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 Travel_Word_Problems/317173: The river is flowing from point A to B at a rate of 15 miles per hour. A boat moves on still water at 45 miles per hour. If it takes David 1 hour and 15 minutes to ride the boat on the river from A to B, how long does it take him to make the return trip from B to A?1 solutions Answer 227194 by ankor@dixie-net.com(15652)   on 2010-06-24 19:43:44 (Show Source): You can put this solution on YOUR website!The river is flowing from point A to B at a rate of 15 miles per hour. A boat moves on still water at 45 miles per hour. If it takes David 1 hour and 15 minutes to ride the boat on the river from A to B, how long does it take him to make the return trip from B to A? : Let t = time in hrs to go from B to A : change 1 hr 15 min to 1.25 hrs : Write a distance equation: dist = speed * time : A-B dist = B-A dist 1.25(45+15) = t(45-15) 1.25(60) = 30t 75 = 30t t = t = 2.5 hrs ; : Check solution by finding the distances 1.25(60) = 75 2.5(30) = 75
 Equations/317166: Bill had x dollars and he bought y apples for 16 cents each and z pears for 12 cents each. How many cents did he have left?1 solutions Answer 227187 by ankor@dixie-net.com(15652)   on 2010-06-24 19:20:52 (Show Source): You can put this solution on YOUR website!Bill had x dollars and he bought y apples for 16 cents each and z pears for 12 cents each. How many cents did he have left? : Cents left = 100x - (16y + 12z)
 Travel_Word_Problems/317219: 2 runners are running a track one runner runs it in 24 min, the other runner in 36 minutes when will they both be at the same spot?1 solutions Answer 227177 by ankor@dixie-net.com(15652)   on 2010-06-24 18:36:09 (Show Source): You can put this solution on YOUR website!2 runners are running a track one runner runs it in 24 min, the other runner in 36 minutes when will they both be at the same spot? : Prime factor both values 24: 2*2*2*3 36: 2*2*3*3 LCM 2*2*2*3*3 = 72 minutes : one runner completes 3 laps one runner completes 2 laps
 Radicals/317287: Write in simplified radical form by rationalizing the denominator. is the answer (-32-18sqrt(3))/(-13)1 solutions Answer 227175 by ankor@dixie-net.com(15652)   on 2010-06-24 18:18:43 (Show Source): You can put this solution on YOUR website!is the answer yes, but since everything is negative, you can write it:
 Mixture_Word_Problems/317102: it is neccessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 40 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strenght 1 solutions Answer 227148 by ankor@dixie-net.com(15652)   on 2010-06-24 16:52:13 (Show Source): You can put this solution on YOUR website!it is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 40 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength : Let x = amt of solution to be removed, and amt of pure antifreeze to be added : .20(40-x) + x = .40(40) : 8 - .2x + x = 16 : -.2x + x = 16 - 8 : .8x = 8 x = x = 10 liters removed and 10 liters of pure antifreeze added : : Check .2(30) + 10 = .4(40) 6 + 10 = 16
 Age_Word_Problems/317079: Kimberly is twice as old as ryan. in 4 years she will be 7 years older than ryan. how old is kimberly now?1 solutions Answer 227141 by ankor@dixie-net.com(15652)   on 2010-06-24 16:40:42 (Show Source): You can put this solution on YOUR website!Kimberly is twice as old as ryan. k = 2r : in 4 years she will be 7 years older than ryan. : This statement is made to confuse, K is 7 yrs older than R now, in 4 years, and until death, Just say k = r + 7 replace k with 2r from the 1st statement 2r = r + 7 2r - r = 7 r = 7 is R's present age and obviously 2(7) = 14 is Kimberly's present age
 Polynomials-and-rational-expressions/317189: A 12ft diameter Jacuzzi is installed on a square outdoor deck measuring y ft by y ft. Find a polynomial for the remaining area of the deck.1 solutions Answer 227095 by ankor@dixie-net.com(15652)   on 2010-06-24 14:21:44 (Show Source): You can put this solution on YOUR website!A 12ft diameter Jacuzzi is installed on a square outdoor deck measuring y ft by y ft. Find a polynomial for the remaining area of the deck. : Let A = remaining area of the deck, (radius of the Jacuzzi = 6') : A = A = y^2 - 113.1
 Mixture_Word_Problems/316843: The EdHelper dairy farm needs to create a mix of 1,438 liters of milk, which contains 13.89% butterfat. The farm will use milk from Jason's farm, which contains 8% butterfat and milk from Dylan's farm, which contains 15% butterfat. How many liters of milk should the dairy purchase from Dylan's farm?1 solutions Answer 226990 by ankor@dixie-net.com(15652)   on 2010-06-23 21:50:55 (Show Source): You can put this solution on YOUR website!needs to create a mix of 1,438 liters of milk, which contains 13.89% butterfat. Jason's farm, contains 8% butterfat and milk from Dylan's farm, which contains 15% butterfat. How many liters of milk should the dairy purchase from Dylan's farm? : let d = amt of 15% milk from Dylan the resulting total is to be 1438 liters, therefore (1438-d) = amt of 8% milk : At typical mixture equation .08(1438-d) + .15d = .1389(1438) 115.04 - .08d + .15d = 199.7382 -.08d + .15d = 199.7382 - 115.04 .07d = 84.6982 d = d = 1209.97 liters of 15% from Dylan : : See if that is true .08(228) + .15(1210) = .1389(1438) 18.24 + 181.5 = 199.74; confirms our solution
 Travel_Word_Problems/316841: Olivia lives thirty-two miles from work. This morning, she left for work at 8:43 a.m. There was construction for the first twenty miles, so Olivia only drove at an average speed of seventeen mph around the construction area. If Olivia needs to be at work by 10:11 a.m., what should be her average speed for the rest of the way to work?1 solutions Answer 226974 by ankor@dixie-net.com(15652)   on 2010-06-23 20:51:15 (Show Source): You can put this solution on YOUR website!Olivia lives thirty-two miles from work. This morning, she left for work at 8:43 a.m. There was construction for the first twenty miles, so Olivia only drove at an average speed of seventeen mph around the construction area. If Olivia needs to be at work by 10:11 a.m., what should be her average speed for the rest of the way to work? : Summarize what we know about this 1st 20 mi, 17 mph last 12 mi, drove at a higher speed (s) : total time to make the trip: 10:11 - 8:43 = 1:28 min or 1.47 hrs : Write a time equation: time = dist/speed slow time + fast time = total time + = 1.47 multiply by 17s, results 20s + 17(12) = 17s(1.47} 20s + 204 = 24.99s 204 = 24.99s - 20s 204 = 4.99s s = s = 40.88 ~ 41 mph speed on the last 12 mi : : See if that's true, find the times 20/17 = 1.1765 hrs 12/41 = .29 hrs ------------------- total: 1.469 ~ 1.47 hrs
 Numbers_Word_Problems/316952: Find three consecutive odd whole numbers such that the sum of their squares is a four-digit whole number whose digits are all the same. 1 solutions Answer 226904 by ankor@dixie-net.com(15652)   on 2010-06-23 16:53:04 (Show Source): You can put this solution on YOUR website!Find three consecutive odd whole numbers such that the sum of their squares is a four-digit whole number whose digits are all the same : Three consecutive odd numbers x, (x+2), (x+4); resulting 4 number digit = y : x^2 + (x+2)^2 + (x+4)^2 = 1000y+100y+10y+y : x^2 + x^2+4x+4 + x^2+8x+16 = 1111y : x^2 + x^2 + x^2 + 4x + 8x + 4 + 16 = 1111y : 3x^2 + 12x + 20 = 1111y : y = : Find the value for x which gives an integer value to y (the table of a TI83 was a great help!) x=41, y=5 : 41^2 + 43^2 + 45^2 = 5555
 Problems-with-consecutive-odd-even-integers/316791: 1) Find two consecutive even numbers such that the difference of one-half of the larger and two-fifths of the smaller is equal to five. 2)Find three consecutive numbers such that the sum of one-third of the first and one-seventh of the second is two less that one-half of the third. Help me please.1 solutions Answer 226875 by ankor@dixie-net.com(15652)   on 2010-06-23 14:56:43 (Show Source): You can put this solution on YOUR website!1) Find two consecutive even numbers such that the difference of one-half of the larger and two-fifths of the smaller is equal to five. Two consecutive even numbers; x, (x+2), (we can us decimals here 2/5 = .4) .5(x+2) - .4x = 5 .5x + 1 - .4x = 5 .5x - .4x = 5 + 1 .1x = 4 x = x = 40 40,42 are the numbers : Check .5(42) - .4(40) = 21 - 16 = 5 : ; 2)Find three consecutive numbers such that the sum of one-third of the first and one-seventh of the second is two less that one-half of the third x, (x+1), (x+2) x + (x+1) = (x+2) - 2 Get rid of those annoying fractions, multiply by 42, results: 14x + 6(x+1) = 21(x+2) - 42(2) : 14x + 6x + 6 = 21x + 42 - 84 : 20x + 6 = 21x - 42 : 6 + 42 = 21x - 20x : 48 = x : 48, 49, 50 are the three numbers : Check solution (48) + (49) = (50) - 2 16 + 7 = 25 - 2
 Quadratic_Equations/316746: h= -16t2 +80t + 50 Use this position polynomial to calculate the following: The height of the object after 2 seconds The height of the object after 5 seconds The maximum height of the object How long the the object will take to reach the ground? 1 solutions Answer 226869 by ankor@dixie-net.com(15652)   on 2010-06-23 14:34:44 (Show Source): You can put this solution on YOUR website!h= -16t^2 +80t + 50 ; Use this position polynomial to calculate the following: : The height of the object after 2 seconds h = -16(2^2) + 80(2) + 50 h = -16(4) + 160 + 50 h = -64 + 160 + 50 h = 146 ft ; The height of the object after 5 seconds Do the same as above, using t=5 : The maximum height of the object Find the axis of symmetry; x = -b/(2a) in this equation x=t; a=-16: b=80; t = t = t = 2.5 sec; the max height will occur in 2.5 sec Substitute 2.5 for t to find the max height h = -16(2.5^2) + 80(2.5) + 50 h = -16(6.25) + 200 + 50 h = -100 + 200 + 50 h = 150 ft is max height : How long the the object will take to reach the ground? when it strikes the ground, h=0, write the equation -16t^2 + 80t + 50 = 0; solve for t using the quadratic formula a=-16, b=80, c=50 I'll let you do the math here, the positive solution ~ 5.5 sec
 Miscellaneous_Word_Problems/316799: At a toy factory, each worker assembles one toy at a time and can assemble a total of 48 toys in 2 hours. At that rate, how many toys can 4 workers assemble in 3 hours?1 solutions Answer 226860 by ankor@dixie-net.com(15652)   on 2010-06-23 14:12:50 (Show Source): You can put this solution on YOUR website!each worker assembles one toy at a time and can assemble a total of 48 toys in 2 hours. then 48/2 = 24 toys per man-hour : At that rate, how many toys can 4 workers assemble in 3 hours? 4 working for 3 hrs: 4*3 = 12 man-hours then 12 * 24 = 288 toys
 Linear-systems/316769: Could someone help me with this problem? I am confused? Bayside Insurance offers two health plans. Under Plan A, Sam would have to pay the first \$80 of his medical bills, plus 35% of the rest. Under Plan B, Sam would pay the first \$230, but only 20% of the rest. For what amount of medical bills will Plan B save Sam money? Assume he was over \$230 in bills. Sam would save with Plan B if he had more than \$_____ in bills.1 solutions Answer 226858 by ankor@dixie-net.com(15652)   on 2010-06-23 14:05:48 (Show Source): You can put this solution on YOUR website!Bayside Insurance offers two health plans. Under Plan A, Sam would have to pay the first \$80 of his medical bills, plus 35% of the rest. Under Plan B, Sam would pay the first \$230, but only 20% of the rest. : Let b = amt of the medical bill Let p = amt he has to pay after insurance pays : Write an equation for plan A p = .35(b-80) + 80 : Write an equation for plan B p = .20(b-230) + 230 : For what amount of medical bills will Plan B save Sam money? Assume he was over \$230 in bills. Sam would save with Plan B if he had more than \$_____ in bills. : Plan A amt > Plan B amt .35(b-80) + 80 > .20(b-230) + 230 .35b - 28 + 80 > .20b - 46 + 230 .35b + 52 > .20b + 184 .35b - .20b > 184 - 52 .15b > 132 b > b > \$880, when his bill exceeds \$880, he would save money with plan B : : It will help you understand, if you substitute 880 for b in both equations and find out the actual amt he will pay
 Travel_Word_Problems/316801: Marco’s speed riding up a hill is 40% of his speed riding down the hill. It takes him two hours longer to ride up the hill than it takes him to ride down the hill. How long, in hours, does it take him to ride down the hill? Express your answer as a common fraction.1 solutions Answer 226831 by ankor@dixie-net.com(15652)   on 2010-06-23 13:12:50 (Show Source): You can put this solution on YOUR website!Marco’s speed riding up a hill is 40% of his speed riding down the hill. It takes him two hours longer to ride up the hill than it takes him to ride down the hill. How long, in hours, does it take him to ride down the hill? Express your answer as a common fraction. : Let s = his speed down hill then .4s = his speed up hill : Let one way distance = 10 : Write a time equation: time = dist/speed : Time up - time down = 2 hrs - = 2 hrs multiply by .4s, results 10 - .4(10) = 2(.4s) : 10 - 4 = .8s : 6 = .8s s = s = 7.5 is the downhill speed then .4(7.5) = 3 is the uphill speed : Find the time to ride down hill 10/7.5 = 1 hr : Check solution by finding the time uphill 10/3 = 3 hr, a two hr difference
 Problems-with-consecutive-odd-even-integers/316462: The product of two integers is positive and equals twice the sum of the integers. Find the pair of integers.1 solutions Answer 226684 by ankor@dixie-net.com(15652)   on 2010-06-22 21:49:57 (Show Source): You can put this solution on YOUR website!The product of two integers is positive and equals twice the sum of the integers. Find the pair of integers. : 2(x+y) = xy 2x + 2y = xy 2x + 2y - xy = 0 2y - xy = -2x y(2-x) = -2x y = we know 2 can't be a solution try x=3 y = y = y = 6 : The two integers, 3 & 6
 Rectangles/316479: Two squares have total area 85 cm^2 and total perimeter 52 cm. what is the area in cm^2 of the large square ? 1 solutions Answer 226674 by ankor@dixie-net.com(15652)   on 2010-06-22 21:24:44 (Show Source): You can put this solution on YOUR website!Two squares have total area 85 cm^2 and total perimeter 52 cm. what is the area in cm^2 of the large square ? : Let x = side of the large square then x^2 = it's area : Let y = side of small square then y^2 = it's area : "Two squares have total area 85 cm^2" x^2 + y^2 = 85 : " total perimeter 52 cm." 4x + 4y = 52 simplify, divide by 4 x + y = 13 y = (13-x) : replace y with (13-x) in the total area equation x^2 + (13-x)^2 = 85 FOIL x^2 + 169 - 26x + x^2 = 85 Combine as a quadratic equation 2x^2 - 26x + 169 - 85 = 0 2x^2 - 26x + 84 = 0 Factor this to (2x-12)(x-7) = 0 Two solutions x = 7 and 2x = 12 x = 6 : Area of the larger square: 7^2 = 49 sq/cm ; : Check solution y = 13-7 y = 6 cm then 6^2 = 36cm is the small square area total area: 49 + 36 = 85 : Check the perimeter 49 + 36 = 85; 4(7) + 4(6) = 52
 Length-and-distance/316631: If a boat travels downstream for one hour and travels twelve miles and returns upstream to the starting point and the trip requires four hours how fast is the current1 solutions Answer 226636 by ankor@dixie-net.com(15652)   on 2010-06-22 19:58:32 (Show Source): You can put this solution on YOUR website!If a boat travels downstream for one hour and travels twelve miles and returns upstream to the starting point and the trip requires four hours how fast is the current : Let s = speed of boat in still water Let c = speed of the current : Write a distance equation for each trip: 1(s + c) = 12 4(s - c) = 12 : Simplify the second equation; divide by 4, subtract from the 1st equation s + c =12 s - c = 3 -----------subtraction eliminates s, find c 2c = 9 c = c = 4.5 mph is the current : : : Check solution, find the speed of the boat s + 4.5 = 12 s = 12 - 4.5 s = 7.5 mph speed of the boat Check solution in the return equation 4(7.5 - 4.5) = 4(3) = 12
 logarithm/316458: An amplifier has an input power of 5 mW. The output power is 100 mW. What is the decibel gain to the nearest decibel?1 solutions Answer 226632 by ankor@dixie-net.com(15652)   on 2010-06-22 19:46:37 (Show Source): You can put this solution on YOUR website!An amplifier has an input power of 5 mW. The output power is 100 mW. What is the decibel gain to the nearest decibel? : The decibel gain equation: db = 10*log : In this problem p1 = 5 mw; p2 = 100 mw : db = 10*log : db = 10*log(20) : db = 10*1.301 : db = 13 db gain
 Quadratic_Equations/316415: The kinetic energy, K, of a moving particle acted on by various forces depends quadratically on the velocity, x, of the particle. The particle's energy is 210 ergs when its velocity is 5 meters per second;860 ergs at 10 meters per second; and 2010 ergs at 15 meters per second. What is the quadratic function K(x) that fits this data?1 solutions Answer 226625 by ankor@dixie-net.com(15652)   on 2010-06-22 19:16:07 (Show Source): You can put this solution on YOUR website!The kinetic energy, K, of a moving particle acted on by various forces depends quadratically on the velocity, x, of the particle. The particle's energy is 210 ergs when its velocity is 5 meters per second; 860 ergs at 10 meters per second; and 2010 ergs at 15 meters per second. What is the quadratic function K(x) that fits this data? : Using the form K(x) = ax^2 + bx, find a & b by elimination : x=5; K(x)=210 5^2a + 5b = 210 25a + 5b = 210 Simplify, divide by 5 5a + b = 42 : x=15; K(x)=2010 15^2a + 15b = 2010 225a + 15b = 2010 Simplify, divide by 5 45 + 3b = 402 : Multiply the simplified version of the 1st equation by 3, subtract from above 45a + 3b = 402 15a + 3b = 126 --------------subtraction eliminates b, find a 30a = 276 a = a = 9.2 : Find b using 5a + b= 42 5(9.2) + b = 42 b = 42 - 46 b = -4 : The quadratic function: k(x) = 9.2x^2 - 4x : It fits exactly for x=5 and x=15 : Check the fit using x=10; k(x) = 9.2(10^2) - 4(10) k(x) = 920 - 40 k(x) = 880 a slight difference, should be 860 : Graphically; k(x) on the y axis
 Quadratic_Equations/316621: A number of students go to a game costing a tital of \$80. Eight studnets are ill and cant go. Each of the remaining kids have to pay \$ 0.50 each. how many studenst went on teh bus?. thanksyou so much!1 solutions Answer 226609 by ankor@dixie-net.com(15652)   on 2010-06-22 18:14:33 (Show Source): You can put this solution on YOUR website!A number of students go to a game costing a total of \$80. Eight students are ill and can't go. Each of the remaining kids have to pay \$ 0.50 each. how many students went on the bus?. : Let s = the number of students that actually go then (s+8) = number that were scheduled to go : Actual cost (per student) - anticipated cost = .50 - = .50 multiply equation by s(s+8), results 80(s+8) - 80s = .50s(s+8) : 80s + 640 - 80s = .5s^2 + 4s Arrange as a quadratic equation on the right 0 = .5s^2 + 4s - 640 Get rid of the decimal, multiply by 2 s^2 + 8s - 1280 = 0 This will factor because we know it has to be an integer solution (s+40)(s-32) = 0 the positive solution s = 32 students actually went on the bus : : Check this by finding the cost of each scenario 80/32 = 2.50; actual price 80/40 = 2.00; we can see each had come up with 50 cents
 Radicals/316390: If the average radius of the orbit of Venus is 0.723 AU, then how many years does it tale for Venus to complete one orbit of the sun? Use the following information to solve. According to Kepler's third law of planetary motion, the ratio T^2 over R^3 has the same value for every planet in our solar system. R is the average radius of the orbit of the planet measured in astronomical units (AU), and T is the number of years it takes for one compete orbit of the sun. Jupiter orbits the sun in 11.86 years with an average radius of 5.2 AU, whereas Saturn orbits the sun in 29.46 years.1 solutions Answer 226571 by ankor@dixie-net.com(15652)   on 2010-06-22 16:30:20 (Show Source): You can put this solution on YOUR website!If the average radius of the orbit of Venus is 0.723 AU, then how many years does it tale for Venus to complete one orbit of the sun? Use the following information to solve. According to Kepler's third law of planetary motion, the ratio T^2 over R^3 has the same value for every planet in our solar system. R is the average radius of the orbit of the planet measured in astronomical units (AU), and T is the number of years it takes for one compete orbit of the sun. Jupiter orbits the sun in 11.86 years with an average radius of 5.2 AU, whereas Saturn orbits the sun in 29.46 years. ; Remember the earth to find Kepler's value: 1^2 yr over 1^3 astronomical unit = 1 : = 1 T^2 = .732^3 T = T = .61476 yrs
 logarithm/316456: The signal to a speaker causes .5 amps of current. The signal level is increased to 2.5 amps. What is the gain, rounded to the nearest decibel? I'm really stuck, please help me!1 solutions Answer 226558 by ankor@dixie-net.com(15652)   on 2010-06-22 16:08:17 (Show Source): You can put this solution on YOUR website!The signal to a speaker causes .5 amps of current. The signal level is increased to 2.5 amps. What is the gain, rounded to the nearest decibel? : The decibel gain formula using current: db = 20log where I1=.5, I2=2.5 : db = 20log db = 20log(5) db = 20*.69897 db = 13.9794 ~ 14 db gain
 Quadratic_Equations/316623: A theater has 300 suscribers who each pay \$400 for a season ticket. A theater wants to raise the ticket by \$20. For each \$20 increase tehy loose 10 suscribers. At what price can they maxamize the revenue? thanks a bunch!1 solutions Answer 226548 by ankor@dixie-net.com(15652)   on 2010-06-22 15:39:28 (Show Source): You can put this solution on YOUR website! theater has 300 suscribers who each pay \$400 for a season ticket. A theater wants to raise the ticket by \$20. For each \$20 increase they lose 10 subscribers. At what price can they maximize the revenue? : Let x = no. \$20 raises in price, and no. of 10 subscriber losses : Revenue = no. of subscribers * ticket price r = (300-10x) * (400+20x) FOIL r = 120000 + 6000x - 4000x - 200x^2 A quadratic equation r(x) = -200x^2 + 2000x + 120000 maximum occurs at the axis of symmetry, find that x = -b/(2a) in this equation a = -200, b=2000 x = x = +5 : Max revenue occurs when ticket price raise is \$20 * 5 or \$100 to \$500 You will lose 5*10 = 50 subscribers or 250 so the revenue will be: 500 * 250 = \$125,000 : You can also check this by finding the vertex of this equation Substitute 5 for x and solve for r(x)
 Travel_Word_Problems/316542: a motor boat maintained speed of 27 miles per hour relative to the water going 20 miles upstream and returning. The total time of the trip was 1.5 hours. What is the speed of the current?1 solutions Answer 226516 by ankor@dixie-net.com(15652)   on 2010-06-22 13:44:26 (Show Source): You can put this solution on YOUR website!a motor boat maintained speed of 27 miles per hour relative to the water going 20 miles upstream and returning. The total time of the trip was 1.5 hours. What is the speed of the current? : Let c = speed of the current then (27-c) = effective speed upstream and (27+c) = effective speed downstream : Write a time equation; time = dist/speed : Time up + time down = 1.5 hrs + = 1.5 Multiply equation by (27-c)(27+c), results 20(27+c) + 20(27-c) = 1.5(27-c)(27+c) : 540 + 20c + 540 - 20c = 1.5(729-c^2) : 1080 = 1093.5 - 1.5c^2 : 1.5c^2 = 1093.5 - 1080 : 1.5c^2 = 13.5 c^2 = c^2 = 9 c = c = 3 mph is the speed of the current : : See if that's true, find the time of each 20/30 = .67 20/24 = .83 ------------- totals:1.5 hrs
 Polynomials-and-rational-expressions/316154: How do i factor the following question completely: 1 solutions Answer 226329 by ankor@dixie-net.com(15652)   on 2010-06-21 21:42:28 (Show Source): You can put this solution on YOUR website!How do i factor the following question completely: : Using the special factoring formulas: This can be factored as "the sum of cubes" which is: (x^3+y^3) = (x+y)(x^2-xy+y^2) : =
 Rectangles/316155: Please help. I am still stumped. A rectangle has a perimeter of 82 inches with a diagonal of 29 inches. What is the length and width of the rectangle?1 solutions Answer 226268 by ankor@dixie-net.com(15652)   on 2010-06-21 16:59:14 (Show Source): You can put this solution on YOUR website!A rectangle has a perimeter of 82 inches with a diagonal of 29 inches. What is the length and width of the rectangle? : Write the perimeter equation 2L + 2W = 82 simplify, divide by 2 L + W = 41 L = (41-W); we can use this form for substitution : Write the pythag equation; a^2 + b^2 = c^2, where a=L, b=W, c=29 L^2 + W^2 = 29^2 L^2 + W^2 = 841 : Substitute (41-W) for L (41-W)^2 + W^2 = 841 : FOIL (41-W)(41-W) (1681 - 41W - 41W + W^2) + W^2 = 841 1681 - 82W + W^2 + w^2 = 841 : Arrange as a quadratic equation on the left: 2W^2 - 82W + 1681 - 841 = 0 2W^2 - 82W + 840 = 0 : Simplify, divide by 2 W^2 - 41W + 420 = 0 : Factor (W-20)(W-21) = 0 : Two solutions W = 20 and W = 21 : Find the Length when W=20 L = 41-W L = 41-20 L = 21 and Find the Length when W=21 L = 41-W L = 41-21 L = 20 : See if that checks out, find the diagonal (hypotenuse) d = d = 29 is the diagonal : YOu can confirm the solutions in the perimeter equation