Rs.303.85 Cost of Video plug value of x in (1) 3x+7y=1100 911.54 +7y=1100 7 y = 1100 -911.54 7 y = 188.46 y =Rs.26.92 Audio
 Linear_Algebra/445381: What are the solutions to 6x+3y+z=19 x-3y+2z=21 17x-2y+3z=861 solutions Answer 306806 by mananth(12270)   on 2011-05-05 06:47:14 (Show Source): You can put this solution on YOUR website!6x+3y+z =19--------------1 x-3y+2z=21--------------2 17x-2y+ 2z=86-----------3 consider equation 1 &2 Eliminate y Add the two 7x+3z=40-------------4 consider equation 2 & 3 Eliminate y 7x+3z=40--------------5 Multiply 2 by -2 Multiply 3 by 3 we get -2x+6y-4z=-42 51x-6y+ 6z=258 Add the two 49x+2z=216 -------------5 5 Consider (4) & (5) Eliminate z Multiply 4 by -7 Multiply (5) by 1 we get -49x-21z=-280 49x+2z=216 Add the two -19z=-64 /-19 z=3.37 Plug the value of z in 5 49x+6.74=216 49x=209.26 x=4.27 plug value of x & z in 1 25.62+3y+3.37=19 3y=-25.62-3.37+ 19 y=-9.99 m.ananth@hotmail.ca
 Quadratic_Equations/445401: A rectangular garden with dimensions 18yd by 24yd is to have a sidewalk of uniform width placed completely around the inside of its border in such a way that the area of the remaining garden is 216 yd. how wide is the sidewalk?1 solutions Answer 306804 by mananth(12270)   on 2011-05-05 06:30:27 (Show Source): You can put this solution on YOUR website!Let the width of sidewalk be x .. Length of ground =24 Width = 18 Area = 432 M^2 Area of sidewalk = 68M^2 (24-2x)(18-2x)=216 432-48x-36x+4X^2=216 4X^2-84x-216=0 /4 x^2-21x-54=0 (x-18)(x-3)=- x=18 OR x=3 the with is obviously 3 yards
 Triangles/445399: a garden has the shape of a right triangle with one leg 5 meters longer than the other. the hypotenuse is 5 meters less than twice the length of the shorter leg what is the length of the shorter leg?1 solutions Answer 306800 by mananth(12270)   on 2011-05-05 06:10:13 (Show Source): You can put this solution on YOUR website!shorter leg =x longer leg = x+5 hyp=2x-5 ... Apply Pythagoras theorem x^2+(x+5)^2=(2x-5)^2 x^2+x^2+10x+25=4x^2-20x+25 group the terms 2x^2-30x=0 2x(x-15)=0 so x= 15 .. 15^2+20 ^2= 625 (2x-5)^2= 625
 Age_Word_Problems/445406: A father is 3 times older than his son now. In 10 years time their combined ages will b 68. How old are they now?1 solutions Answer 306798 by mananth(12270)   on 2011-05-05 06:01:52 (Show Source): You can put this solution on YOUR website!son =x father = 3x .. after 10 years son = x+10 father= 3x+10 ... x+10+3x+10= 68 4x+20=68 4x=48 x=12 yera son's age father = 36 years
 Age_Word_Problems/445412: Mary is twice as old as John and half as old as Bob.in 22 years time, Bob will be twice as old as John. how old is Mary?1 solutions Answer 306796 by mananth(12270)   on 2011-05-05 05:59:32 (Show Source): You can put this solution on YOUR website!Mary =x John= x/2 (because mary is twice Bob's age) Bob = 2x ( mary is 1/2 John's age) After 22 years Bob = 2x+22 John = x/2 + 22 2x+22= 2(x/2+22) 2x+22=x+44 2x-x=44-22 x=22 Mary's age
 Geometry_Word_Problems/445368: A ladder 26 ft long is placed 10 ft from the base of a house. How high up the side of the house does the ladder reach?1 solutions Answer 306791 by mananth(12270)   on 2011-05-04 23:47:00 (Show Source): You can put this solution on YOUR website!let the height be x using pythagoras theorem x^2+10^2=26^2 x^2+100=676 x^2=576 x= sqrt576 x=24 feet the height
 Radicals/445296: The time (sec) it takes for an object to fall from a height of h(ft) is expressed by the following equation: H = 16t^2. Solve the equation for t. 1 solutions Answer 306790 by mananth(12270)   on 2011-05-04 22:23:37 (Show Source):
 Polynomials-and-rational-expressions/445311: I need help answering this math problem. 81x^2 over 5x^2-10x+5* 5x-5 over 9x can you help me and explain how to get to the answer thank you1 solutions Answer 306789 by mananth(12270)   on 2011-05-04 22:21:30 (Show Source): You can put this solution on YOUR website!81x^2 over 5x^2-10x+5* 5x-5 over 9x
 Surface-area/445280: what is the surface area of 3 ft by 3 ft by 4 ft/1 solutions Answer 306780 by mananth(12270)   on 2011-05-04 21:49:19 (Show Source): You can put this solution on YOUR website!2(3*3)+2(3*4)+2(2*3) 18+24+12=54 sq.ft
 Evaluation_Word_Problems/445292: factor completely m^4-n^41 solutions Answer 306778 by mananth(12270)   on 2011-05-04 21:47:05 (Show Source):
 Money_Word_Problems/445229: Here's my problem: I don't know how to write an algebraic equation to work this out. Please help, thank you very much. John bought two computers. One desktop and one laptop. Before finance charges, the laptop cost \$1000 more than the desktop. John paid for the computers using two different financing plans. For the desktop, the interest rate was 8.5% per year, and the laptop was 7.5% per year. The total finance charges for one year were \$915. How much did the desktop computer cost before finance charges?1 solutions Answer 306762 by mananth(12270)   on 2011-05-04 20:38:26 (Show Source): You can put this solution on YOUR website!Laptop x Cost Desktop ----------y Cost x-y=1000 .............1 0.075x+0.085y=915 .............2 Eliminate y multiply (1)by 0.085 Multiply (2) by 1 0.085 x -0.085 y = 85 0.075 x +0.085y = 915 Add the two equations 0.16 x= 1000 / 0.16 x = 6,250.00 plug value of x in (1) x-y=1000 6250-y= 1000 -y=1000 -6250 -y=-5250 y=5250.00