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 Average/504473: A batsman in his 17th inning makes 85 scores and thereby increases his average by 3. His average after 17th inning is?1 solutions Answer 339693 by ankor@dixie-net.com(15656)   on 2011-09-26 16:31:18 (Show Source): You can put this solution on YOUR website!A batsman in his 17th inning makes 85 scores and thereby increases his average by 3. His average after 17th inning is? : let a = his average after the 17th inning then (a-3) = his average before the 17th : a = multiply both sides by 17 17a = 16(a-3) + 85 17a = 16a - 48 + 85 17a - 16a = 37 a = 37 his average after 17 innings
 Rate-of-work-word-problems/504467: A can do a work in 8 days and B in 12 days. How long will A and B take to do the same work together?1 solutions Answer 339690 by ankor@dixie-net.com(15656)   on 2011-09-26 16:16:53 (Show Source): You can put this solution on YOUR website!: A can do a work in 8 days and B in 12 days. How long will A and B take to do the same work together? : Let t = time required when working together Let the completed job = 1 : + = 1 multiply by 24 to clear the denominator, results: 3t + 2t = 24 t = t = 4.8 days working together
 Rate-of-work-word-problems/504465: if 20 men can do a piece of work in 8 days, then how many men can finish the same work in 10 days?1 solutions Answer 339689 by ankor@dixie-net.com(15656)   on 2011-09-26 16:11:31 (Show Source): You can put this solution on YOUR website!if 20 men can do a piece of work in 8 days, 20 * 8 = 160 man-days to complete the job : then how many men can finish the same work in 10 days? let m = no. of men required to do the job in 10 days 10m = 160 m = m = 16 men
 Geometry_Word_Problems/504433: The combined area of a square and a rectangle is 116 square centimeters. The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of the rectangle is 2 centimeters more than its width.Find the dimensions of the square and the rectangle?1 solutions Answer 339687 by ankor@dixie-net.com(15656)   on 2011-09-26 16:08:14 (Show Source): You can put this solution on YOUR website!The combined area of a square and a rectangle is 116 square centimeters. The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of the rectangle is 2 centimeters more than its width. Find the dimensions of the square and the rectangle? : x = the side of the square and the width of the rectangle : Adding the two areas x^2 + x(x+2) = 116 x^2 + x^2 + 2x = 116 A quadratic equation 2x^2 + 2x - 116 = 0 Solve this using the quadratic formula: a=2; b=2; c=-116
 Travel_Word_Problems/504654: A tire of a moving bicycle has radius 16 in. If the tire is making 2 rotations per second, find the bicycle's speed in miles per hour.1 solutions Answer 339679 by ankor@dixie-net.com(15656)   on 2011-09-26 15:07:16 (Show Source): You can put this solution on YOUR website!A tire of a moving bicycle has radius 16 in. If the tire is making 2 rotations per second, find the bicycle's speed in miles per hour. : 2 * circumference * 3600 sec divided by inches in a foot and feet in a mile : Put this in your calc: = 11.434 mph
 Equations/504668: Solve for x: c(x+2)-5=b(x-3) I have several problems like this for my homework and I'm completely stuck. Thanks for the help =)1 solutions Answer 339676 by ankor@dixie-net.com(15656)   on 2011-09-26 14:35:22 (Show Source): You can put this solution on YOUR website!c(x+2)- 5 = b(x-3), solve for x : cx + 2c - 5 = bx - 3b : perform the necessary operations to get the x's on the left cx - bx = -3b - 2c + 5 ; Factor out x x(c-b) = -3b - 2c + 5 : Divide both sides by (c-b) x =
 Inequalities/504360: 1/(1-8x)= 5 the parenthesis are not supposed to be parenthesis, they are supposed to be absolute value signs I know i have to isolate the absolute value but im confused as exactally which method to use in order to do that.....not sure if i should switch to a neg. or multiply by 1/5 im bogged....and having extreme brain farts. SEMPER!!1 solutions Answer 339668 by ankor@dixie-net.com(15656)   on 2011-09-26 13:47:36 (Show Source): You can put this solution on YOUR website!= 5 multiply both sides by|1-8x|, results: 1 = 5|1 - 8x| Rewrite it to 5|1 - 8x| = 1 divide both sides by 5 |1 - 8x| = or |1 - 8x| = .2 Remove the abs 1st solution 1 - 8x = .2 -8x = .2 - 1 -8x = -.8 Multiply both sides by -1 8x = .8 x = x = .1 : 2nd solution 1 - 8x = -.2 -8x = -.2 - 1 -8x = -1.2 multiply both sides by -1 8x = 1.2 x = x = .15 : x = .1, .15 : Did this do to your brain, what fiber is supposed to do the digestive tract?
 Exponents/504475: please help me to solve this equation.. 1 solutions Answer 339655 by ankor@dixie-net.com(15656)   on 2011-09-26 12:42:32 (Show Source): You can put this solution on YOUR website!This is not an equation, no equal sign, so you can solve it, only simplify it. The reciprocal gets rid of the -1 exponent and changes the ^-2 to ^2 =
 Polynomials-and-rational-expressions/503831: Find b and c so that y= -20x^2 +bx +c has vertex (-5,-3). Thanks, i already know that b= -200 but wasnt sure how to get c 1 solutions Answer 339565 by ankor@dixie-net.com(15656)   on 2011-09-25 21:58:33 (Show Source): You can put this solution on YOUR website!Find b and c so that y= -20x^2 +bx +c has vertex (-5,-3). Thanks, i already know that b= -200 but wasn't sure how to get c : So you have -20x^2 - 200x + c = y Replace x and y -20(-5^2) - 200(-5) + c = -3 -500 + 1000 + c = -3 500 + c = -3 c = -3 - 500 c = -503
 Linear-systems/504229: how do you do the elimination method for this question The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of \$38. The school took in \$52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket. 1 solutions Answer 339562 by ankor@dixie-net.com(15656)   on 2011-09-25 21:27:35 (Show Source): You can put this solution on YOUR website!let s = price of the senior cit ticket let c = price of a child's ticket : Write an equation for each statement: : On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of \$38. 3s + 1c = 38 ; The school took in \$52 on the second day by selling 3 senior citizen tickets and 2 child tickets. 3s + 2c = 52 : Write the two equation for elimination 3s + 2c = 52 3s + 1c = 38 ----------------subtraction eliminates s, find c 0 + 1c = \$14 for one child ticket : Find s using the equation 3s + 1c = 38, replace c with 14 3s + 14 = 38 3s = 38 - 14 3s = 24 s = 24/3 s = \$8 for each senior : : You can check these solutions using the 2n equation F
 Expressions-with-variables/504080: i need to know how to do this problem: f/2-19=-17 can you help i didn't get instruation on how to do it by my teacher? 1 solutions Answer 339560 by ankor@dixie-net.com(15656)   on 2011-09-25 21:09:43 (Show Source): You can put this solution on YOUR website!Assume the problem is: - 19 = -17 Add 19 to both sides - 19 + 19 = -17 + 19 = +2 multiply both sides by 2 to get rid of the denominator, this leaves us with f = 4 : : Check this in the original problem replacing f with - 19 = -17 2 - 19 = -17 -17 = -17; confirms our solution
 Travel_Word_Problems/504055: Robert goes for a walk at a speed of 3 miles per hour. Two hours later Roger attempts to overtake him by jogging at the rate of 7 miles per hour. How long will it take him to reach Robert?1 solutions Answer 339559 by ankor@dixie-net.com(15656)   on 2011-09-25 21:04:03 (Show Source): You can put this solution on YOUR website!Robert goes for a walk at a speed of 3 miles per hour. Two hours later Roger attempts to overtake him by jogging at the rate of 7 miles per hour. How long will it take him to reach Robert? : Let t = jogging time of Roger when overtakes Robert then (t+2) = walking time of Robert when he is overtaken : When this happens, they will both have traveled the same distance. Write distance equation: dist = speed * time ; Rog dist = Rob dist 7t = 3(t+2) 7t = 3t + 6 7t - 3t = 6 4t = 6 t = 6/4 t = 1.5 hrs of for Rog to overtake Rob : : Check by finding the distances, they should be equal 7*1.5 = 10.5 mi 3(3.5) = 10.5 mi
 expressions/504178: What is (x+5)^3+8=0?1 solutions Answer 339557 by ankor@dixie-net.com(15656)   on 2011-09-25 20:54:06 (Show Source): You can put this solution on YOUR website!What is (x+5)^3 + 8 = 0 Subtract 8 from both sides (x+5)^3 = -8 Find the cube root of both sides x + 5 = -2 x = -2 - 5 x = -7 : : Check solution in original problem (-7+5)^3 + 8 = 0 (-2)^3 + 8 = 0 -8 + 8 = 0; confirms our solution of x=-7
 Angles/504114: A supplement of an angle is six more than three times the angle's complement. Write an equation to represent the problem and solve for the angle, its complement, and its supplement. 1 solutions Answer 339545 by ankor@dixie-net.com(15656)   on 2011-09-25 19:54:11 (Show Source): You can put this solution on YOUR website!A supplement of an angle is six more than three times the angle's complement. Write an equation to represent the problem and solve for the angle, its complement, and its supplement. : Let x = the angle then (180-x) = it's supplement and (90-x) = it's complement : The equation for the given statement: (180-x) = 3(90-x) + 6 180 - x = 270 - 3x + 6 -x + 3x = 276 - 180 2x = 96 x = 96/2 x = 48 degrees is the angle then 180 - 48 = 132 degrees is the supplement and 90 - 48 = 42 degrees is the complement ; : Check our solutions in the given statement: "A supplement of an angle is six more than three times the angle's complement." 132 = 3(42) + 6 132 = 126 + 6; confirms our solutions
 Geometry_Word_Problems/504107: The perimeter of a triangle is 93 centimeters. If two sides are equally long and the third side is 9 centimeters longer than the others, find the lengths of the three sides.1 solutions Answer 339543 by ankor@dixie-net.com(15656)   on 2011-09-25 19:46:09 (Show Source): You can put this solution on YOUR website!The perimeter of a triangle is 93 centimeters. If two sides are equally long and the third side is 9 centimeters longer than the others, find the lengths of the three sides. : Let x = the length of the equal sides then (x+9) = the length of the 3rd side : 2x + (x+9) = 93 3x = 93 - 9 3x = 84 x = x = 28 is the length of the equal sides and 28+9 = 37 is the length of the 3rd side
 Travel_Word_Problems/503969: A bus traveled 50 miles per hour and reached its destination in 6 hours. How much longer would the trip have taken if the bus traveled 45 miles per hour?1 solutions Answer 339542 by ankor@dixie-net.com(15656)   on 2011-09-25 19:42:16 (Show Source): You can put this solution on YOUR website!A bus traveled 50 miles per hour and reached its destination in 6 hours. How much longer would the trip have taken if the bus traveled 45 miles per hour? : Find the distance of the trip: 50 * 6 = 300 miles : Find the time at 45 mph: 300/45 = 6 hrs : It would have hr or 40 min longer
 Radicals/503812: 1 solutions Answer 339536 by ankor@dixie-net.com(15656)   on 2011-09-25 19:17:47 (Show Source): You can put this solution on YOUR website! Factor inside the radical to reveal perfect squares extract the square root of these square
 Travel_Word_Problems/503911: A man came upon a bridge, he knew a train was coming soon, but he thought he could make it before the train came. As he was 1/3 across the bridge he heard the train coming at 45 miles per hour. The man figured he had choice, he could run directly to the end of the bridge and get there at the exact same time as the train, but he also knew he could run back toward the train and get to the near end of the bridge just as the train got there. How fast does the man run?1 solutions Answer 339501 by ankor@dixie-net.com(15656)   on 2011-09-25 16:15:16 (Show Source): You can put this solution on YOUR website!A man came upon a bridge, he knew a train was coming soon, but he thought he could make it before the train came. As he was 1/3 across the bridge he heard the train coming at 45 miles per hour. The man figured he had choice, he could run directly to the end of the bridge and get there at the exact same time as the train, but he also knew he could run back toward the train and get to the near end of the bridge just as the train got there. How fast does the man run? : From the information given we can say that if he runs away from the train, he will be 2/3 across bridge when the train enters the bridge The train travels the full length of the bridge in the same time the man runs the remaining 1/3 length of the bridge. therefore: * 45 = 15 mph is how fast the man runs
 Angles/503789: pete stopped, but tim kept running for 11 laps more. by the end of the run-a-thon, pete and tim had run 45 laps around the school playground altogether. how many laps had each boy run? 1 solutions Answer 339492 by ankor@dixie-net.com(15656)   on 2011-09-25 15:46:46 (Show Source): You can put this solution on YOUR website!pete stopped, but tim kept running for 11 laps more. by the end of the run-a-thon, pete and tim had run 45 laps around the school playground altogether. how many laps had each boy run? : let L = no. of laps run by Pete then (L+11) = no. of laps run by Tim : L + (L+11) = 45 2L = 45 - 11 2L = 34 L = 17 laps run by Pete and 28 laps run by Tim : : Check 17 + 28 = 45
 Rate-of-work-word-problems/503778: A highway took 48 men 30 weeks to construct. 75 days into the construction phase, 8 men resigned, Assuming that all men worked 7 days a week find the total number of days the project was delayed1 solutions Answer 339466 by ankor@dixie-net.com(15656)   on 2011-09-25 14:29:46 (Show Source): You can put this solution on YOUR website!A highway took 48 men 30 weeks to construct. 75 days into the construction phase, 8 men resigned, Assuming that all men worked 7 days a week find the total number of days the project was delayed : Find the number of man-days to complete the highway (change weeks to days) 48 * (30*7) = 10,080 man-days : 75 days into the construction phase, 8 men resigned, 48 * 75 = 3600 10080 - 3600 = 6480 more man-days required to complete the job Let m = no. of days required by the 40 remaining men to complete the job 40m = 6480 m = m = 162 days more days after the resignation of 8 men : Assuming that all men worked 7 days a week find the total number of days the project was delayed 30*7 = 210 days planned with 48 men but 75 + 162 = 237 days actually required ; 237 - 210 = 27 day delay in completing the job
 Travel_Word_Problems/503860: Both car A and car B leave school at the same time, traveling in the same direction. Car A travels at a constant speed of 77 km/h, while car B travels at a constant speed of 87 km/h. How far is Car A from school 3.2 h later? Answer in units of km.1 solutions Answer 339463 by ankor@dixie-net.com(15656)   on 2011-09-25 14:07:24 (Show Source): You can put this solution on YOUR website!Both car A and car B leave school at the same time, traveling in the same direction. Car A travels at a constant speed of 77 km/h, while car B travels at a constant speed of 87 km/h. How far is Car A from school 3.2 h later? Answer in units of km. : Write a distance equation; dist = speed * time ; Car A dist = 3.2(77) = 246.4 km from the school : I don't see what Car B has to do with this problem!
 Geometry_Word_Problems/503532: You have a wire that is 53 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minium? 1 solutions Answer 339364 by ankor@dixie-net.com(15656)   on 2011-09-24 21:50:40 (Show Source): You can put this solution on YOUR website!You have a wire that is 53 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum? : Let x = circumference of the circle then (53-x) = the perimeter of the square and = the side of the square and = the area of the square : Find the area of the circle using the circumference find the radius (r) 2*pi*r = x r = r = Find the area of the circle A = Replace r with A = * = * cancel pi into 39.48 A = Total area of circle and square A = + = + : convert these fractions to decimal coefficients A(x) = .0796x^2 + .0625x^2 - 6.625x + 175.5625 A(x) = .1421x^2 - 6.625x + 175.5625 : Find the axis of symmetry of this quadratic equation (min area) x = x = x = 23.31 cm is the circumference when they have min area
 Rate-of-work-word-problems/503630: Todd contracted to paint a house for \$480. It took him 4 hours longer than he anticipated, so he earned \$0.50 less per hour than he originally calculated. How long had he anticipated it would take him to paint the house?1 solutions Answer 339342 by ankor@dixie-net.com(15656)   on 2011-09-24 20:01:53 (Show Source): You can put this solution on YOUR website!Todd contracted to paint a house for \$480. It took him 4 hours longer than he anticipated, so he earned \$0.50 less per hour than he originally calculated. How long had he anticipated it would take him to paint the house? : Let t = no. of hr he anticipated to paint the house then (t+4) = no. of hrs he actually required to paint the house : = the hourly pay he anticipated : - = .50 multiply by t(t+4), results 480(t+4) - 480t = .5t(t+4) 480t + 1920 - 480t = .5t^2 + 2t 1920 = .5t^2 + 2t A quadratic equation .5t^2 + 2t - 1920 = 0 Multiply by 2 to give t^2 a coefficient of 1 t^2 + 4t - 3840 = 0 You can use the quadratic formula to find t, however this will factor to: (t+64)(t-60) = 0 the positive solution t = 60 hrs he anticipated to paint the House : : Confirm this by finding the actual hourly pair 480/64 = \$7.50, actual pay 480/60 = \$8.00, hoped for pay
 Travel_Word_Problems/503644: The cold-water faucet fills a bathtub in 12min, and the hot-water faucet fills the bathtub in 10min. If you remove the stopper, a full tub will empty in 6min. How long will it take to fill the tub if both faucets are on and the stopper is removed?1 solutions Answer 339336 by ankor@dixie-net.com(15656)   on 2011-09-24 19:41:41 (Show Source): You can put this solution on YOUR website!The cold-water faucet fills a bathtub in 12min, and the hot-water faucet fills the bathtub in 10min. If you remove the stopper, a full tub will empty in 6min. How long will it take to fill the tub if both faucets are on and the stopper is removed? : Let t = time to fill the tub with both faucets and drain open Let a full tub = 1 : + - = 1 multiply by 60, to clear the denominators 60* + 60* - 60* = 1 cancel the denominators and you have: 5t + 6t - 10t = 60 11t - 10t = 60 t = 60 minutes
 Travel_Word_Problems/503468: A truck driving 260 miles over a flat interstate at a constant rate of 50 miles per hour gets 7 miles to the gallon. Fuel cost \$3.50 per gallon. For each mile per hour increase in speed, the truck loses a tenth of a mile per gallon in its mileage. Driver gets \$27.50 per hour in wages and fixed cost for running the truck amount to \$11.33 per hour. What Constant Speed (between 50 mph and the speed limit of 65 mph) should the truck drive to minimize the total cost of the trip? A. Let's start out by finding how long the trip will take? B. Now, with this time known, how much will it cost to pay the driver and run the truck? I need help with just setting up the problem and doing A and B, this is a huge math project and I think If i can have help with the first couple few I can do the rest.1 solutions Answer 339290 by ankor@dixie-net.com(15656)   on 2011-09-24 15:44:30 (Show Source): You can put this solution on YOUR website!A truck driving 260 miles over a flat interstate at a constant rate of 50 miles per hour gets 7 miles to the gallon. Fuel cost \$3.50 per gallon. For each mile per hour increase in speed, the truck loses a tenth of a mile per gallon in its mileage. Driver gets \$27.50 per hour in wages and fixed cost for running the truck amount to \$11.33 per hour. What Constant Speed (between 50 mph and the speed limit of 65 mph) should the truck drive to minimize the total cost of the trip? ; A. Let's start out by finding how long the trip will take? = 5.2 hrs to make the 260 mi trip at 50 mph : B. Now, with this time known, how much will it cost to pay the driver and run the truck? 5.2 * 27.50 = \$143.00, for the driver 5.2 * 11.33 = \$58.92, for the truck ---------------------- total cost: \$201.92 : Cost for gas: * 3.50 = \$130.00 for gas (at 50 mph) add to the above cost: 201.92 + 130 = \$331.92 total for the 260 mi trip : Correct a math error above, but also: : "What Constant Speed (between 50 mph and the speed limit of 65 mph) should the truck drive to minimize the total cost of the trip? : Speed affects time which affects cost Speed also affect gas mileage let s = speed then = time and = amt of gas required : Write a cost equation which is in terms of speed (s) Cost = driver time + truck time + gas used C(s) = *27.50 + *11.33 + *3.50
 absolute-value/503003: a two digit number is such that it is equal to 4 times the sum of it's digits. when 27 is added to the number the total is equal to the same number when it's digits are interchanged. what is the number. 1 solutions Answer 339183 by ankor@dixie-net.com(15656)   on 2011-09-23 21:59:52 (Show Source): You can put this solution on YOUR website!let x = the 10's digit let y = the units then 10x+y = the number : "a two digit number is such that it is equal to 4 times the sum of it's digits." 10x + y = 4(x+y) 10x + y = 4x + 4y 10x - 4x = 4y - y 6x = 3y simplify, divide by 2 2x = y : "when 27 is added to the number the total is equal to the same number when it's digits are interchanged." 10x + y + 27 = 10y + x 10x - x + 27 = 10y - y 9x + 27 = 9y simplify, divide by 9 x + 3 = y Replace y with 2x, (from the 1st statement) x + 3 = 2x 3 = 2x - x x = 3 y = 2(3) y = 6 and 36 is the number : : Check this in the 1st statement: a two digit number is such that it is equal to 4 times the sum of it's digits. 36 = 4(3+6); confirms our solutions
 Numbers_Word_Problems/502992: five times the difference of anumber and two is the same as four times the number. find the number 1 solutions Answer 339168 by ankor@dixie-net.com(15656)   on 2011-09-23 20:25:08 (Show Source): You can put this solution on YOUR website!five times the difference of a number and two is the same as four times the number. find the number : write an equation for exactly for what it says: 5(n-2) = 4n you should be able to solve this now
 Travel_Word_Problems/503002: John drove his car into the shop to fix the oil leak in his engine. Once finished, his car was faster. He drove home in only 25 minutes when it took him 40 minutes to get there. If he was traveling an average of 32 miles per hour going there, how fast did he drive home?1 solutions Answer 339163 by ankor@dixie-net.com(15656)   on 2011-09-23 20:12:02 (Show Source): You can put this solution on YOUR website!John drove his car into the shop to fix the oil leak in his engine. Once finished, his car was faster. He drove home in only 25 minutes when it took him 40 minutes to get there. If he was traveling an average of 32 miles per hour going there, how fast did he drive home? : Change minutes to hours = hrs = hrs : Let s = his speed going home : The distance there and back are equal, write a dist equation; Dist = time * speed : s = (32) mult both side by 12 5s = 8(32) 5s = 256 s = s = 51.2 mph return speed : : Confirm this by finding the distances, they should be equal *51.2 = 21.33 mi *32 = 21.33 mi