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 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
 Polynomials-and-rational-expressions/503159: using the steps to the foil method can you break down how to get the answer to this (4z-u)(6z+4u)? 1 solutions Answer 339160 by ankor@dixie-net.com(15656)   on 2011-09-23 19:57:15 (Show Source): You can put this solution on YOUR website!(4z-u)(6z+4u)? First: mult the first two terms: 4z*6z = 24z^2 Outer: mult the first & last terms: 4z*4u = 16zu Inner: mult the inner terms: -u*6z = -6zu Last: mult the last terms: -u*4u = -4u^2 : Put them together 24z^2 + 16zu - 6zu - 4u^2 : the middles are like terms combine them 24z^2 + 10zu - 4u^2
 Rational-functions/503204: Please help!! I have to show a table of values for -3x + 4y = -12. I have no idea. I keep trying to show how to figure it out but I cant. Thanks so much!! 1 solutions Answer 339120 by ankor@dixie-net.com(15656)   on 2011-09-23 16:47:51 (Show Source): You can put this solution on YOUR website!show a table of values for -3x + 4y = -12. Convert equation to the slope/intercept form -3x + 4y = -12 4y = 3x - 12 divide by 4 y = x - 3 : We will construct a table using x values of -3 to + 3 Substitute -3 for x and find y y = (-3) - 3 y = - 3 y = - y = y = -5.25 do the same for x=-2, -1, 0, +1, +2, +3, The table x | y ------- -3 |-5.25 -2 | -1 |-3.75 0 | +1 |-2.25 +2 | +3 |-.75 : You can fill in the missing y values
 Word_Problems_With_Coins/502910: Maria has 20 coins in her pocket, all nickels and dimes. The total value of the coins is \$1.35. How many of each type of coin does she have in her pocket? PLEASE I NEED HELP ASAP if you could help me show HOW you got to there that would be so helpful :) THANK YOU!!!1 solutions Answer 339115 by ankor@dixie-net.com(15656)   on 2011-09-23 16:27:05 (Show Source): You can put this solution on YOUR website!Maria has 20 coins in her pocket, all nickels and dimes. The total value of the coins is \$1.35. How many of each type of coin does she have in her pocket? : let n = no. of nickels let d = no. or dimes ; Write an equation for each statement: "Maria has 20 coins in her pocket, all nickels and dimes." n + d = 20 n = (20-d), use this form for substitution : "The total value of the coins is \$1.35." .05n + .10d = 1.35 From the 1st statement, substitute n with (20-d) .05(20-d) + .10d = 1.35 1 - .05d + .10d = 1.35 .05d = 1.35 - 1 .05d = .35 d = d = 7 dimes : You can find n, yourself, check that the total is 1.35
 Expressions-with-variables/502917: How do u write "2 less that the product of 3 and a number x is at least 14" ?1 solutions Answer 339114 by ankor@dixie-net.com(15656)   on 2011-09-23 16:18:45 (Show Source): You can put this solution on YOUR website!How do u write "2 less that the product of 3 and a number x is at least 14" ? : Just write down what it says: -2 + 3*x => 14 then arrange it as it is normally written, with the unknown first 3x - 2 => 14
 Miscellaneous_Word_Problems/503165: Urgent Response. Can a tutor be so kind to help with solving this problem? AKI's Bicycle Shop designs has determined that when x hundred bicycles are built,the average cost per bicycle is given by C(x)=0.1x^2-11.2x+9.232 where C(x) is in hundreds of dollars. How many bicycles should the shop build? _____1 solutions Answer 339111 by ankor@dixie-net.com(15656)   on 2011-09-23 15:57:19 (Show Source): You can put this solution on YOUR website!AKI's Bicycle Shop designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.1x^2-11.2x+9.232 where C(x) is in hundreds of dollars. How many bicycles should the shop build? _____ : I assume they want to find the no. of bikes that will give minimum cost per bike : This is a quadratic equation where the minimum can be found by using the axis of symmetry formula: x = -b/(2a) In this equation a = .1, b = -11.2 therefore x = = x = 56 hundred bikes for min cost per bike
 Exponential-and-logarithmic-functions/502985: How to use exponentials to solve the following equation. (ii) 7+3e(to the power x)=3/e(to the power x+6) +71 solutions Answer 339100 by ankor@dixie-net.com(15656)   on 2011-09-23 14:59:15 (Show Source): You can put this solution on YOUR website!How to use exponentials to solve the following equation. (ii) 7+3e(to the power x)=3/e(to the power x+6) +7 : 7 + 3 = + 7 Subtract 7 from both sides 3 = Change the sign of the exponent to give us the reciprocal = when the numerators are equal, the denominators are equal, therefore: = therefore -x = x + 6 -6 = x + x -6 = 2x x = -3 : : Check this in the original equation 7 + 3 = + 7 Change the sign of the exponent to give us the reciprocal 7 + = + 7
 Problems-with-consecutive-odd-even-integers/503020: Subtract the complex expressions, and simplify. (-4.5 + 4.4i) – (3.2 – 9.6i) i need help with this one1 solutions Answer 339093 by ankor@dixie-net.com(15656)   on 2011-09-23 13:43:09 (Show Source): You can put this solution on YOUR website!Subtract the complex expressions, and simplify. (-4.5 + 4.4i) – (3.2 – 9.6i) removing the brackets, that have a neg in front changes the signs -4.5 + 4.4i - 3.2 + 9.6i Group like terms -4.5 - 3.2 + 4.4i + 9.6i Add like terms -7.7 + 14i
 Numbers_Word_Problems/502890: A two digit number is 3 times the sum of it's digits. The number is also 45 less than the number formed by reversing the digits and the original number. What is the original number?1 solutions Answer 338995 by ankor@dixie-net.com(15656)   on 2011-09-22 21:55:45 (Show Source): You can put this solution on YOUR website!Let x = the 10's digit, let y = the units : A two digit number is 3 times the sum of it's digits. 10x + y = 3(x+y) 10x + y = 3x + 3y 10x - 3x = 3y - y 7x = 2y : The number is also 45 less than the number formed by reversing the digits and the original number. 10x + y = 10y - x - 45 10x - x = 10y - y - 45 9x = 9y - 45 simplify, divide by 9 x = y - 5 : In the 1st simplified equation replace x with (y-5) 7(y-5) = 2y 7y - 35 = 2y 7y - 2y = 35 5y = 35 y = 35/5 y = 7 is the units digit (original number) and x = 7 - 5 x = 2 is the 10's digit : 27 is the number : : Check it in the statement: "A two digit number is 3 times the sum of it's digits. 27 = 3(7+2)
 Square-cubic-other-roots/502787: How Do You Simplify The Square Root Of 3 Times The Square Root Of 28 ?1 solutions Answer 338990 by ankor@dixie-net.com(15656)   on 2011-09-22 21:46:55 (Show Source): You can put this solution on YOUR website!How Do You Simplify The Square Root Of 3 Times The Square Root Of 28 ? Same as = Factor 84 to reveal the perfect square extract the square root of 4
 expressions/502765: Using the pemdas formula, I need to put 6, 6, 6, and 6 to equal 6. I am having difficulty trying to come up with the sum of 6. Please help.1 solutions Answer 338985 by ankor@dixie-net.com(15656)   on 2011-09-22 21:40:21 (Show Source): You can put this solution on YOUR website!Using the pemdas formula, I need to put 6, 6, 6, and 6 to equal 6. I am having difficulty trying to come up with the sum of 6. : How about 6(6-6)+6 = 6?
 Miscellaneous_Word_Problems/502757: Joey and Sally are on a hiking trip. It will be dark in 1.5 hours. They have to decide whether to stop for the night or hike to the camp site at the base of a tower they can see in distance. They know the height of the tower is 315 metres and they use a clinometer to determine the angle of elevation to the top of the tower is 4. Joey and Sally have been walking at 3.5 km/hr . Should they stop for the night or continue walking?1 solutions Answer 338979 by ankor@dixie-net.com(15656)   on 2011-09-22 21:30:00 (Show Source): You can put this solution on YOUR website!Joey and Sally are on a hiking trip. It will be dark in 1.5 hours. They have to decide whether to stop for the night or hike to the camp site at the base of a tower they can see in distance. They know the height of the tower is 315 metres and they use a clinometer to determine the angle of elevation to the top of the tower is 4. : Use the tangent of 4 degrees to find the distance (d) to the tower (side adjacent) and side opposite = 315 tan(4) = d = d = 4507.71 meters ~ 4.5 km to the base of the tower : Joey and Sally have been walking at 3.5 km/hr . Should they stop for the night or continue walking? : they are about 4.5 km from the tower, find the time to walk this dist at 3.5 km/hr = 1.287 hrs, they should make it with about 13 min to spare
 Inequalities/502728: how do you add a fraction with a negative number? -1/3x=-6 1 solutions Answer 338974 by ankor@dixie-net.com(15656)   on 2011-09-22 21:15:41 (Show Source): You can put this solution on YOUR website!x = -6 Multiply both sides by -1, to get rid of the negatives x = 6 Multiply both sides by 3 3*x = 3(6) gets rid of the fraction 1x = 18 or just x = 18 : : Check this in the original equaton
 test/502789: Angela is driving a Ferrari along the interstate at a constant speed of 55mph. A Volkswagon one-half mile behind her that is moving at a constant speed passed her in 90 seconds. How many miles per hour is the speed of the Volkswagon?1 solutions Answer 338970 by ankor@dixie-net.com(15656)   on 2011-09-22 21:11:36 (Show Source): You can put this solution on YOUR website!Angela is driving a Ferrari along the interstate at a constant speed of 55mph. A Volkswagon one-half mile behind her that is moving at a constant speed passed her in 90 seconds. How many miles per hour is the speed of the Volkswagon?: : Let v = the Volkswagon speed : Change 90 sec to hrs: 90/3600 = .025 hrs : Write a time equation: time = dist/speed : = .025 hrs .5 = .025(v-55) .5 = .025v - 1.375 .5 + 1.375 = .025v 1.875 = .025v v = v = 75 mph is the Volkswagon
 Divisibility_and_Prime_Numbers/502321: Find the prime factorization for the number 1560 and write the answer using exponents.1 solutions Answer 338889 by ankor@dixie-net.com(15656)   on 2011-09-22 15:48:19 (Show Source): You can put this solution on YOUR website!Find the prime factorization for the number 1560 and write the answer using exponents. : The way I did it; if even, divide by 2, if even, divide by 2 again, if odd divide by 3, if 0 or 5 divide by 5, until you get a prime number : 2 * 2 * 2 * 3 * 5 * 13 2^3 * 5 * 13
 Travel_Word_Problems/502461: Linda drove from Phila. to NYC at the rate of 50 mph. She made the trip from NYC to Phila., along the same route, traveling at 40 mph. Her total driving time was 3.6 hours. Find the distance between Phila. and NYC.1 solutions Answer 338885 by ankor@dixie-net.com(15656)   on 2011-09-22 15:35:30 (Show Source): You can put this solution on YOUR website!Linda drove from Phila. to NYC at the rate of 50 mph. She made the trip from NYC to Phila., along the same route, traveling at 40 mph. Her total driving time was 3.6 hours. Find the distance between Phila. and NYC. : Let d = dist from Philly to NY Write a time equation, time = dist/speed : To time + return time = 3.6 hrs + = 3.6 multiply by 200 to clear the denominators, results 4d + 5d = 200(3.6) 9d = 720 d = 720/9 d = 80 mi ; : Check this by finding the actual time of each trip 80/50 = 1.6 hrs 80/40 = 2.0 hrs ----------------- total: 3.6 hrs
 Problems-with-consecutive-odd-even-integers/502374: sqrt-108 Simplify the following expression; express in terms of i. help1 solutions Answer 338884 by ankor@dixie-net.com(15656)   on 2011-09-22 15:28:03 (Show Source): You can put this solution on YOUR website!sqrt-108 Simplify the following expression; express in terms of i. : Extract the square root of -1 factor 108 to reveal a perfect square extract the square root of 36
 Travel_Word_Problems/502437: I need help on the word problem. Alex and Betty walk at 4 mph to their car. It takes them almost an hour. In their car, they travel (at 16 mph) the same distance as they walked. All together, their walking and traveling by car took exactly one hour. How long did they walk?1 solutions Answer 338881 by ankor@dixie-net.com(15656)   on 2011-09-22 15:01:44 (Show Source): You can put this solution on YOUR website!Alex and Betty walk at 4 mph to their car. It takes them almost an hour. In their car, they travel (at 16 mph) the same distance as they walked. All together, their walking and traveling by car took exactly one hour. How long did they walk? : Let t = time spent walking (in hrs) then it said the round trip took 1 hr therefore: (1-t) = time spent driving : The walking dist and the driving dist is the same, write a dist equation: dist = speed * time : walk dist = drive dist 4t = 16(1-t) 4t = 16 - 16t 4t + 16t = 16 20t = 16 t = t = .8 hrs walking : : : Check this (.2 hrs driving) 4(.8) = 3.2 mi 16(.2)= 3.2 mi; confirms our solution of .8 hrs spend walking
 Surface-area/502413: how can I know how many gallions of paints to cover my living room that measures 30ft by 18ft?1 solutions Answer 338878 by ankor@dixie-net.com(15656)   on 2011-09-22 14:52:54 (Show Source): You can put this solution on YOUR website!how can I know how many gallons of paints to cover my living room that measures 30ft by 18ft? : Find the area of the painted area. If you are covering all 4 walls and the ceiling is 8 ft high: 2(30*8) + 2(18*8) = 2(240) + 2(144) = 768 sq/ft, if you include the ceiling, add another 30*18 = 540 sq/ft : Of course it will probably be a little less because of doors and windows, but this will give you a good idea : Paint cans tell you how many sq ft it will cover, usually around 450 sq/ft Divide the total area you are going to paint by that amt, round it up to the nearest gallon. : If you are changing the color drastically you may need to paint it twice.
 Proportions/502322: a masons can build a 12 meters long wall in 4 days. find how many masons are required to build the 27 meters long wall in 3 days?1 solutions Answer 338877 by ankor@dixie-net.com(15656)   on 2011-09-22 14:32:20 (Show Source): You can put this solution on YOUR website! a masons can build a 12 meters long wall in 4 days. : The number of man-days per meter requires: = man-days per meter : : find how many masons are required to build the 27 meters long wall in 3 days? : A 27 meter wall requires 27 * = = 9a man-days m = no. of masons required 3m = 9a Divide by3 m = 3a 3a masons required to accomplish this
 percentage/502227: I am having problems with this word problem: Raul paid a total of \$26.40 for a meal. This total included a 20% tip. How much was the cost of the meal?1 solutions Answer 338788 by ankor@dixie-net.com(15656)   on 2011-09-21 21:55:36 (Show Source): You can put this solution on YOUR website!Raul paid a total of \$26.40 for a meal. This total included a 20% tip. How much was the cost of the meal? : Let m = cost of the meal : Meal + tax = 26.40 m + .20m = 26.40 1.2m = 26.40 m = m = \$22 for the meal : : Check this meal alone cost = 22 tip cost: .2(22) = 4.40 -------------------------- total, meal & tip 26.40
 Rate-of-work-word-problems/501622: if 24 adult can finish a work in 16 days and 16 children can finish the same work in 48 days then how much time it would take one adult and 1 child to finish the work? 1 solutions Answer 338722 by ankor@dixie-net.com(15656)   on 2011-09-21 16:38:47 (Show Source): You can put this solution on YOUR website!if 24 adult can finish a work in 16 days and 16 children can finish the same work in 48 days then how much time it would take one adult and 1 child to finish the work? : We know it takes 24*16 = 384 man-days to do the job or 16*48 = 768 child-days (twice as many as man-days) Therefore: 2 child-days = 1 man-day : "then how much time it would take one adult and 1 child to finish the work? let d = no. of days for 1 child and 1 man to do the job : 1 child and 1 man = 1.5 man : 1.5d = 384 d = d = 256 days for one man and one child to do the job : :
 Miscellaneous_Word_Problems/501599: write equation Mrs. Beal. a retiree will lose some retirement benefits if she earns over \$8000 per year working at baby sister.if she has already earned \$6500, for how many more hours may she work at \$7.50 per hour without losing her retirement benefits?1 solutions Answer 338711 by ankor@dixie-net.com(15656)   on 2011-09-21 16:21:15 (Show Source): You can put this solution on YOUR website!Mrs. Beal. a retiree will lose some retirement benefits if she earns over \$8000 per year working at baby sister.if she has already earned \$6500, for how many more hours may she work at \$7.50 per hour without losing her retirement benefits? : h = = 200 hrs : : Check this 200(7.50) + 6500 = 8000
 Linear-systems/501602: Solve the following system (if possible) and place your answer below: 3/x - 2/y = -30 2/x - 3/y = -301 solutions Answer 338707 by ankor@dixie-net.com(15656)   on 2011-09-21 16:07:31 (Show Source): You can put this solution on YOUR website! : Multiply the 1st equation by 2, the 2nd equation by 3: -------------subtraction eliminates x, find y + 30y = 5 y = y = : Find x using the 1st equation - = -30 + 12 = -18 -18x = 3 x = x = : : Check solutions in the 2nd equation - -12 - 18 = -30
 Reduction-of-unit-multipliers/501723: In a downhill ski race, Margo posted a time of 2 minutes and 24 seconds for a course 2.1 miles long. How many miles per hour did she average for the race?1 solutions Answer 338703 by ankor@dixie-net.com(15656)   on 2011-09-21 15:47:38 (Show Source): You can put this solution on YOUR website!In a downhill ski race, Margo posted a time of 2 minutes and 24 seconds for a course 2.1 miles long. How many miles per hour ? : Change 2 min 24 sec to 144 sec : = 68.57 sec/mi : Convert to mph (3600 sec in 1 hr) = 52.5 mph
 Money_Word_Problems/501722: when you use your car for business you are able to deduct expenses on your income tax. Milage rates are 55.5 cents per mile. How many miles did the tax-payer drive who deducted &8880.00.1 solutions Answer 338701 by ankor@dixie-net.com(15656)   on 2011-09-21 15:32:58 (Show Source): You can put this solution on YOUR website!when you use your car for business you are able to deduct expenses on your income tax. Milage rates are 55.5 cents per mile. How many miles did the tax-payer drive who deducted &8880.00. : = 16,000 miles, that's pretty easy, isn't it?
 Miscellaneous_Word_Problems/501561: The height of an object tossed upward with an initial velocity of 104 feet per second is given by the formula h = -16t^2 + 104t, where h is the height in feet and t is the same time in seconds. Find the time required for the object to return to its point of departure. Please, I need this problem to be solved by tomorrow night (9/21/2011). Thanks.1 solutions Answer 338700 by ankor@dixie-net.com(15656)   on 2011-09-21 15:29:17 (Show Source): You can put this solution on YOUR website!The height of an object tossed upward with an initial velocity of 104 feet per second is given by the formula h = -16t^2 + 104t, where h is the height in feet and t is the same time in seconds. Find the time required for the object to return to its point of departure. : the point of departure (ground level) h = 0, therefore -16t^2 + 104t = 0 Factor out -16t, results -16t(t - 6.5) = 0 Two solutions t = 0 sec, when object is tossed, it as at ground level and t = 6.5 sec, when object returns to earth
 Travel_Word_Problems/501784: Maria paints portraits that she sells for \$30 each. Her cost, C, is C= 160+16n, where n = number of portraits sold. Write an inequality to represent the number of portraits she needs to sell to earn a profit of at least \$300 1 solutions Answer 338696 by ankor@dixie-net.com(15656)   on 2011-09-21 15:17:29 (Show Source): You can put this solution on YOUR website!Maria paints portraits that she sells for \$30 each. Her cost, C, is C= 160+16n, where n = number of portraits sold. Write an inequality to represent the number of portraits she needs to sell to earn a profit of at least \$300 : Revenue; r = 30n cost; c = 160 + 16n r - c = profit; therefore : 30n - (160+16n) => 300 30n - 160 - 16n => 300 30n - 16n = 300 + 160 14n => 460 n => n => 33 portraits to make at least \$300 : : : Check this 30(33) = \$990 revenue 160 + 16(33) = \$688 cost ----------------------- profit: \$302 : You can check this with 32 portraits and see it will be less than \$300 profit
 Travel_Word_Problems/501761: The Fortune Family leaves home at 6:00 AM to go on vacation. They travel 50 miles per hour. Their next door neighbor, the Bissets leave home at 8:00 AM to go on vacation. They travel at 60 miles per hour. If the Fortunes and Bissets are traveling the same route to the same location, after how many hours will the Bissets be 40 miles ahead of the Fortunes? I am having the hardest time with this problem! I am not even sure how to begin to set it up, let alone solve it.1 solutions Answer 338684 by ankor@dixie-net.com(15656)   on 2011-09-21 14:43:09 (Show Source): You can put this solution on YOUR website!The Fortune Family leaves home at 6:00 AM to go on vacation. They travel 50 miles per hour. Their next door neighbor, the Bissets leave home at 8:00 AM to go on vacation. They travel at 60 miles per hour. If the Fortunes and Bissets are traveling the same route to the same location, after how many hours will the Bissets be 40 miles ahead of the Fortunes? : Let t = travel time of the Bissets The Fortune family leaves two hr earlier, therefore (t+2) = travel time of Fortunes : Write a distance equation, dist = speed * time : B's dist - F's dist = 40 mi 60t - 50(t+2) = 40 60t - 50t - 100 = 40 10t = 40 + 100 10t = 140 t = t = 14 hrs for the B's to be 40 mi ahead of the F's ; : We can confirm this by finding the actual dist each drove in 14 & 16 hrs 60*14 = 840 mi 50*16 = 800 mi --------------- differ: 40 mi : : Hey don't sound so discouraged, did this make sense to you? Develop a thought pattern that translates each phrase to a simple expression or equation. Then use the dist, time, speed relationships that I am sure you know. Let me know what you think, please. C
 Travel_Word_Problems/501780: Hi, My daughter who is in sixth grade got this question: A lorry travels from Town A to Town B in 4 & 1/5 hrs. A car travels from Town B to Town A in 3 hrs. If both started at the same time, after how long did they pass across each other? She is not allowed to use formulas and equations involving x, y etc. Can you please explain how to solve this without using equations? Thanks. 1 solutions Answer 338662 by ankor@dixie-net.com(15656)   on 2011-09-21 13:51:26 (Show Source): You can put this solution on YOUR website!A lorry travels from Town A to Town B in 4 & 1/5 hrs. A car travels from Town B to Town A in 3 hrs. If both started at the same time, after how long did they pass across each other? : I can't see how you can solve this without some equations, and why would you not want to? I assume we can use numbers and rules that govern there relationships. Anyway, there is mathematical relationship between these values which is used in electronics, called the "product over sum" relationship : = = 1.75 hrs travel time when they met : : : I admit I used algebra equations to confirm that this is right, in case you're interested. Choose a value for the distance between the towns, I chose 21 mi a multiple of 4.2 and 3 Found the speed: 21/4.2 = 5 mph and 21/3 = 7 mph, let t = time for them to meet 5t + 7t = 21 12t = 21 t = t = 1.75 hrs