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mananth answered: 12270 problems
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Geometry_Word_Problems/380483: total revenue is the total amount of money taken in by a business. an appliance firm determines that when it sells x washing machines the total revenue, R, in dollars, is given by the polynomial R=239.46x-0.1x^2. what is the total revenue from the sale of 165 washers 1 solutions Answer 270072 by mananth(12270)   on 2010-12-03 23:33:28 (Show Source): You can put this solution on YOUR website! R=239.46x-0.1x^2 .. x= 165 plug value of 165 R=(239.46*165)-(0.1*(165)^2) R= $36,788.40 ... m.ananth@hotmail.ca

Word_Problems_With_Coins/380398: Bruce has $5.15 in dimes and quarters. He has 8 more quarters than dimes. How many quarters does he have. 1 solutions Answer 270071 by mananth(12270)   on 2010-12-03 23:29:25 (Show Source): You can put this solution on YOUR website! let dimes be x quarters = x+8 .. 10x+25(x+8)=515 10x+25x+200=515 35x+200=515 -80 35x=315 /35 x=9 the number of dimes quarters = 9+8 =17 ... check 10*9 +17*25=90+425=515 ... m.ananth@hotmail.ca

Miscellaneous_Word_Problems/380474: The perimeter of a rectangle is 50m. If the width was doubled and the length was increased by 20m, the perimeter would be 100m. What are the length and width of the rectangle? 1 solutions Answer 270070 by mananth(12270)   on 2010-12-03 23:09:46 (Show Source): You can put this solution on YOUR website! The perimeter of a rectangle is 50m. If the width was doubled and the length was increased by 20m, the perimeter would be 100m. What are the length and width of the rectangle? ... let width be w length = l .. Area A = l*w=50 m^2 l= 50/w ... second rectangle width = 2w length = l+20 Perimeter of second rectangle =2*(2w+(l+20)) P=2(2w+l+20) P=4w+2l+40 plug the value of l above P=4w+2(50/w)+40 100=4w+100/w+40 multiply by w 100w=4w^2+100+40w re write 4w^2-100w+40w+100=0 4w^2-60w+100=0 /4 w^2-15w+25=0 find the roots w1,w2 using quadratic formula .. discriminant = 125 w1=((15+sqrt(125))/2) w1=13.1 meters ... the width w2 will be negative so ignore length = 50/13.1 length = 3.82 meters ... CHECK perimeter of second rectangle plug w & l 2*(2*13.1+((3.82+20))=100 ... m.ananth@hotmail.ca

Miscellaneous_Word_Problems/380481: Joe has a collection of nickels and dimes that is worth $6.00. If the number of dimes was doubled and the number of nickels was increased by 6, the value of the coins would be $9.90. How many dimes does he have? 1 solutions Answer 270055 by mananth(12270)   on 2010-12-03 22:41:47 (Show Source): You can put this solution on YOUR website! let nickels be x dimes = y .. 5x+10y=600 /5 x+2y=120...................1 .. dimes 2y nickels increased by 6 = x+6 .. 5(x+6)+10*2y=900 5x+30+20y=900 5x+20y=900-30 5x+20y=870 /5 x+4y=174......................2 ... multiply (1) by -1 -x-2y=-120 add this to (2) x-x+4y-2y=174-120 2y=54 /2 y=27 the number of dimes plug value of y in (1) x+2y=120 x+54=120 x=66 -------- nickels .. CHECK 5*66+10*27=330+270=600 m.ananth@hotmail.ca

expressions/380477: (x-0.8)(x-0.5) 1 solutions Answer 270046 by mananth(12270)   on 2010-12-03 22:32:13 (Show Source): You can put this solution on YOUR website! (x-0.8)(x-0.5) (x(x-0.5)-0.8(x-0.5)) .. x^2-0.5x-0.8x+0.04 .. x^2-1.3x+0.04 ... m.ananth@hotmail.ca

Miscellaneous_Word_Problems/380475: solve by system of equations. The sum of the digits of a two digit number is 12. If 18 is added to the number, the digits will be reversed. Find the number. please show all your work to help me understand 1 solutions Answer 270041 by mananth(12270)   on 2010-12-03 22:22:21 (Show Source): You can put this solution on YOUR website! let the number be xy. x ten's place y units place ... x+y = 12......................1 ... 10x+y is the number .. 10x+y+18= 10y+x 10x-x+y-10y=-18 9x-9y=-18 /2 x-y =-2........................2 add 1 & 2 2x=12-2 2x=10 /2 x=5 .. x+y =12 so y=7 .. the number is 57 ... m.ananth@hotmail.ca

Miscellaneous_Word_Problems/380469: Solve by system of equations. THe sum of the digits of a two digit number is 13. If the digits of the number are reversed,the new number is 27 less than the origional number. Find the number. i have so far 10y+x = 10x+y-27 ?? show all work please 1 solutions Answer 270039 by mananth(12270)   on 2010-12-03 22:17:52 (Show Source): You can put this solution on YOUR website! You have not set up another equation let the number be x y x+y= 13.....................1 10y+x = 10x+y-27 10y-y+x-10x=-27 9y-9x==-27 /9 y-x=-3......................2 .. add 1 & 2 2y= 13-3 2y=10 /2 y=5 .. x+y = 13 so x=8 .. The number is 85 .. m.ananth@hotmail.ca

Functions/380407: 17. Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points. (-7,-2) and (1,7) Type an integer or simplified fraction. 1 solutions Answer 270037 by mananth(12270)   on 2010-12-03 22:12:12 (Show Source): You can put this solution on YOUR website! (-7,-2) and (1,7) ... slope m of a line = (y2-y1)/(x2-x1) m=(7-(-2))/(1-(-7)) m=9/8 .. The line parallel to the line passing through above points will have same slope m= 9/8 ... For line perpedicular it will have a slope which is negative reciprocal of the slope m=-8/9 ... m.ananth@hotmail.ca

percentage/380449: Use an inequality to solve the problem. Be sure to show the inequality and all of your work. One side of a triangle is 2 cm shorter than the base, x. The other side is 8 cm longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least 30 cm? 1 solutions Answer 270034 by mananth(12270)   on 2010-12-03 22:04:41 (Show Source): You can put this solution on YOUR website! base =x one side = x-2 other side = x+8 .. the perimeter should be at least 30 if not more x+x-2+x+8>=30 3x+6>=30 -6 3x-6+6>=36 3x>=24 /3 x>=8 .. m.ananth@hotmail.ca

Travel_Word_Problems/380457: Two cars travelling in opposite directions were 360 km apart at the end of two hrs. If one car travels 6kph faster than the other, find the average speed of the slower car. 1 solutions Answer 270032 by mananth(12270)   on 2010-12-03 21:57:04 (Show Source): You can put this solution on YOUR website! speed of one car = x mph speed of second car = x+6 mph .. they are in opposite directions so add up the speeds x+x+6 = 2x+6 mph. distance = 240 miles .. r=d/t r=240/(2x+6) 2=240/(2x+6) multiply by (2x+60 2(2x+6)=240 4x+12=240 -12 4x=240-12 4x=228 /4 x=57 mph speed of one car speed of other car = x+6 = 57+6 = 63 mph .. m.ananth@hotmail.ca

Polynomials-and-rational-expressions/380458: how do you put the followig equation in intercept form: 12x+2y=-6 1 solutions Answer 270031 by mananth(12270)   on 2010-12-03 21:51:57 (Show Source): You can put this solution on YOUR website! 12x+2y=6 -12x 12x-12x+2y=-12x+6 2y=-12x+6 /2 y=-6x+3 .. m.ananth@hotmail.ca

Polynomials-and-rational-expressions/380460: find a polynomial for the perimeter and the area. the length of this rectangle is n+3 and the width is n 1 solutions Answer 270030 by mananth(12270)   on 2010-12-03 21:50:11 (Show Source): You can put this solution on YOUR website! width = n length = n+3 .. Perimeter P= 2(l+w) P=2(n+n+3) P=2(2n+3) P=4n+6 units ... Area A=l*w A=n(n+3) A=n^2+3n square units ... m.ananth@hotmail.ca

Graphs/380425: y-2>-13 Solve. Then graph 1 solutions Answer 270007 by mananth(12270)   on 2010-12-03 20:16:26 (Show Source): You can put this solution on YOUR website! y-2>-13 Solve. Then graph y-2>-13 +2 y+2-2>-13+2 y>-11 ... the boundary ... y>-11 .. ... m.ananth@hotmail.ca

Equations/380440: 1 solutions Answer 270003 by mananth(12270)   on 2010-12-03 20:10:42 (Show Source): You can put this solution on YOUR website! 12-4(p-4)=3p 12-4p+(-4)*(-4)=3p 12-4p+16=3p 28-4p=3p +4p 28-4p+4p=3p+4p 28=7p /7 28/7 = 7p/7 4=p .. p=4 .. m.ananth@hotmail.ca

Miscellaneous_Word_Problems/380439: I hope someone can help me. I do not understand word problems and I need it worked out. Please help me. Avoiding a collision. A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car’s new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing? Thank you! 1 solutions Answer 269999 by mananth(12270)   on 2010-12-03 20:06:48 (Show Source): You can put this solution on YOUR website! A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car’s new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing? ... The car, the train & the crossing are at right angle at any given time. So it is a right triangle situation .. distance between car & train = 50 meters distance between car & crossing = 30 meters .. apply pythagoras theorem train to crossing be x m .. x^2+30^2=50^2 x^2+900=2500 x^2=2500-900 x^2=1600 x= +/- 40 ... so x = 40 meters, distance of car from crossing. m.ananth@hotmail.ca

Proportions/380438: the scale on a map approximately 5/8 inches to 20 miles. if the distance from city A and city B measures 8.5 inches on the map, how far are the two cities 1 solutions Answer 269994 by mananth(12270)   on 2010-12-03 20:01:20 (Show Source): You can put this solution on YOUR website! 5/8 " = 20 miles .. 8.5 " = ? ... ... ... .. x=20*68/5 x=4*68 x=272 miles ... m.ananth@hotmail.ca

Quadratic_Equations/380432: A plane traveled a distance of 800 miles and returned the same distance. If the rate returning is 40 miles per hour faster than the rate going, and if the total flight took 8 hours, how fast did the plane travel on the return trip? 1 solutions Answer 269993 by mananth(12270)   on 2010-12-03 19:54:26 (Show Source): You can put this solution on YOUR website! Distance = 800 miles . speed going = x mph distance = 800 miles : speed = x+40 mph. ... time going +time returning=8 .. t=d/r 800/x+800/(x+40 )= 8 .. lcd = x(x+40) 800(x+40)+800x /x(x+40)=8 800x+32000+800x=8x^2+320x 8x^2-1600x+320x-32000=0 8x^2-1280x-32000=0 /8 x^2-160x-4000=0 .. find the roots x1,x2 using quadratic formula discriminant = 41600 x1=((160+sqrt(41600))/2 x1= 181.98 = 182 mph x2 is negative so reject. return trip speed = x+40 = 182 +40 = 222 mph ... m.ananth@hotmail.ca

Travel_Word_Problems/380435: Alex drove 270 miles to the University of Phoenix (UOP) in the same time as Stephanie drove 330 miles to UOP. If Stephanie drove 10 miles per hour faster than Alex, then how fast did each of them drive? 1 solutions Answer 269987 by mananth(12270)   on 2010-12-03 19:44:21 (Show Source): You can put this solution on YOUR website! Alex speed = xmph: distance = 270 miles Stephanie speed = x+10 mph: 330 miles .. time Alex= time Stephanie t=d/r 270/x=330/(x+10) cross multiply 270(x+10)=330x 270x+2700=330x 330x-270x=2700 30x=2700 /30 x=90 mph : speed Alex 90+10 = 100 ... speed ... Stephanie ... m.ananth@hotmail.ca ..

Inequalities/380428: 5>-2x+4 or 8≤-4x+3 Solve the compound inequality? 1 solutions Answer 269985 by mananth(12270)   on 2010-12-03 19:37:11 (Show Source): You can put this solution on YOUR website! 5>-2x+4 +2x 2x+5>4 -5 2x>-1 /2 x>-1/2 ... 8<=-4x+3 add 4x 4x+8<=3 -8 4x<=-5 /4 x<=-5/4 .. -1/2 ...

Graphs/380429: 3x+4y≤12 Solve and graph the inequality on a plane? 1 solutions Answer 269979 by mananth(12270)   on 2010-12-03 19:16:46 (Show Source): You can put this solution on YOUR website! -3x /4 ... The boundary ... Sinxe y<= something all the values on the line and below the line are solutions . The area below the line is shaded. ... m.ananth@hotmail.ca

Mixture_Word_Problems/380200: one number is eight more than a second number. six times the first is 8 less than 5 times the second. 1 solutions Answer 269840 by mananth(12270)   on 2010-12-03 08:29:21 (Show Source): You can put this solution on YOUR website! let one number be x the other number is 8 more so it will be x+8 .. 6x=5(x+8)-8 6x=5x+40-8 6x=5x+32 -5x x=32 the other number is x+8 = 32+8 =40 .. m.ananth@hotmail.ca

Travel_Word_Problems/380183: Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 85 miles per hour. The eastbound train travels at 95 miles per hour. How long will it take for the two trains to be 252 miles apart? Do not do any rounding. 1 solutions Answer 269839 by mananth(12270)   on 2010-12-03 05:57:43 (Show Source): You can put this solution on YOUR website! The two trains are moving away from each other. train 1 speed = 85 mph train 2 speed = 95 mph. ... combined speed = 190 mph .. distance = 252 miles t=d/r t=252/190 t = 1.32 hours After 1.32 hours they will be 252 miles apart .. m.ananth@hotmail.ca

Travel_Word_Problems/380186: 2 boys on bicycles, 20 miles apart, began racing toward each other. The instant they started, a fly on the handle bar of one of the bikes started flying toward the other bike's handle bar. As soon as it reached, it turned around and went to the other bike and so on until the bikes met. If each bike had a constant speed of 10 mph, and the fly was travelling 15 mph constantly, how far did the fly travel? 1 solutions Answer 269838 by mananth(12270)   on 2010-12-03 05:53:09 (Show Source): You can put this solution on YOUR website! each rider speed = 10 mph distance apart 20 mile .. so they meet midway that is 10 miles. .. to travel 10 miles the rider takes 10/10 = 1 hour. They meet after 1 hour. .. speed of fly = 15 mph. the fly keeps flying for one hour to and fro from the riders. It flies for 1 hour : so distance it flies = 15 miles. .. m.ananth@hotmail.ca

Miscellaneous_Word_Problems/380161: A boy went out into the barangay on his bike at 5kph. He rested two hrs. and returned home along the same road at the rate of 3 kph. If he was gone for 6 hrs, how far was the barangay from his home? 1 solutions Answer 269837 by mananth(12270)   on 2010-12-03 04:10:39 (Show Source): You can put this solution on YOUR website! let the barangay distance be x km riding speed = 5kph riding time forward = x/5 hours ... riding time return = x/3 hours ... rest = 2 hours .. x/5 + x/3 + 2 = 6 LCD = 30 (6x+10x+60)/30=6 16x+60 = 30*6 16x+60=180 16x=180-60 16x=120 x=7.5 km the distance to barangay ... m.ananth@hotmail.ca

Miscellaneous_Word_Problems/380166: Two cars 240 km apart traveled toward each other at the same time. If the first car's speed is 55 kph and the other is 65 kph, how long would it take them to meet? 1 solutions Answer 269836 by mananth(12270)   on 2010-12-03 04:03:07 (Show Source): You can put this solution on YOUR website! Distance = 240 km .. one car speed = 65 kph other car speed = 55 kph .. add up their speed =120 kph .. t=d/r t=240/120 t= 2hours .... they will meet ... m.ananth@hotmail.ca

Proportions/380179: Rise and run. If the rise is 3/2 and the run is 5, then what is the ratio of the rise to the run? 1 solutions Answer 269835 by mananth(12270)   on 2010-12-03 03:59:57 (Show Source): You can put this solution on YOUR website! (3/2) / 5 = (3/2)*1/5 .... =3/10

Miscellaneous_Word_Problems/380163: Every morning, Don Miguel exercises by walking a certain distance at an average of 4 kph, rests for 20 min. and rides back along the same road on his chauffer-driven limousine at an average speed of 60 kph. If the total time of travel is one hr. and 15 min. how far does he walk? 1 solutions Answer 269824 by mananth(12270)   on 2010-12-03 02:06:19 (Show Source): You can put this solution on YOUR website! let the distance he walks be x speed of walking = 4 kph time walking = x/4 hours .. t=d/r d=4x r=60 kph time driven = x/60 hours ... rest = 20/60 = 1/3 hours .. time walk + time drive + rest = 1 h 15 mins (= 1 1/4 hour = 5/4 hours) ... x/4 + x/60 + 1/3 = 5/4 - 1/3 x/4 +x/60 = 5/4-1/3 x/4+x/60 = (15-4)/12 x/4+x/60 = (11)/12 LCD = 60 (15x+x)/60 = 11/12 cross multiply 12*16x=660 192x=660 /192 x=660/192 x= 3.44 km the distance he walked. ... m.ananth@hotmail.ca

Quadratic_Equations/380165: Bob and Kevin both have square vegetable gardens. Kevin's garden is 10 feet longer than Bob's garden, and its area is four times the area of Bob's garden. What are the dimensions of Bob's garden? 1 solutions Answer 269820 by mananth(12270)   on 2010-12-03 01:19:14 (Show Source): You can put this solution on YOUR website! Bob's garden -side length be x feet Area = x*x=x^2 .. Kevin's garden - side length = x+10 feet .. so area = (x+10)*(x+10) =x^+20x+100 .. x^2+20x+100=4x^2 3x^2-20x-100=0 3x^2-30x+10x-100=0 3x(x-10)+10(x-10)=0 (x-10)(3x+10)=0 x= 10 Bob's garden dimensions = 10 feet by 10 feet ... m.ananth@hotmail.ca

Miscellaneous_Word_Problems/380160: A passenger bus traveling at the rate of 70km/hr leaves the station 2 hrs. after a cargo truck left and overtakes it in 5 hrs. What is the rate of the cargo truck? 1 solutions Answer 269819 by mananth(12270)   on 2010-12-03 01:08:01 (Show Source): You can put this solution on YOUR website! cargo truck speed be x km/h .. they are travelling one behind the other passenger bus catches up = 70-x mph. .. cargo truck has already traveled 2 hours when the bus starts. so it has traveled 2x km. .. The bus catches up after time t=5 .. t = d/r 5=2x/(70-x) multiply by (70-x) 5(70-x)=2x 350-5x=2x +5x 350=2x+5x 350=7x /7 350/7 = x 50=x .. the speed of cargo truck = 50 km/hr. ... m.ananth@hotmail.ca

Miscellaneous_Word_Problems/380159: Two cars 240 km apart started at the same time and traveled toward each other at the rates of 60 kph and 45 kph. In how many hrs. will they meet? 1 solutions Answer 269818 by mananth(12270)   on 2010-12-03 01:01:09 (Show Source): You can put this solution on YOUR website! They are moving towards each other so add up the speeds .. 60+45 = 105 kph .. distance apart = 240 km .. t=d/r t=240/105 t= 2.28 hours they will meet after 2.28 hours .. m.ananth@hotmail.ca

Miscellaneous_Word_Problems/380158: Gerald and John agreed to start from the same point and go in opposite directions every morning for a jog. If Gerald runs at a speed of 3km/hr ans John has a speed of 4km/hr,in how many hrs. will they be 14 km apart? 1 solutions Answer 269817 by mananth(12270)   on 2010-12-03 00:57:44 (Show Source): You can put this solution on YOUR website! Gerald runs at a speed of 3km/hr John has a speed of 4km/hr, in how many hrs. will they be 14 km apart .. they are running in opposite directions add up speeds 4+3=7 km/hr .. distance = 14 km ... t= d/r t= 14/7 t= 2 After 2 hours they will be 14 km apart ... m.ananth@hotmail.ca