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 Travel_Word_Problems/359623: A Car travels 240 mi. A second car, traveling 12 mph faster than the first, makes the same trip in 1 hour less time. Find the speed of each car1 solutions Answer 256786 by ankor@dixie-net.com(15649)   on 2010-10-21 20:07:46 (Show Source): You can put this solution on YOUR website!A Car travels 240 mi. A second car, traveling 12 mph faster than the first, makes the same trip in 1 hour less time. Find the speed of each car : Let s = speed of the slower car then (s+12) = speed of the faster : Write a time equation; time = dist/speed : Slow car time - fast car time = 1 hr - = 1 : Multiply by s(s+12), results 240(s+12) - 240s = s(s+12) : 240s + 2880 - 240s = s^2 + 12s Combine as a quadratic equation on the right 0 = s^2 + 12s - 2880 Factors to (s+60)(s-48) = 0 positive solution s = 48 mph is the speed of the slower car then 48 + 12 = 60 mph is the faster car : Check solution by finding the times of each - = 5 - 4 = 1 hr; confirms our solutions
 Geometry_Word_Problems/359799: the swimming pool is 12 feet by 20 feet there is a 3 foot wide cement sidewalk all around the pool. what is the outside perimeter of the sidewalk? I think it's 88 feet?1 solutions Answer 256763 by ankor@dixie-net.com(15649)   on 2010-10-21 18:35:44 (Show Source): You can put this solution on YOUR website!the swimming pool is 12 feet by 20 feet there is a 3 foot wide cement sidewalk all around the pool. what is the outside perimeter of the sidewalk? You're right, a 3' sidewalk adds 6' to each dimension
 Expressions-with-variables/359617: For problems 5 and 6, solve the system of equations using SUBSTITUTION to eliminate one variable. If the system has no solution, indicate that is is inconsistent. If it has infinite solutions, indicate that it is dependent. If the system has a solution, CHECK YOUR ANSWER. 5. y=2x 3x+y=20 CHECK (if possible) 6. 4x+2y=6 2x+y=3 CHECK (if possible) I would really really appreciate help with this one because I don't really know what to do. Can someone help me, please?? Thanks so much!! :)1 solutions Answer 256762 by ankor@dixie-net.com(15649)   on 2010-10-21 18:30:17 (Show Source): You can put this solution on YOUR website!For problems 5 and 6, solve the system of equations using SUBSTITUTION to eliminate one variable. If the system has no solution, indicate that is is inconsistent. If it has infinite solutions, indicate that it is dependent. If the system has a solution, CHECK YOUR ANSWER. 5. y = 2x: this means we can substitute 2x for y in the 2nd equation, and find x 3x + y = 20 3x + 2x = 20 5x = 20 x = 4: divided both sides by 5 : We know that y = 2x, therefore y = 2(4) y = 8 : The solution x=4; y=8, : Check this in the 2nd equation 3x + y = 20 Substitute the values for x and y 3(4) + 8 = 20 12 + 8 = 20; equality checks the solutions : : 6. 4x + 2y =6 2x + y = 3 Rearrange this equation to use for substitution in the 1st equation y = -2x + 3; subtracted 2x from both sides : Replace y with (-2x+3)in the 1st equation 4x + 2(-2x+3) = 6 4x - 4x + 6 = 6 4x - 4x = 6 - 6 0 = 0, dependent, an infinite number of solutions
 Travel_Word_Problems/359546: Jim and John drive from point A to point B in separate cars. Jim leaves at 6 am and arrives at 4 pm. John leaves at 10 am and arrives at 3 pm. Assume both men drive at constant speeds. Find when John catches up with Jim1 solutions Answer 256750 by ankor@dixie-net.com(15649)   on 2010-10-21 17:21:59 (Show Source): You can put this solution on YOUR website!Jim and John drive from point A to point B in separate cars. Jim leaves at 6 am and arrives at 4 pm. John leaves at 10 am and arrives at 3 pm. Assume both men drive at constant speeds. Find when John catches up with Jim. : Let d = distance from A to B Jim's travel time: 10 hrs (6am to 4pm) Jon's travel time: 5 hrs (10am to 4pm : Let t = Jon's travel time when he catches Jim Then (t+4) = Jim's travel time when this happens (Jim leave 4 hrs earlier) and we know = Jim's speed and = Jon's speed : When Jon catches Jim, they will have traveled the same distance; Dist = speed * time. (t+4) = *t multiply both sides by 10 to get rid of the denominators, results d(t+4) = 2dt divide both sides by d t + 4 = 2t 4 = 2t - t t = 4 hrs, Jon's travel time then 4 + 4 = 8 hrs; Jim's travel time : 10 am + 4 hrs = 2 pm when Jon overtakes Jim :
 Linear-systems/359544: An electric power company charges its consumers \$ 0.40 per kilowatt for the first 100 kilowatts in a month, \$ 0.50 per kilowatt for the second 100 kilowatts, and \$ 0.60 for each additional kilowatt beyond. Mary pays \$ 120 for electricity used in last month.How much electricity did her family consume in the month?1 solutions Answer 256592 by ankor@dixie-net.com(15649)   on 2010-10-21 09:53:26 (Show Source): You can put this solution on YOUR website!An electric power company charges its consumers \$ 0.40 per kilowatt for the first 100 kilowatts in a month, \$ 0.50 per kilowatt for the second 100 kilowatts, and \$ 0.60 for each additional kilowatt beyond. Mary pays \$ 120 for electricity used in last month. How much electricity did her family consume in the month? : Let x = total no. of kwh used in a month : .6(x-200) + .5(100) + .4(100) = 120 .6x - 120 + 50 + 40 = 120 .6x - 30 = 120 .6x = 120 + 30 .6x = 150 x = x = 250 kwh used : : See if this is true .4(100) = 40 .5(100) = 50 .6(50) = 30 --------------- total\$ = 120 : : Did this make sense to you?
 Quadratic_Equations/359467: A baseball is hit straight upwards with an initial velocity of 72 feet per second and leaves the bat at an initial height of 3 feet. Write a formula, s(t), that models the height of the baseball after t seconds.1 solutions Answer 256587 by ankor@dixie-net.com(15649)   on 2010-10-21 09:39:56 (Show Source): You can put this solution on YOUR website!A baseball is hit straight upwards with an initial velocity of 72 feet per second and leaves the bat at an initial height of 3 feet. Write a formula, s(t), that models the height of the baseball after t seconds. : s(t) = -16t^2 + 72t + 3 Where s(t) = height after t seconds -16t^2 = the downward pull of gravity 72t = initial upward velocity 3 = initial height of the bat :
 Travel_Word_Problems/359367: A motorist travels 90 miles at a rate of 20 miles per hour. If he returns the same distance at an average rate of 40 miles per hour, what is his average speed for the entire trip, in miles per hour?1 solutions Answer 256574 by ankor@dixie-net.com(15649)   on 2010-10-21 09:10:55 (Show Source): You can put this solution on YOUR website!A motorist travels 90 miles at a rate of 20 miles per hour. If he returns the same distance at an average rate of 40 miles per hour, what is his average speed for the entire trip, in miles per hour? : Let a = average speed for the trip : Write a time equation, time = dist/speed : Go time + return time = total time + = : Multiply by 40a to clear the denominators, then solve for a
 Travel_Word_Problems/359378: Hello:) so i have a math problem that i dont quite understand! I dont have my math book so i can't look up how to do the problem. The question is: Marcus and Beth leave college traveling in opposite directions on a straight road. Beth drives 13 miles faster than Marcus. After 4 hours they are 452 miles apart. Find their rates. 1 solutions Answer 256479 by ankor@dixie-net.com(15649)   on 2010-10-20 21:31:02 (Show Source): You can put this solution on YOUR website!Marcus and Beth leave college traveling in opposite directions on a straight road. Beth drives 13 miles faster than Marcus. After 4 hours they are 452 miles apart. Find their rates. Let b = B's driving rate Let m = M's driving rate : Write a distance equation: dist = time * rate : M's dist + B's dist = 452 4m + 4b = 452 : It says,"Beth drives 13 miles faster than Marcus."; the equation for this is: b = (m+13) : Replace b with (m+13) in the 1st equation 4m + 4(m+13) = 452 4m + 4m + 52 = 452 8m = 452 - 52 8m = 400 m = m = 50 mph, then b = 50 + 13 b = 63 mph : : See if that's true 4(50) + 4(63) = 452
 Numbers_Word_Problems/359259: Hi, Hello i am Vanessa my daughter is really having hard time with this and i would like to know what is the answer and how you got it so i could help her learn how to do it.My friend gave me this website just now and she and i dont know it please answer fast. A number has 4 digits. No digits in the number are repeated. The digit in the tens place is three times the digit in the thousands place. The number is odd. The sum of the digits in the number is 27. What is the number?1 solutions Answer 256446 by ankor@dixie-net.com(15649)   on 2010-10-20 20:03:31 (Show Source): You can put this solution on YOUR website!A number has 4 digits. No digits in the number are repeated. The digit in the tens place is three times the digit in the thousands place. The number is odd. The sum of the digits in the number is 27. What is the number? : Let w = the thousands digit Let x = the 100's Let y = the 10's Let z = the units : The digit in the tens place is three times the digit in the thousands place. y = 3w Use some an assumption and some logic here With a total of 27, we have to assume one digit is 9, w has to be less than 4 let y = 9 then w = 3 : So we have: 3 + x + 9 + z = 27 12 + x + z = 27 x + z = 27 - 15 x + z = 15 there are only 2 single digit pairs that add up to 15 6 & 9 7 & 8 we have already used 9 (no repeats), it must be 7 & 8 the last digit has to be odd, therefore we have x = 8 z = 7 : Our number: 3897
 Matrices-and-determiminant/359168: The road from Tedium to Excitement is uphill for 5 miles, level for 4 miles, and then downhill for 6 miles. John Mayer walks from Excitement to Tedium in 4 hours. Later he walks halfway from Tedium to Excitement and back again in 3 hours and 55 minutes. Finally he walks all the way to Excitement from Tedium in 3 hours and 52 minutes. What are his rates going uphill, downhill, and on level ground assuming that these rates remain constant?1 solutions Answer 256442 by ankor@dixie-net.com(15649)   on 2010-10-20 19:39:19 (Show Source): You can put this solution on YOUR website!The road from Tedium to Excitement is uphill for 5 miles, level for 4 miles, and then downhill for 6 miles. John Mayer walks from Excitement to Tedium in 4 hours. Later he walks halfway from Tedium to Excitement and back again in 3 hours and 55 minutes. Finally he walks all the way to Excitement from Tedium in 3 hours and 52 minutes. What are his rates going uphill, downhill, and on level ground assuming that these rates remain constant? : Let u = uphill rate Let f = flat rate Let d = downhill rate : Write a time equation for each statement: Time = dist/rate We are going to do it in minutes, change it to hrs later : "John Mayer walks from Excitement to Tedium in 4 hours." + + = 240 : "he walks halfway from Tedium to Excitement and back again in 3 hours and 55 min." + + = 235 (halfway is 7.5 mi) : "he walks all the way to Excitement from Tedium in 3 hours and 52 minutes." + + = 232 : What are his rates going uphill, downhill, and on level ground assuming that these rates remain constant? : Use elimination on the 1st and 2nd equations + + = 240 + + = 235 -----------------------------------------Subtraction eliminates d - = 5 : Multiply the 1st equation by 6 and the 3rd equation by 5 + + = 1410 + + = 1160 --------------------------------------------------Subtraction eliminates d again + = 250 : Multiply the 1st 2 unknown equation by 10, add to the above equation + = 250 - = 50 ------------------addition eliminates f, find u = 300 u = u = miles per minute, that's * 60 = 3 mph up hill : Use the equation: - = 5 to find f,(were dealing mi/min here) - = 5 20 - = 5 - = 5 - 20 = -15 f = + mi/min, that's * 60 = 4 mph on the flat area : We can use the 1st equation, using hrs, to find d + + = 4 2 + 1 + 5/d = 4 5/d = 4 - 3 5/d = 1 d = 5 mph down hill : Summarize here u = 3 mph uphill f = 4 mph level d = 5 mph down hill : : See if this works int he original 3rd equation, using hrs + + = 3 hr 52 min 1.67 + 1 + 1.2 = 3.87 hrs which is 3 hrs, .87*60 = 52.2 min, close enough
 Age_Word_Problems/359136: Joan's age was a factor of her grandfather's age for 6 consectutive years. What were her grandfather's ages during this time? 1 solutions Answer 256330 by ankor@dixie-net.com(15649)   on 2010-10-20 14:35:03 (Show Source): You can put this solution on YOUR website!Joan's age was a factor of her grandfather's age for 6 consecutive years. What were her grandfather's ages during this time? : Looking at 6 consecutive numbers without a prime number over 60, came up with: gr|Joan ----------- 62| 2 63| 3 64| 4 65| 5 66| 6
 Linear_Algebra/358851: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 11 hours of burning, a candle has a height of 23.4 centimeters. After 30 hours of burning, its height is 12 centimeters. What is the height of the candle after 13 hours?1 solutions Answer 256322 by ankor@dixie-net.com(15649)   on 2010-10-20 14:18:57 (Show Source): You can put this solution on YOUR website!Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 11 hours of burning, a candle has a height of 23.4 centimeters. After 30 hours of burning, its height is 12 centimeters. What is the height of the candle after 13 hours? : Assign the given values as follows: x1 = 11; y1 = 23.4 x2 = 30; y2 = 12 : Find the slope using: m = m = = : Find the equation using the point/slope formula: y - y1 = m(x - x1) y - 23.4 = (x - 11) y - 23.4 = x + y = x + + 23.4 y = x + + 23.4 y = x + + y = x + y = x + 30, is the equation : What is the height of the candle after 13 hours? x = 13 y = (13) + 30 y = + 30 y = -7.8 + 30 y = 22.2 cm after 13 hrs
 Equations/358880: Throwing a wrench. An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The height of the wrench above the ground after t seconds is given by S (t) = -16t^2 – 32t + 128 a) What is the height of the wrench after 1 second? b) How long does it take for the wrench to reach the ground? 1 solutions Answer 256199 by ankor@dixie-net.com(15649)   on 2010-10-20 08:32:22 (Show Source): You can put this solution on YOUR website!worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The height of the wrench above the ground after t seconds is given by S(t) = -16t^2 – 32t + 128 : a) What is the height of the wrench after 1 second? S(t) = the height, t=1; therefore: S(t) = -16(1^2 - 32(1) + 128 S(t) = -16 - 32 + 128 S(t) = 80 ft after one second : b) How long does it take for the wrench to reach the ground? Replace height [S(t)] with ground level, which is 0 -16t^2 - 32t + 128 = 0 Simplify and change the signs, divide equation by -16 t^2 + 2t - 8 = 0 Factor (t+4)(t-2) = 0 The positive solution is all we want here t = 2 seconds for the wrench to reach the ground : : We can prove this: S(t) = -16(2^2) - 32(2) + 128 S(t) = -16(4) - 64 + 128 S(t) = -64 - 64 + 128 S(t) = 0 : : Did this make sense to you now?
 Miscellaneous_Word_Problems/358752: one house can fill a goldfish pond in 84 minutes, and two hoses can fill the same pond in 35 minutes. find how long it takes the second hose alone to fill the pond?1 solutions Answer 256085 by ankor@dixie-net.com(15649)   on 2010-10-19 22:08:52 (Show Source): You can put this solution on YOUR website!one house can fill a goldfish pond in 84 minutes, and two hoses can fill the same pond in 35 minutes. find how long it takes the second hose alone to fill the pond? : Let x = time for the 2nd hose to fill the pond by itself : Let the completed job = 1 (a full pond) : Each hose will do a fraction of the job, the two fractions add up to 1 : + = 1 Multiply by 84x, results 35x + 84(35) = 84x 2940 = 84x - 35x 2940 = 49x x = x = 60 min for the 2nd hose alone, (but that's without the house getting involved)
 Travel_Word_Problems/358579: A zebra can run30 mph. A tiger can run 50 mph.if the tiger has run 70 miles further than the zebra, how many minutes have they been running 1 solutions Answer 256074 by ankor@dixie-net.com(15649)   on 2010-10-19 21:39:08 (Show Source): You can put this solution on YOUR website! A zebra can run 30 mph. A tiger can run 50 mph. If the tiger has run 70 miles further than the zebra, how many minutes have they been running : Let t = no. of hrs they have been running : Let z = no. of miles run by the zebra then (z+70) = no. of miles run by the tiger : Write two distance equations 30t = z and 50t = (z+70) Replace z with 30t 50t = 30t + 70 50t - 30t = 70 20t = 70 t = t = 3.5 hrs but they want it in minutes: 3.5 * 60 = 210 minutes : : Check solution by finding the distances 3.5(50) = 175 mi 3.5(30) = 105 mi ----------------- differs: 70 mi
 Graphs/358676: The function W(d)=0.112d approximates the amount, in centimeters, of water that results from d cm of snow melting. Find the amount of water that results from snow melting from depths of 18cm, 28cm and 95 cm. Can you help me do this problem correctly?1 solutions Answer 256046 by ankor@dixie-net.com(15649)   on 2010-10-19 20:28:42 (Show Source): You can put this solution on YOUR website!The function W(d)=0.112d approximates the amount, in centimeters, of water that results from d cm of snow melting. Find the amount of water that results from snow melting from depths of 18cm, 28cm and 95 cm. : This is not hard, d is the number of cm of snow, W(d) is amt of water it makes : W(d) = .112d Substitute 18 cm for d W(d) = .112*18 W(d) = 2.016 cm of water : Same with d=28cm W(d) = .112d Substitute 28 cm for d W(d) = .112*28 W(d) = 3.136 cm of water : You should be able to find it when d=95 cm now
 Travel_Word_Problems/358588: A cattle train left Miami and traveled toward New York. 14 hours later a diesel train left traveling at 45 km/h in an effort to catch up to the cattle train. After traveling for four hours the diesel train finally caught up. What was the cattle trains average speed?1 solutions Answer 255957 by ankor@dixie-net.com(15649)   on 2010-10-19 16:28:59 (Show Source): You can put this solution on YOUR website!A cattle train left Miami and traveled toward New York. 14 hours later a diesel train left traveling at 45 km/h in an effort to catch up to the cattle train. After traveling for four hours the diesel train finally caught up. What was the cattle trains average speed? : Let s = cattle train speed : The cattle train will be traveling 14 + 4 = 18hrs when the diesel catches up : When the diesel overtakes the cattle, they will have traveled the same distance Write a distance equation; dist = speed * time : Cattle dist = diesel dist 18s = 4*45 18s = 180 s = 10 kmh is the cattle train : Both travel 180 km
 Equations/358316: Solve for r in the formula S = L - rL where S is the sale price, L is the list price, and r is the discount rate.1 solutions Answer 255883 by ankor@dixie-net.com(15649)   on 2010-10-19 13:55:06 (Show Source): You can put this solution on YOUR website!Solve for r in the formula S = L - rL : Factor out L S = L(1 - r) : Divide both sides by L = 1 - r Rearrange r = 1 -
 Human-and-algebraic-language/358073: Twice the small number is 5 more than 2/3 the larger number. Three times the larger number is 4 less than 15 times the smaller number. Find the value of both numbers.1 solutions Answer 255658 by ankor@dixie-net.com(15649)   on 2010-10-18 20:20:31 (Show Source): You can put this solution on YOUR website!Let x = the large number Let y = the small number : Write an equation for each statement: : Twice the small number is 5 more than 2/3 the larger number. 2y = x + 5 Get rid of that annoying fraction, multiply by 3, results: 6y = 2x + 15 -2x + 6y = 15 : Three times the larger number is 4 less than 15 times the smaller number. 3x = 15y - 4 3x - 15y = -4 : Use elimination here, multiply the 1st equation by 3, and the 2nd equation by 2 -6x + 18y = 45 +6x - 20y = -8 -------------------adding eliminates x, find y -12y = 37 y = : Use the 1st equation to find x -2x + 6() = 15 -2x + ) = 15 Multiply by 2 -4x - 37 = 30 -4x = 30 + 37 -4x = 67 x = : A couple nasty fractions, see if they work in the 2nd equation 3x - 15y = -4 Substitute 3() - 15( = -4 + ( = -4 multiply by 12 to get rid of those annoying fractions 3(201) + 555 = -48 -603 + 555 = -48; it does work, amazing isn't it!
 Linear_Algebra/357809: OK, I have spent every waking second trying to figure this out. d=sqrt(2h) I made my height easy, 6 mile, or 30,680 feet. I know R stands for the radius of the Earth which is approximately 3,960 miles. This is what I have come up with...not good, but it's all I have: (r+h)^2=r^2+d^2 simplifying (r+h)^2 i get r^2+2rh+h^2=r^2+d^2 I need to move r^2 to get d^2 alone so I now have 2rh+h^2=d^2 now to get d standing completely alone I have to radical both sides? ([square root]2hr+h^2)=d ?? Then I just plug in my numbers and get it. But i keep coming up with a ridiculous number like...d=47556miles. The closest I have gotten to a reasonable answer is 3,966 miles and thats my total sum of r and h, so i know thats wrong. Ok here's my question. I'm in a plan, 6 miles in the air, what's the distance that I should be able to see the horizon using d=sqrt(2h)? I'm so lost. Please and THANK YOU!!!!1 solutions Answer 255588 by ankor@dixie-net.com(15649)   on 2010-10-18 16:35:02 (Show Source): You can put this solution on YOUR website!the formula for dist to horizon: d = ; h in ft. gives d in miles : So if you are 6 mi high you are 6(5280) 31680 ft high d = d = 251.7 mi so horizon
 Money_Word_Problems/357803: A parking lot is 75 feet wide by 60 feet long. It is being torn up to install a sidewalk of uniform width all the way around. If the area of the new parking lot is 2/3 of the original one, find the width of the sidewalk.1 solutions Answer 255572 by ankor@dixie-net.com(15649)   on 2010-10-18 16:08:27 (Show Source): You can put this solution on YOUR website!A parking lot is 75 feet wide by 60 feet long. It is being torn up to install a sidewalk of uniform width all the way around. If the area of the new parking lot is 2/3 of the original one, find the width of the sidewalk. : Find the original area; 75 * 60 = 4500 sq/ft Find 2/3 of that: * 4500 = 3000 sq/ft, is the new parking lot area : Let x = the width of the sidewalk then the dimensions of new parking lot will be: (75-2x) by (60-2x) : the area equation (75-2x)*(60-2x) = 3000 FOIL 4500 - 150x - 120x + 4x^2 = 3000 A quadratic equation 4x^2 - 270x + 4500 - 3000 = 0 4x^2 - 270x + 1500 = 0 simplify, divide by 2 2x^2 - 135x + 750 = 0 Solve for x using the quadratic formula: In this equation: a=2; b=-135, c=750 : : Two solutions x = x = 61.4; obviously not a good solution and x = x = 6.1 ft is the width of the side walk : : We can check this by finding the area with this value (75-2(6.1)) * (60-2(6.1)) = 62.8 * 47.8 = 30001.84 ~ 3000, close enough
 Travel_Word_Problems/357816: Tom drives 500 miles on the first day. On the second day, he drives twice as long and his average speed is 4/5 of that on the first day. How long does he drive on the second day?1 solutions Answer 255487 by ankor@dixie-net.com(15649)   on 2010-10-18 11:37:47 (Show Source): You can put this solution on YOUR website!om drives 500 miles on the first day. On the second day, he drives twice as long and his average speed is 4/5 of that on the first day. How long does he drive on the second day? : 2(*500) = 800 mi
 Evaluation_Word_Problems/357716: A carpenter makes bookcases in two sizes, large and small. It takes 6 hours to make a large bookcase and 2 hours to make a small bookcase. The profit on a large bookcase is \$50 and the profit on a small bookcase is \$20. The carpenter can only spend 24 hours per week making bookcases and must make at least two of each size per week. .....i need to find the constraints.1 solutions Answer 255486 by ankor@dixie-net.com(15649)   on 2010-10-18 11:24:48 (Show Source): You can put this solution on YOUR website!A carpenter makes bookcases in two sizes, large and small. let a = no. of large bookcases Let b = no. of small : It takes 6 hours to make a large bookcase and 2 hours to make a small bookcase. "The carpenter can only spend 24 hours per week making bookcases" 6a + 2b =< 24 : The profit on a large bookcase is \$50 and the profit on a small bookcase is \$20. p = 50a + 20b : must make at least two of each size per week. a => 2 b => 2
 Evaluation_Word_Problems/357851: A woman with a basket of eggs finds that if she removes the eggs from the basket 3 or 5 at a time, there is always 1 egg left. However, if she removes the eggs 7 at a time, there are no eggs left. If the basket holds up to 100 eggs, how many eggs does she have? Explain your reasoning.1 solutions Answer 255484 by ankor@dixie-net.com(15649)   on 2010-10-18 11:18:55 (Show Source): You can put this solution on YOUR website!A woman with a basket of eggs finds that if she removes the eggs from the basket 3 or 5 at a time, there is always 1 egg left. However, if she removes the eggs 7 at a time, there are no eggs left. If the basket holds up to 100 eggs, : We know that the no. of eggs is a multiple of 7 The units digit is 1 or 6, because of the 5 That leaves 21, 56, 91 the 3 tell us it has to be 91 eggs
 Geometry_Word_Problems/357914: Find the measure of angle that the second hand of an accurate clock rotates in 20 seconds. 1 solutions Answer 255479 by ankor@dixie-net.com(15649)   on 2010-10-18 11:08:41 (Show Source): You can put this solution on YOUR website!Find the measure of angle that the second hand of an accurate clock rotates in 20 seconds. : * 360 = 120 degrees
 Length-and-distance/357774: THE THE HOME BASE OF THE NAVY BLUE ANGELS IS IN PENSACOLA, FLORIDA. tHE ANGELS SPEND THEIR WINTERS IN eL cAENTRO, CALIFORNIA. aSSUME THEY FLY 900 MILES PER HR WHEN THEY FLY FROM PENSACOLA TO EL CENTRO IN THEIR F/A-18 HORNETS. ON EVERY TRIP THEIR C130 TRANSPORT LEAVES BEFORE THEM, CARRYING SUPPLIES AND SUPPORT STAFF. THE C130 TRAVELS AT 370 MILES PER HR. oN A TRIP FROM PENSACOLA TO EL CENTRO HOW LONG BEFORE THE HORNET LEAVES SHOULD C130 LEAVE IF ITS TO ARRIVE 3 HRS BEFORE THE HORNETS? THE FLYING DISTANCE BETWEEN PENASACOLA AND EL CENTRO IS 1720 MILES. 1 solutions Answer 255457 by ankor@dixie-net.com(15649)   on 2010-10-18 10:11:48 (Show Source): You can put this solution on YOUR website!THEY FLY 900 MILES PER HR WHEN THEY FLY FROM PENSACOLA TO EL CENTRO IN THEIR F/A-18 HORNETS. ON EVERY TRIP THEIR C130 TRANSPORT LEAVES BEFORE THEM, CARRYING SUPPLIES AND SUPPORT STAFF. THE C130 TRAVELS AT 370 MILES PER HR. oN A TRIP FROM PENSACOLA TO EL CENTRO HOW LONG BEFORE THE HORNET LEAVES SHOULD the C130 LEAVE IF ITS TO ARRIVE 3 HRS BEFORE THE HORNETS? THE FLYING DISTANCE BETWEEN PENASACOLA AND EL CENTRO IS 1720 MILES. : Let t = time for C130 to arrive 3 hrs before F-18's : Write a time equation, time = dist/speed : t = + 3 - t = 4.64865 + 3 - 1.91111 t = 5.73754 hrs or about 5 hrs 44 min before the F-18's :
 Word_Problems_With_Coins/357564: Please HELP!!!! Peter Parker has a piggy that bank contains only nickels and dimes. The total value of the coins in Pete's bank is \$2.75. If the nickels were dimes and the dimes were nickels, the total value of the coins would be \$3.25. Find the number of nickels in Parker's bank.1 solutions Answer 255357 by ankor@dixie-net.com(15649)   on 2010-10-17 21:17:51 (Show Source): You can put this solution on YOUR website!a piggy that bank contains only nickels and dimes. The total value of the coins in Pete's bank is \$2.75. If the nickels were dimes and the dimes were nickels, the total value of the coins would be \$3.25. Find the number of nickels: : Let n = no. of nickels Let d = no. of dimes : Write an equation for each statement: : "The total value of the coins in Pete's bank is \$2.75." .05n + .10d = 2.75 : "If the nickels were dimes and the dimes were nickels, the total value of the coins would be \$3.25." .10n + .05d = 3.25 : Multiply the above equation by 2, subtract the 1st equation .20n + .10d = 6.50 .05n + .10d = 2.75 -----------------------subtraction eliminates d, find n .15n = 3.75 n = n = 25 nickels : : Check solution: find d using the 1st equation .05(25) + .10d = 2.75 1.25 + .10d = 2.75 .10d = 2.75 - 1.25 .10d = 1.50 d = d = 15 dimes : Find the total using the 2nd equation .10(25) + .05(15) = 2.50 + .75 = 3.25; confirms our solution
 Linear-systems/357470: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 13. What is the original number?1 solutions Answer 255277 by ankor@dixie-net.com(15649)   on 2010-10-17 17:10:04 (Show Source): You can put this solution on YOUR website!When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 13. What is the original number? : x = the 10s digit, y = the units then 10x + y = the original number and 10y + x = the reversed number : Rev number = orig number + 9 10y + x = 10x + y + 9 10y - y = 10x - x + 9 9y = 9x + 9 simplify, divide by 9 y = x + 1 : "the sum of the digits of the original number is 13. " (kind of silly, the sum of the digits is the same original or reversed, right?" anyway x + y = 13 : Rearrange the y = x + 1 and add to the above equation -x + y = 1 +x + y = 13 ------------addition eliminates x, find y 2y = 14 y = 7 : I'll let you find x, and check it in the 1st equation
 Travel_Word_Problems/357468: Maria drove from Chicago, Illinois, to Milwaukee, Wisconsin, a distance of 90 miles, at a mean speed of 65 miles per hour. On her return trip, the traffic was much heavier, and her mean speed was 42 miles per hour. Find Maria's mean speed for the round trip. HINT: Divide the total distance by the total time. (Round the answer to one decimal place.)1 solutions Answer 255263 by ankor@dixie-net.com(15649)   on 2010-10-17 16:16:46 (Show Source): You can put this solution on YOUR website!Maria drove from Chicago, Illinois, to Milwaukee, Wisconsin, a distance of 90 miles, at a mean speed of 65 miles per hour. On her return trip, the traffic was much heavier, and her mean speed was 42 miles per hour. Find Maria's mean speed for the round trip. : Let s = average speed for the round trip : Write a time equation; time = dist/speed : to time + return time = total time + = 1.3846 + 2.1429 = 3.5275 = s = s = 51.0 mph average speed for the round trip
 Quadratic_Equations/357404: Hi Stuck on a particular problem Question Find the values of x for which i) 3x-5>x+13 ii) x^2-4x-12>0 Would appreciate any help1 solutions Answer 255258 by ankor@dixie-net.com(15649)   on 2010-10-17 15:47:03 (Show Source): You can put this solution on YOUR website!i) 3x - 5 > x + 13 Add 5 to both sides, eliminates -5 on the left 3x > x + 13 + 5 Subtract x from both sides 3x - x > 18 2x > 18 divide both sides by 2 x > x > 9 : ii) x^2 - 4x - 12 > 0 Factors to (x-6)(x+2) > 0 x > 6; expression greater than 0 above +6 x < -2; expression is greater than 0 below -2 : Graphically, this can be seen