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# Recent problems solved by 'mananth'

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 Linear_Algebra/363033: Find the value of k if the line through the points (k+1, k-2) and (3,4) is parallel to the line through the points (3,1) and (6,-1).1 solutions Answer 258763 by mananth(12270)   on 2010-10-28 06:36:06 (Show Source): You can put this solution on YOUR website!Find the value of k if the line through the points (k+1, k-2) and (3,4) is parallel to the line through the points (3,1) and (6,-1). .. (k+1, k-2) and (3,4) slope of this line =4-(k-2)/3-(k+1) =6-k/2-k ... (3,1) and (6,-1). slope is -1-1/6-3 =-2/3 .. the lines are parallel so slopes are equal 6-k / 2-k = -2/3 3(6-k)=-2(2-k) 18-3k=-4+2k 18+4=2k+3k 22=5k k=22/5 ... m.ananth@hotmail.ca
 Travel_Word_Problems/363039: I am a little rusty with my math, I understand that mass can change the speed of an object when in earth's gravity. but i need to know the basic math on Flight time - to velocity. like this : how far can an object go traveling 3375 m/sec for 4 sec. i can't recall if it was Devision or X or some other.1 solutions Answer 258761 by mananth(12270)   on 2010-10-28 06:25:30 (Show Source): You can put this solution on YOUR website!how far can an object go traveling 3375 m/sec for 4 sec. ... in speed , distance & time problems the basic equation is distance = speed * time d=rt r=3375m/s t=4 d= 3375*4=13,500 meters .. m.ananth@hotmail.ca
 Linear_Algebra/363034: Are the points (-1,8), (1,2), and (4,-7) on the same line? Explain your reasoning1 solutions Answer 258760 by mananth(12270)   on 2010-10-28 06:20:32 (Show Source): You can put this solution on YOUR website!Are the points (-1,8), (1,2), and (4,-7) on the same line? Explain your reasoning ... find the slope of the line passing through (-1,8) (1,2) m=2-8/1-(-1) =-6/2 =-3 ... form an equation using (-1,8). If the other two points satisfy the equation then all points are collinear. y-8=-3(x-(-1) y-8=-3x-3 y=-3x-3+8 y=-3x+5 .. point 1,2 2=-3(1)+5 2=-3+5 2=2 ( TRUE) point (4,-7) -7=-3*4+5 -7=-12+5 -7=-7 (TRUE) so the lines are collinear ... m.ananth@hotmail.ca
 Quadratic_Equations/362893: mary works due north from home.her husband ben works due east.they leave from work at the same time. by the time mary is 5 miles from home the distance between them is one mile more than ben distance from home. how far is ben? __ miles ??1 solutions Answer 258758 by mananth(12270)   on 2010-10-28 04:10:53 (Show Source): You can put this solution on YOUR website!let Ben be x miles from home then they will be x+1 miles away when Mary is 5 miles from home. Since they are travelling east and north they form right triangle Pythagoras theorem .. (x+1)^2=x^2+5^2 x^2+2x+1=x^2+25 2x=24 x= 12 miles ben is 12 miles from home ... m.ananth@hotmail.ca
 Travel_Word_Problems/362914: Jeff starts driving at 55 miles per hour from the same point that lauren starts driving at 60 miles per hour. They drive in opposite directions, and Lauren has a half-hour head start. How long will they be able to talk on their cell phones that have a 280-mile range?1 solutions Answer 258757 by mananth(12270)   on 2010-10-28 04:05:35 (Show Source): You can put this solution on YOUR website!Jeff speed = 55mph lauren speed =60 mph ... they are moving away from each other so effective speed = 60+55 = 115 mph range of mobile = 280 miles ... t= distance/speed t=280/115 t = 2.4 hours they can be in contact on their cell ... m.ananth@hotmail.ca
 Proportions/362898: Again, not sure if it's a proportion problem... at the same time of day, a man who is 52 inches tall casts a 66- inch shadow and his son casts a 33-inch shadow. What is the height of the man's son? some of the choices are 26 in, 78 in, 99 in, or 27 in. heeeelp! :D1 solutions Answer 258754 by mananth(12270)   on 2010-10-28 03:53:13 (Show Source): You can put this solution on YOUR website! x= 33*52/66 x=26 height = 26 " .. m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/362899: the length of a rectangle is three feet more than twice the width . the area of the rectangle is 9 square feet. find the length and the width.1 solutions Answer 258753 by mananth(12270)   on 2010-10-28 03:50:20 (Show Source): You can put this solution on YOUR website!width =x length = 2x+3 area =9 ... x(2x+3)=9 2x^2+3x=9 2x^2+3x-9=0 2x^2+6x-3x-9=0 2x(x+3)-3(x+3)=0 (x+3)(2x-3)=0 x= 3/2 feet the width . length = 2x+3 = 6 feet .. m.ananth@hotmail.ca
 Geometry_Word_Problems/362910: QUESTION TONY HAS GOT HIS KITE STUCK AT THE TOP OF A VERY TALL TREE. HE KNOWS THE STRING ON HIS KITE IS 20 M LONG. WHEN HE PULLS THE STRING TIGHT AND HOLDS THE VERY END ON THE GROUND IT TOUCHES 17 M FROM THE BOTTOM OF THE TREE. IF THE GROUND IS FLAT, HOW TALL IS THE TREE?1 solutions Answer 258752 by mananth(12270)   on 2010-10-28 03:47:23 (Show Source): You can put this solution on YOUR website!the tree ,string & and the ground form a right triangle string = hypotenuse = 20m distance from tree =17 m so height^2 = 20^2-17^2 =400-289 =111 height = sqrt(111) = 10.5 m height of tree ... m.ananth@hotmail.ca
 Evaluation_Word_Problems/362995: Students can buy tickets to a basketball game for \$1. The admission for nonstudents is \$2. If 350 tickets are sold and the total receipts are \$450, how many student tickets are sold?1 solutions Answer 258750 by mananth(12270)   on 2010-10-28 03:42:09 (Show Source): You can put this solution on YOUR website!Students can buy tickets to a basketball game for \$1. The admission for nonstudents is \$2. If 350 tickets are sold and the total receipts are \$450, how many student tickets are sold? ... let student tickets sold be x--------------\$1 non student will be 350-x---------------\$2 .. 1*x+2(350-x)=450 x+700-2x=450 -x=-250 x= 250 student tickets .. m.ananth@hotmail.ca
 Square-cubic-other-roots/363003: a rectangle has a length twice as long as it is wide, and an area of 242meter squared. determine the length and width of the rectangle.1 solutions Answer 258749 by mananth(12270)   on 2010-10-28 03:35:20 (Show Source): You can put this solution on YOUR website!width = x length = 2x Area = x*2x = 2x^2 2x^2= 242 /2 x^2= 121 take square root x= 11 m the width length = 22 m m.ananth@hotmail.ca
 Travel_Word_Problems/363005: A plane flies 400 miles with the wind and 320 miles against the wind in the same length of time. If the speed of the wind is 20 mph, what is the speed of the plane in still air?1 solutions Answer 258748 by mananth(12270)   on 2010-10-28 03:32:45 (Show Source): You can put this solution on YOUR website!A plane flies 400 miles with the wind and 320 miles against the wind in the same length of time. If the speed of the wind is 20 mph, what is the speed of the plane in still air? let speed in still air be x mph .. distance = 400 speed with wind = x+20 time = 400/(x+20) ... against wind distance = 320 speed = x-20 time = 320/(x-20) ... both times are equal 400/(x+20)= 320/(x-20) 400(x-20)=320(x+20) 400x-8000=320x+6400 400x-320x=8000+6400 80x=14400 x=180 mph ... m.ananth@hotmail.ca
 Age_Word_Problems/363009: Ms X drove at the speed of 45 Km/hr from home to a resort. Returning over the same route she got stuck in traffic and took an hour longer, also she could drive only at the speed of 40 Km/hr. How many kilometers did she drive each way?1 solutions Answer 258747 by mananth(12270)   on 2010-10-28 03:25:41 (Show Source): You can put this solution on YOUR website!let resort distance be x miles x/45 = time to go to resort. ... return time = x/40 ... x/40-x/45=1 .. 45x-40x /40*45 =1 5x=1800 /5 x=360 miles ... m.ananth@hotmail.ca
 Surface-area/363014: x^3-64r^3= thanks so much1 solutions Answer 258745 by mananth(12270)   on 2010-10-28 03:19:54 (Show Source): You can put this solution on YOUR website!x^3-64r^3= (x)^3-(4r)^3 (x-4)(x^2+4x+16) ... m.ananth@hotmail.ca
 Surface-area/363015: 16s^2+72s=-811 solutions Answer 258744 by mananth(12270)   on 2010-10-28 03:16:55 (Show Source): You can put this solution on YOUR website!16s^2+72s=-81 16s^2+72s+81=0 it is a perfect square (4s)^2+2*4*9+(9)^2 =(4s+9)^2 .. m.ananth@hotmail.ca
 Surface-area/363016: the product of two consecutive positive intergers is 19 more than their sum.find the integers... thank you1 solutions Answer 258743 by mananth(12270)   on 2010-10-28 03:14:27 (Show Source): You can put this solution on YOUR website!let the integers be x,x+1 x(x+1)=x+x+1+19 x^2+x=2x+20 x^2-x-20=0 (x-5)(x+4)=0 x= 5 OR -4 the numbers are 5,6 and -4,-3 ... m.ananth@hotmail.ca ...
 Word_Problems_With_Coins/363018: 40 coins , nickel, dimes and quarters worth \$4.05. 7 more nickels than dimes. How many quarters ?1 solutions Answer 258742 by mananth(12270)   on 2010-10-28 03:10:25 (Show Source): You can put this solution on YOUR website!dimes=x nickels=x+7 .. nickels + dimes = 2x+7 quarters = 40-(2x+7) .. 405 cents 10x+5(x+7)+25(40-2x-7)=405 10x+5x+35+825-50x=405 -35x=-825-35+405 -35x=-455 x= 13 dimes nickels = x+7 = 20 quarters = 7 .. m.ananth@hotmail.ca 7*25+20*5+10*13=405
 Human-and-algebraic-language/363010: Carla has \$2.40 in nickels and dimes.Deron has \$5.50 in dimes and quarters. Deron has as many dimes as Carla has nickles and as many quarters as Carla has dimes/ How many of each coin does Carla have?1 solutions Answer 258741 by mananth(12270)   on 2010-10-28 03:03:33 (Show Source): You can put this solution on YOUR website!Carla has \$2.40 in nickels and dimes.Deron has \$5.50 in dimes and quarters. Deron has as many dimes as Carla has nickles and as many quarters as Carla has dimes/ How many of each coin does Carla have? .. let carla have x nickels & y dimes 5x+10y=240.................1 Deron has x dimes & y quarters 10x+25y=550.................2 ... multiply equation 1 by -2 -10x-20y=-480 add it to equation 2 10x-10x+25y-20y=550-480 5y=70 y=14 dimes carla has plug value of y in equation 1 5x+140=240 5x=100 x=20 nickels carla has . m.ananth@hotmail.ca
 Surface-area/363012: 64^2c-112c+49 thanks1 solutions Answer 258739 by mananth(12270)   on 2010-10-28 01:59:30 (Show Source): You can put this solution on YOUR website!64^2c-112c+49 .. 64c^2-56c-56c+49 8c(8c-7)-7(8x-7) (8c-7)^2 ... m.ananth@hotmail.ca
 Money_Word_Problems/363007: A company manufactures both mountain bikes and trail bikes.The cost of materials for a mountain bike is \$70, and the cost of materials for a trail bike is \$50. The cost of labor to manufacture a trail bike is \$80, and the cost of labor to manufacture a trail bike is \$40. During a week in which the company has budgeted \$2500 for materials and \$2600 for labor, how many mountain bikes does the company plan to manufacture?1 solutions Answer 258738 by mananth(12270)   on 2010-10-28 01:51:33 (Show Source): You can put this solution on YOUR website!materials for a mountain bike is \$70, cost of materials for a trail bike is \$50. cost of labor to manufacture a mountain bike is \$80, cost of labor to manufacture a trail bike is \$40. .. budgeted \$2500 for materials \$2600 for labor, ... let x be mountain bikes y be trail bikes .. 70x+50y=2500.......................1 80x+40y=2600.......................2 ... multiply equation 1 by -8 & equation 2 by 7 -560x-400y=-20000 560x+280y=18200 add the two -120y= -1800 /-120 y=1800/-120 y =15 trail bikes plug the value of y 70x+50*15=2500 70x=2500-750 70x=1750 x= 25 mountain bikes ... m.ananth@hotmail.ca
 Age_Word_Problems/363008: A man is 24 years older than his son. In two years, his age will be twice the age of his son. what is the present age of his son? 1 solutions Answer 258736 by mananth(12270)   on 2010-10-28 01:26:41 (Show Source): You can put this solution on YOUR website!A man is 24 years older than his son. In two years, his age will be twice the age of his son. what is the present age of his son? ... son's age = xyears father's age = x=24 years .. after 2 years son = x+2 father = x+24+2= x+26 .. x+26=2(x+2) x+26=2x+4 2x-x=26-4 x=22 years son's age father's age = 24+22=46 years .. m.ananth@hotmail.ca
 Word_Problems_With_Coins/362991: could you show me how to set this problem up. A collection of nickels, dimes and quarters totals \$3.40. the total number of coins is 32, and there are twice as many dimes as quarters. how many of each are there. Thank you!!1 solutions Answer 258724 by mananth(12270)   on 2010-10-28 00:16:08 (Show Source): You can put this solution on YOUR website!quarters------------dimes----------nickels x------------------2x--------------32-3x value = 340 cents total 32 coins ::: dimes & quarters = 3x ... 25x+10*2x+5(32-3x)=340 25x+20x+160-15x=340 30x=340-160 30x=180 /30 x=6 quarters ... dimes = 2x= 12 nickels = 32-3x= 14 ... m.ananth@hotmail.ca ...
 Rational-functions/362986: Solve The Inequality. 8c-(c-5)>c+27 8c-c+5>c+27 (opened the brackets) 7c+5>c+ 27 (simplified the above) subtract c on both sides 7c-c+5>c-c+27 6c+5>27 subtract 5 on both sides 6c+5-5 >27-5 6c>22 divide both sides by 6 6c/6>22/6 c>22/6 c> 3.6667 This is the final answer 1 solutions Answer 258712 by mananth(12270)   on 2010-10-27 23:51:38 (Show Source): You can put this solution on YOUR website!8c-(c-5)>c+27 ... 8c-c+5>c+27 add -c 8c-c-c+5>27 6c+5>27 add -5 6x+5-5>27-5 6x>22 /6 x>22/6 ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/362980: (7x^2-12)^(1/4)=x Can you show the steps to solving this question?1 solutions Answer 258708 by mananth(12270)   on 2010-10-27 23:47:37 (Show Source): You can put this solution on YOUR website!(7x^2-12)^(1/4)=x Raise it by 4 power (7x^2-12)^(1/4 *4)= x^4 7x^2-12=x^4 x^4-7x^2+12=0 x^4-4x^2-3x^2+12=0 x^2(x^2-4)-3(x^2-4)=0 (x^2-4)(x^2-3)=0 (x+2)(x-2)(x^2-3)=0 x= +/- 2 x=+/- sqrt(3) ... m.ananth@hotmail.ca
 Human-and-algebraic-language/362957: Twice the difference of a number and 8 is equal to three times the sum of the number and 4. find the number.1 solutions Answer 258706 by mananth(12270)   on 2010-10-27 23:43:05 (Show Source): You can put this solution on YOUR website!let the number be x 2x-8= 3(x+4) 2x-8=3x+12 3x-2x=-12-8 x=-20 ... m.ananth@hotmail.ca