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# Recent problems solved by 'mananth'

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 Travel_Word_Problems/324904: How long does it take for an airplane to fly 5,220 miles at a constent speed of 555mmph?1 solutions Answer 232621 by mananth(12270)   on 2010-07-23 04:26:03 (Show Source): You can put this solution on YOUR website!distance = 5220 miles speed = 555 mph .. time = distance / speed Time = 5220/555 =9.40 hours
 Rate-of-work-word-problems/324901: Sally can paint a room in 6 hours while it takes Steve 8 hours to paint the same room. How long would it take them if they worked together?1 solutions Answer 232620 by mananth(12270)   on 2010-07-23 04:22:35 (Show Source): You can put this solution on YOUR website!LET PAINTING THE ROOM BE 1JOB Sally can do the job in 6 hours she does 1/6 of the job in 1 hour Steve takes 8 hours to do the job. he does 1/8 of the job in in 1 hour. together they do 1/6 + 1/8 of the job in 1 hour 1/6 + 1/8 = 4+3/24 = 7/24 of the job in 1 hour For doing 1 job together they will take 24/7 hours = 3.42 hours
 Rectangles/324864: the perimeter of rectangle is 120ft. the length of rectangle is twice the width. find the length and the width of the rectangle. the perimeter of traingle is 110 cm. one side is twice the second side. the third side is 30 cm more the than second side. find the length of each side.1 solutions Answer 232619 by mananth(12270)   on 2010-07-23 01:17:41 (Show Source): You can put this solution on YOUR website!let width be x length of rectangle = 2x ,, Perimeter of rectangle = 2L+2W 2x+4x=120 6x=120 x=20 feet which is the width .. length = 2x = 2*20 =40 feet .. let second side be x first side will be 2x Third side = x+30 Perimeter = 110 .. Perimeter = aum of all sides x+2x+x+30= 110 4x+30 =110 4x=80 x=20 cm - second side first side = 2x = 40cm third side = x+30 = 20+30=50 cm
 Trigonometry-basics/324883: A consultant charges \$45 for each hour she works on a consultation, plus a flat \$30 consulting fee. How many hours of work are included in a \$210 bill for a consultation?1 solutions Answer 232613 by mananth(12270)   on 2010-07-22 23:35:08 (Show Source): You can put this solution on YOUR website!\$45 for each hour a flat \$30 consulting fee. \$210 bill .. let the number of hours she worked be x \$45 /hour charges for hours= 45x .. 45x + 30 = 210 add -30 to both sides 45x +30-30=210-30 45x=180 x=180/45 x= 4 the number of hours she works.
 Problems-with-consecutive-odd-even-integers/324893: 11:34:34 PM ] Guest : What are the three consecutive even integers such that ten time the first integer is equal to six times the sum of the second and third? [ 11:38:12 PM ] Guest : Hi I have worked on this for hours. College, Susan Intermediate Algebra [ 11:41:05 PM ] : This was my last attempt before asking for help 10x = 6(3x+6) [ 11:42:48 PM ] : 10x = 12x+36 take 12x from both sides [ 11:44:00 PM ] : you get -2x=36 divide both sides by -2 [ 11:44:46 PM ] : x = -18 is this one of the integers? [ 11:47:26 PM ] : help please!!1 solutions Answer 232612 by mananth(12270)   on 2010-07-22 23:14:43 (Show Source): You can put this solution on YOUR website!let the integers be x, x+2, x+4 .. 10 times the first integer = 10x..............1 .. sum of second and third = x+2 +x+4 =2x+6 6 times the sum 6(2x+6) =12x+36................2 equation 1 = equation 2 10x=12x +36 add -12x to both sides 10x-12x= 12x-12x+36 -2x=36 x= 36/-2 x=-18 . first integer x+2 = -18+2=-16 second integer .. x+4 = -18+4 =-14 third integer ... Check 10x= 6(x+x+6) 10*-18=6(-18-18+6) -180=-180 the integers are -18,-16,-14 you are right
 Linear-equations/324861: 2y + 3x = 12 -4y + 5x = -2 How do I solve the above liner equations using the elimination method? Can someone kindly explain it to me thanks 1 solutions Answer 232592 by mananth(12270)   on 2010-07-22 21:38:50 (Show Source): You can put this solution on YOUR website!2y + 3x = 12............1 -4y + 5x = -2...........2 to eliminate a variable the co-efficients of either x or y have to be same in both the equations. If we multiply equation 1 by 2 then the co-fficient of y will be same. multiply and add the equations 2(2y+3x)-4y+5x = 24 -2 4y+6x-4y+5x=22 11x=10 x=22/11 x=2 plug the value of x in equation 1 2y+3*2=12 2y+6=12 2y=12-6 y2y=6 y=3
 Trigonometry-basics/324603: Establish the identity: tan^2(theta)cos^2(theta) + cot^2(theta)sin^2(theta)=11 solutions Answer 232354 by mananth(12270)   on 2010-07-22 04:00:23 (Show Source): You can put this solution on YOUR website!tan^2(theta)cos^2(theta) + cot^2(theta)sin^2(theta)=1 =sin^2 (theta)/cos^2 (theta)*cos^2(theta)+cos^2(theta)/sin^2(theta)*sin^2(theta) =sin^(theta) + cos^2(theta ) = 1
 test/324600: hi i would like your help to help me with this question. Thanks quesion: 1/r=1/r1 + 1/r2 Express r1 in terms of r and r21 solutions Answer 232353 by mananth(12270)   on 2010-07-22 03:42:58 (Show Source): You can put this solution on YOUR website!1/r=1/r1 + 1/r2 add -1/r2 to both sides 1/r - 1/r2 = 1/r1 r2-r / rr2= 1/r1 r1=rr2/r2-r
 Rate-of-work-word-problems/324602: a tank which has an inlet valve through which it get filled in 5 hours and outlet valve through which it becomes empty in 10 hours. when both are open how long will it take to fill the tank?1 solutions Answer 232352 by mananth(12270)   on 2010-07-22 03:38:41 (Show Source): You can put this solution on YOUR website!Filling or draining the complete tank is considered as 1 job filling in 5 hours so 1/5 of the job in 1 hour. .. draining in 10 hours 1/10 of the job in 1 hour .. effective filling when both are open = 1/5 - 1/10 hours 10-5/50= 5/50= 1/10 when both are open 1/10 of the job is done in 1 hour so it will take 10 hours to fill the tank
 Trigonometry-basics/324594: Please explain how to show work for this problem and the answer: Two ships leave a port at the same time. One travels at 20 miles per hour in a direction N 32 degrees E, and the other travels at 28 miles per hour in a direction S 42 degrees E. How far apart are the two ships after 2 hours?1 solutions Answer 232350 by mananth(12270)   on 2010-07-22 03:19:59 (Show Source): You can put this solution on YOUR website!Two ships leave a port at the same time. One travels at 20 miles per hour in a direction N 32 degrees E, and the other travels at 28 miles per hour in a direction S 42 degrees E. How far apart are the two ships after 2 hours? .. One travels at 20 mph for 2 hours . = 40 miles N32 deg E Second travels 28mph for 2 hours . = 56 miles S42 deg E 42 +32 = 74 deg angular distance .. We have to use the law of cosines to find the the distance. distance^2= 40^2+60^2-2(40)(60)cos 74 =1600+3600*4800*cos74 =distance ^2=375.75 distance = sqrt375.75 =66.14 miles apart.
 Travel_Word_Problems/324595: Rene is going to the lake to visit some friends. If the lake is 60 miles away, and Rene is driving at 40 miles per hour the entire time, how long will it take her to get to the lake?1 solutions Answer 232349 by mananth(12270)   on 2010-07-22 02:24:45 (Show Source): You can put this solution on YOUR website!Distance = 60 miles speed = 40 mph .. Time = Distance/ speed Time = 60/40 time = 6/4 =3/2 1 hour 30 minutes
 Square-cubic-other-roots/324596: Question: square root 3 plus square root 27 equals v3 + v27 = 4v3 (note: the "v" really stands for "square root" in the equation) I have the answer- but do not know how solve step by step. Can you help me? Thank you, Drew1 solutions Answer 232348 by mananth(12270)   on 2010-07-22 02:22:06 (Show Source): You can put this solution on YOUR website!sqrt3 +sqrt27 .. sqrt3 + sqrt (3*3*3) sqrt3 + 3sqrt3 sqrt3 is common sqrt3(1+3) sqrt3*4 =4sqrt3
 Angles/324597: the supplement of an angle is 15degrees more than four times its compliment. find the angles its compliment and its supplement?1 solutions Answer 232347 by mananth(12270)   on 2010-07-22 02:12:51 (Show Source): You can put this solution on YOUR website!let the angle be x the complement will be 90-x .. the supplement will be 180-x .. four times the complement = 4(90-x) Add 15 to it 4(90-x)+15 = 180-x 360-4x +15=180-x -4x+x=-360-15+180 -3x=-195 x=-195/-3 x= 65 deg The complement = 90-65=25 deg the supplement of the angle = 180 -x=180-65=115 deg
 Quadratic_Equations/324550: 1 solutions Answer 232317 by mananth(12270)   on 2010-07-21 23:14:00 (Show Source): You can put this solution on YOUR website!x^2+7x= 18 add -18 to both sides x^2+7x-18=18-18 x^2+7x-18=0 x^2+9x-2x-18=0 x(x+9)-2(x+9)=0 (x+9)(x-2)=0 x=-9 OR x=2
 Mixture_Word_Problems/324552: A chemical manufacturer wishes to fill an order of 800 gallons of 25% acid solution. Solution of 25% and 35%are in stock. How many gallons of each solution must be mixed to fill the order?1 solutions Answer 232278 by mananth(12270)   on 2010-07-21 21:41:12 (Show Source): You can put this solution on YOUR website!Why mix . fll the order as it is . since you have stock of 25 % solution
 test/324551: Add. 2x^2+3x+5/x^2+7x + 23+x-2x^2/x^2+7x1 solutions Answer 232274 by mananth(12270)   on 2010-07-21 21:27:24 (Show Source): You can put this solution on YOUR website!(2x^2+3x+5/x^2+7x) +(23+x-2x^2/x^2+7x) .. LCM = x^2+7x .. 2x^2+3x+5 +x-2x^2 +23 / x^2+7x .. 4x+28 / x(x+7) .. 4(x+7) /x(x+7) .. 4/x
 Age_Word_Problems/324354: six years ago i was three times as old as my brother and now i am twice as old; find our present ages?1 solutions Answer 232149 by mananth(12270)   on 2010-07-21 09:33:48 (Show Source): You can put this solution on YOUR website!let brother's age = x my age = 2x .. 6 years ago our ages were: brother - x-6 myself 2x-6 .. I was 3 time his age then 2x-6 = 3(x-6) 2x-6 = 3x-18 3x-2x=18-6 x=12 years brother's age My age now = 24 years. .. Your feedback is very valuable for improving the solution.
 Age_Word_Problems/324356: the sum of the ages of father and son is 55 years.after 16 years the father will be twice as old as his son, what are their present ages?1 solutions Answer 232145 by mananth(12270)   on 2010-07-21 09:29:59 (Show Source): You can put this solution on YOUR website!let the age of son be x father's age = 55-x .. after 16 years their ages will be: son x+16 father 55-x+16= 71-x .. Father's age = twice son's age 71-x= 2(x+16) 71-x = 2x +32 3x= 71-32 3x=39 x=13 years , son's age Father's age = 55-x = 55-13 =42 years Your feedback is very important for improving the solution
 Geometry_Word_Problems/324352: A farmer owns a square field of side with a pole in one of the corners to which he tied his cow with a rope whose length is about is 10 m . what is the area available for the cow to grace. A.150 sq.m b.125sq,m c.75sq.m d. not enough data. 1 solutions Answer 232141 by mananth(12270)   on 2010-07-21 09:24:19 (Show Source): You can put this solution on YOUR website!the rope is 10 m tied at one end of a pole. .. It can move in the field maximum from one side of the square to the other taking a circular path. .. It can graze only an area of 1/4 of the area of a circle with radius 10m. .. Area of circle with radius 10 = pi*10^2 Area = 314 sq. m 1/4 of 314 = 78.5 sq. m
 Volume/324345: Find the volume of the circular cylinder that has 4in radius in 11in height 1 solutions Answer 232137 by mananth(12270)   on 2010-07-21 09:15:15 (Show Source): You can put this solution on YOUR website!4in radius =r 11in height = h .. Volume of cylinder = pi * r^2 * h = pi*4^2*11 =552.9 cu. in
 Travel_Word_Problems/324294: if a car takes 20 minutes to travel 15km how fast is the car going ?1 solutions Answer 232103 by mananth(12270)   on 2010-07-21 04:05:16 (Show Source): You can put this solution on YOUR website!if a car takes 20 minutes to travel 15km how fast is the car going ? .. since distance is in km time has to be changed to hours 20 minutes = 20/60 = 1/3 hours .. speed = distance / time speed = 15 / (1/3) speed = 15*3 = 45 km / hour .. Your feedback is important to improve the solution
 Equations/324297: Hi I would really like help to solve this question. Rewrite the following in a shortened form: (x-3)x(x+3)=? Please show me how to do this and explain it. Thanks.1 solutions Answer 232102 by mananth(12270)   on 2010-07-21 04:01:07 (Show Source): You can put this solution on YOUR website!(x-3)x(x+3) this means x*(x-3)*(x+3) First solve the brackets multiply each term in bracket 1 to each term in bracket 2 x{x*(x+3)-3(x+3)} x{x^2+3x-3x-9} +3x & -3x cancel off x{x^2-9) x^3-9x .. Your feedback is valuable for improving the solution
 Linear-systems/324283: At maximum speed an airplane travels 2,460 miles against the wind in 6 hours. Flying with the wind the plane can travel the same distance in 5 hours. What is the speed of the plane with no wind?1 solutions Answer 232092 by mananth(12270)   on 2010-07-21 00:02:00 (Show Source): You can put this solution on YOUR website!let speed of wind be y mph let speed of plane in still air be x .. Against wind the speed = x-y distance traveled = 2460 2460/x-y= 6 6x-6y= 2460 x-y=410...........1 .. with wind speed = x+y distance is same 2460 2460/x+y=5 5x+5y=2460 x+y=492............2 .. Add equation 1 & 2 x-y+x+y=410+492 2x=902 x= 451 mph speed of plane in still air. .. Plug the value of x in equation 1 451-y=410 y=451-410 y=40 mph the speed of wind . Your feed back about the solution is very important in improvement.
 Miscellaneous_Word_Problems/324274: Suppose Wal-Mart stock is selling at \$59 a share,and Mattel stock is selling at 28 a share. Amy has a maximum of \$6000 to invest. she wishes to purchase four times as many shares of Wal-Mart as Mattel. Only whole shares of stock can be purchased. A) how many shares of each will she purchase? B) how much money will be left over. I have tried figuring it out but can not.1 solutions Answer 232091 by mananth(12270)   on 2010-07-20 23:51:27 (Show Source): You can put this solution on YOUR website!Wal-Mart stock \$59 a share, Mattel stock 28 a share. Amy has a maximum of \$6000 to invest. she wishes to purchase four times as many shares of Wal-Mart as Mattel .. let Mattel shares she buys be x Mattel stock 28 a share. Wal-Mart will be 4x Wal-Mart stock \$59 a share, Amount invested = \$ 6000 .. 28x+59*4x<6000 28x+236x<6000 264x< 6000 x< 6000/264 x<22.4 So she buys 22 shares of Mattel Wal-Mart will be 4x = 4*22=88 shares 88*59 +22*28= 5808 6000-5808=192 She has \$192 balance after buying 22 shares of Mattel & 88 shares of Wal-Mart. CHECK IN the balance \$192 she cannot buy 1 share of Mattel & 4 shares of Wal-Mart which will cost 59*4 +28*1=\$264
 Linear-equations/324254: How are addition and multiplication use to solve a linear equation? Demonstrate by solving "(1/5) x - (2/3) = 6x(2/5)" 1 solutions Answer 232090 by mananth(12270)   on 2010-07-20 23:17:46 (Show Source): You can put this solution on YOUR website!(1/5) x - (2/3) = 6x(2/5) .. Add +2/3 to both sides (1/5) x - (2/3)+2/3 = 6x(2/5)+2/3 .. (1/5) x = 6x(2/5)+(2/3) .. add - 6x(2/5) on both sides (1/5)x -6x(2/5) =6x(2/5) -6x(2/5)+(2/3) .. (1/5)x -6x(2/5) = 2/3 LCM = 5 on left side x-12x /5 =2/3 -11x/5 =2/5 multiply by 5 -11x/5 *5 = 2/5 *5 -11x=2 divide by -11 -5x/-11= 2/-11 x= - 2/11
 Systems-of-equations/323997: Solve the system of equations. 2x-7y=3 -33=-7x+2y 1 solutions Answer 231884 by mananth(12270)   on 2010-07-20 11:06:54 (Show Source): You can put this solution on YOUR website!2x-7y=3 -33=-7x+2y .. 2x-7y=3............1 7x-2y=33...........2 .. multiply equation 1 by 7 and equation 2 by 2 to eliminate x 14x-49y=21 14x-4y=66 subtract 14x-49y-14x+4y=21-66 -45y=-45 y=1 plug the value of y in equation 1 2x-7=3 2x=10 x=5
 Numbers_Word_Problems/323956: the sum of four times a number and three is the same as the difference of twice the number and eleven. find the number. 1 solutions Answer 231883 by mananth(12270)   on 2010-07-20 11:01:21 (Show Source): You can put this solution on YOUR website!let number be x 4 times a number and 3 = 4x+3 .. difference of twice the number and 11 = 2x-11 .. 2x-11=4x+3 4x-2x=-11-3 2x=-14 divide by2 x=-7 te number is -7
 Miscellaneous_Word_Problems/323965: The cost in dollars of manufacturing x refrigerators is 9000 + 400x. the amount received when selling these x refrigerators is 500x dollars. what is the least number of refrigerators that must be manufactured and sold so that the amount received is at least equal to the manufacturing cost ? A 10 B 18 C 45 D 90 E 1001 solutions Answer 231881 by mananth(12270)   on 2010-07-20 10:55:17 (Show Source): You can put this solution on YOUR website!9000+400x is the cost of x refrigerators sales value = 500x They have to be same to break even .. 9000+400x =500x 9000=500x-400x 100x=9000 x= 90 refrigerators
 Percentage-and-ratio-word-problems/323971: In a certain shop , notebooks that normally sell for 59 cents each are on sale at 2 for 99 cents . how much can be saved by purchasing 10 of these notebooks at the sale price ? A \$0.85 B \$0.95 C \$1.10 D \$1.15 E \$2.001 solutions Answer 231879 by mananth(12270)   on 2010-07-20 10:43:50 (Show Source): You can put this solution on YOUR website!normal price = 59 cents .. sale price = 2 for 99 so 1 costs 99/2 = 49.5 cents the difference = 59-49.5 = 9.5 cents / book so for 10 books the difference will be 95 cents OR \$0.95
 Triangles/323991: if you have a triangle with a base of 30ft and a hieght of 20ft what is the hypotenuse?1 solutions Answer 231878 by mananth(12270)   on 2010-07-20 10:40:54 (Show Source): You can put this solution on YOUR website!If they are the legs of a right triangle then hypotenuse ^2= 30^2+40^2 = 900+1600 =2500 sqrt of 2500 = hpotenuse = 25 ft
 Age_Word_Problems/323957: Mary is presently twice as old as Maggy. Ten years ago, Maggy's age was one-third of Mary's then. Ten years from now, Maggy's age will be three-fifths of Mary's age then. How old is each?1 solutions Answer 231875 by mananth(12270)   on 2010-07-20 10:33:53 (Show Source): You can put this solution on YOUR website!Let Maggy's age = x Mary's age = 2x .. ten years later their ages will be Maggie= x+10 Mary = 2x+10 .. x+10 = 3/5 (2x+10) 5(x+10)=3(2x+10) 5x+50=6x+30 6x-5x=50-30 x=20 years Maggie's age Mary's age = 2x = 40 years