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 Equations/523114: given that velocity can be described in terms of the acceleration rate and the time period . . . v=at and given that the time period can be described can be described in terms of the distance covered and the acceleration rate . . . t=square root of 2d/a, how would I convert the equation to describe the velocity in terms of distance and acceleration?1 solutions Answer 347221 by ankor@dixie-net.com(15745)   on 2011-10-29 21:51:25 (Show Source): You can put this solution on YOUR website!given that velocity can be described in terms of the acceleration rate and the time period . . . v=at and given that the time period can be described can be described in terms of the distance covered and the acceleration rate . . . t=square root of 2d/a, how would I convert the equation to describe the velocity in terms of distance and acceleration? : v = a*t replace t with v = we can also write it v = cancel a v =
 Polynomials-and-rational-expressions/523083: I am having trouble understanding how to do this problem. (3a-5)cubed I have the answer but don't know how they got it. Can you please help me????? Thanks, Jill1 solutions Answer 347217 by ankor@dixie-net.com(15745)   on 2011-10-29 21:31:26 (Show Source): You can put this solution on YOUR website! which is (3a-5)*(3a-5)*(3a-5) First FOIL (3a-5)(3a-5) 9a^2 - 5a - 5a + 25 9a^2 - 10a + 25 Multiply this by (3a-5), using the old method of multiplying you learned in grade school. 9a^2 - 10a + 25 . . X . . 3a - 5 ---------------- you should get 27a^3 - 75a^2 + 125a - 125
 Travel_Word_Problems/523129: Trais made a business trip of 234 miles. He averaged 54 mph for the first part of the trip and 60 mph for the second part. If the trip took 4 hours, how long did he travel at each rate?1 solutions Answer 347196 by ankor@dixie-net.com(15745)   on 2011-10-29 20:10:24 (Show Source): You can put this solution on YOUR website!a business trip of 234 miles. He averaged 54 mph for the first part of the trip and 60 mph for the second part. If the trip took 4 hours, how long did he travel at each rate? : Let t = travel time at 60 then (4-t) = travel time at 54 : Write a distance equation: dist = speed * time : dist at 60 + dist at 54 = 234 mi 60t + 54(4-t) = 234 60t + 216 - 54t = 234 60t - 54t = 234 - 216 6t = 18 t = 18/6 t = 3 hrs at 60 mph then 4 - 3 = 1 hr at 54 mph : : Check by finding the distance at each speed 3*60 = 180 1*54 = 54 ----------- total: 234 mi
 Circles/523096: A bicycle tire has a diameter of 14 in. How many feet does the bicycle travel when the wheel makes 20 revolutions? Round to the nearest hundredth of a foot.1 solutions Answer 347182 by ankor@dixie-net.com(15745)   on 2011-10-29 15:30:38 (Show Source): You can put this solution on YOUR website!A bicycle tire has a diameter of 14 in. How many feet does the bicycle travel when the wheel makes 20 revolutions? Round to the nearest hundredth of a foot. : d = d = 879.65 ft
 Linear-equations/523082: please could you let me know: determine the equqtion of the line through the given point with the given slope (2,-5) m=1 thank you1 solutions Answer 347181 by ankor@dixie-net.com(15745)   on 2011-10-29 15:27:13 (Show Source): You can put this solution on YOUR website!(2,-5) m=1 Use the point slope format: y - y1 = m(x-x1) In this problem: x1=2, y1=-5, m=1 : y - (-5) = 1(x - 2) y + 5 = 1x - 2 y = x - 2 - 5 y = x - 7 : : Check this, replace x with 2 y = 2 - 7 y = -5
 Travel_Word_Problems/522807: A trip between two cites 175 miles apart take 1.5 hrs less than by bus. The average speed of the bus is 15 miles per hour less than the train. Find the average speeds of the train and the bus.1 solutions Answer 347167 by ankor@dixie-net.com(15745)   on 2011-10-29 10:46:48 (Show Source): You can put this solution on YOUR website!A trip between two cites 175 miles apart take 1.5 hrs less than by bus. The average speed of the bus is 15 miles per hour less than the train. Find the average speeds of the train and the bus. : Let s = speed of the bus then (s+15) = speed of the train : Write a time equation, time = dist/speed : Train time - Bus time = 1.5 hrs - = 1.5 ; multiply by s(s+15) s(s+15)* - s(s+15)* = 1.5s(s+15) : Cancel out the denominators, results: 175(s+15) - 175s = 1.5s^2 + 22.5s 175s + 2625 - 175s = 1.5s^2 + 22.5s : a quadratic equation 0 = 1.5s^2 + 22.5s - 2625 get rid of the decimals, multiply by 2 3s^2 + 45s - 5250 = 0 You can use the quadratic formula here, but this will factor to: (3s-105)(s+50) = 0 positive solution 3s = 105 s = 105/3 s = 35 mph is the speed of the bus, then 35+15 = 50 mph is the speed of the train : : Check this by finding the actual time of each 175/35 = 5.0 hrs 175/50 = 3.5 hrs ----------------- differs: 1.5 hrs
 Numbers_Word_Problems/522973: the difference of digits of two digit number is 1.five times the sum of the number plus one is equal to the number. find the number1 solutions Answer 347160 by ankor@dixie-net.com(15745)   on 2011-10-29 10:19:55 (Show Source): You can put this solution on YOUR website!the difference of digits of two digit number is 1. five times the sum of the number plus one is equal to the number. find the number : Two digits, a, b then 10a + b = the number : "the difference of digits of two digit number is 1." a - b = 1 : "five times the sum of the number plus one is equal to the number." 5(a+b) + 1 = 10a + b 5a + 5b + 1 = 10a + b 5a - 10a + 5b - b = -1 -5a + 4b = -1 : Use substitution here, multiply the 1st equation by 4, add to the 2nd eq +4a - 4b = 4 -5a + 4b = -1 --------------addition eliminates b, find a -a = 3 a = -3 find b -3 - b = 1 -b = 1 + 3 -b = 4 b = -4 : The number -3(10) + (-4) = -34 is the number : : Usually not a neg answer in these problems, see if this works in the statement: "five times the sum of the number plus one is equal to the number." 5(-3 + (-4)) + 1 = -34 5(-7) + 1 = -34 -35 + 1 = -34; confirms our solution of -34
 Travel_Word_Problems/523006: David and Frank cycle from Islamabad to Lahore, a distance of 210 km, at the speeds of 20 km/hr and 15 km/hr. David reaches Lahore and starts back for Islamabad. How far Lahore will he meet Frank?1 solutions Answer 347159 by ankor@dixie-net.com(15745)   on 2011-10-29 09:52:07 (Show Source): You can put this solution on YOUR website!David and Frank cycle from Islamabad to Lahore, a distance of 210 km, at the speeds of 20 km/hr and 15 km/hr. David reaches Lahore and starts back for Islamabad. How far Lahore will he meet Frank? : Find the time for the faster cyclist to arrive at Lahore t = t = 10.5 hr : Find how far Frank is from Lahore in 10.5 hrs d = 210 -(15*10.5) d = 52.5 km from Lahore when David arrives at Lahore : Find the travel time (m) for them to meet from this point write a distance equation, dist = speed * time 15m + 20m = 52.5 35m = 52.5 m = m = 1.5 hrs for them to meet : Find how far from Lahore in 1.5 hrs 1.5*20 = 30 km from Lahore when they meet
 Travel_Word_Problems/523010: A driver on a highway journey of 50 km travels the first 30 km in exactly 20 mnts and completes the rest of the journey at a constant speed of 100 kmph.find the average speed os the driver in first 30 km1 solutions Answer 347157 by ankor@dixie-net.com(15745)   on 2011-10-29 09:23:43 (Show Source): You can put this solution on YOUR website!A driver on a highway journey of 50 km travels the first 30 km in exactly 20 minutes and completes the rest of the journey at a constant speed of 100 kmph. find the average speed of the driver in first 30 km. : Speed = dist/time change 20 min to hr s = s = 30 * 3 s = 90 km/h
 Expressions-with-variables/522607: Subtract. Simplify if possible. (4-y/y-6)-(4y-9)/6-y Please show work so I understand how you arrived at your answer. Thank you.1 solutions Answer 347108 by ankor@dixie-net.com(15745)   on 2011-10-28 21:53:53 (Show Source): You can put this solution on YOUR website!Subtract. Simplify if possible. - : on the 2nd denominator we can factor out -1, to make the denominators the same - : this changes the sign so we have: + : the denominators are the same so we can write it, then combine like terms: = =
 Points-lines-and-rays/522909: which equations that satisfy this fact? A is the midpoint of SM. .S------.A------.M <---- this is supposed to represent a line lol SA = AM SA + AM = SM SM + AM = SA AM + SM = SA Thank you for taking the time to help me out! :) 1 solutions Answer 347105 by ankor@dixie-net.com(15745)   on 2011-10-28 21:41:45 (Show Source): You can put this solution on YOUR website!A is the midpoint of SM. .S------.A------.M <---- this is supposed to represent a line lol SA = AM SA + AM = SM the others don't
 Rate-of-work-word-problems/522803: if it takes 7 people 15 days to do a job, how long will it take 3 people to do the same job.1 solutions Answer 347101 by ankor@dixie-net.com(15745)   on 2011-10-28 21:34:57 (Show Source): You can put this solution on YOUR website!If it takes 7 people 15 days to do a job, how long will it take 3 people to do the same job. : Find the number of man-days to do the job: 7 * 15 = 105 man-days to do the job : Let d = number of days required for 3 men to do the job 3d = 105 d = 105/3 d = 35 days for 3 men to do it.
 Money_Word_Problems/522735: Pete gets paid \$35 per hour to fix the blinking lights at the top of the radio transmission towers, and this week, since there ate no thunderstorms in the forecast, he plans to work 5 hours overtime. By week's end, the government will have taken out \$462 in taxes from his check, leaving him a total of \$1,463. How many hours does pete normally work per week? HELP PLEASSSE! 1 solutions Answer 347097 by ankor@dixie-net.com(15745)   on 2011-10-28 21:15:23 (Show Source): You can put this solution on YOUR website!Pete gets paid \$35 per hour to fix the blinking lights at the top of the radio transmission towers, and this week, since there ate no thunderstorms in the forecast, he plans to work 5 hours overtime. By week's end, the government will have taken out \$462 in taxes from his check, leaving him a total of \$1,463. How many hours does pete normally work per week? : Find his gross, (total made for the week) 1463 + 462 = \$1925 : Assume he gets time & a half for overtime: 1.5*5*35 = \$262.50 for the 5 hrs OT : Let x = normal number of hours worked per week (no overtime) : normal pay = gross - overtime pay 35x = 1925 - 262.50 35x = 1662.50 x = x = 47.5 hrs
 Age_Word_Problems/522324: Use an algebraic approach to solve the problem. (Objective 2) Aura took three biology exams and has an average score of 87. Her second exam score was 7 points better than her first, and her third exam score was 4 points better than her second exam. What were her three exam scores? (lowest score) (highest score) 1 solutions Answer 347093 by ankor@dixie-net.com(15745)   on 2011-10-28 20:54:59 (Show Source): You can put this solution on YOUR website!Aura took three biology exams and has an average score of 87. = 87 a + b + c = 3(87) a + b + c = 261 : Her second exam score was 7 points better than her first, b = a+7 or a = b-7 : and her third exam score was 4 points better than her second exam. c = b+4 : a + b + c = 261 Replace a and c (b-7) + b + (b+4) = 261 3b - 3 = 261 3b = 261 + 3 3b = 264 b = 264/3 b = 88 : You should be able to find a and c now What were her three exam scores? (lowest score)
 Age_Word_Problems/522747: Dear Tutor, I am having a hard time trying to work out this problem. Would you please be so kind as to try and help me. This is the question: John is 3 times younger than his dad's age. The sum of their ages is 79. Find Johns age as a fraction. I tied by saying 79 divide by 3 and got 26 and a third but I would like to know for sure. Thank you for taking the time to help me kind regards Tracey1 solutions Answer 347091 by ankor@dixie-net.com(15745)   on 2011-10-28 20:24:29 (Show Source): You can put this solution on YOUR website!I would do it this way : John is 3 times younger than his dad's age. d = 3j but they want John's age as a fraction, divide both sides by 3 j = d : The sum of their ages is 79. d + j = 79 : replace j with d 1d + d = 79 : 1 1/3 = 4/3, so write it d = 79 : multiply both sides by 3, to get rid of the denominators 4d = 3(79) 4d = 237 d = 237/4 d = 59.25 is Dad's age then j = 59.25 j = 19.75 or 19 yr is John's age : : Check this by finding the sum of their ages 59.25 19.75 ----- 79.00
 real-numbers/522598: Please help solve: 5/z=7/z-1/5 Please show steps you took for completion. Thank you! 1 solutions Answer 347087 by ankor@dixie-net.com(15745)   on 2011-10-28 20:09:35 (Show Source): You can put this solution on YOUR website!solve: subtract 7/z from both sides combine like terms get rid of the negatives, mult both sides by -1 Cross multiply 1z = 2(5) z = 10 : : Check solution in original problem, replace z with 10 1/5 is 2/10
 Travel_Word_Problems/522755: A train when moves at an average speed of 40 kmph reaches it's destination on time. if the average speed becomes 35 kmph, then it reaches the destination 15 minutes late. Find the length of the journey? 1 solutions Answer 347084 by ankor@dixie-net.com(15745)   on 2011-10-28 20:00:25 (Show Source): You can put this solution on YOUR website!A train when moves at an average speed of 40 kmph reaches it's destination on time. if the average speed becomes 35 kmph, then it reaches the destination 15 minutes late. Find the length of the journey? : Let d = the length of the journey : Change 15 min to .25 hr : Write a time equation; time = dist/speed : Slow time - required time = .25 hrs - = .25 multiply by 280, 280* - 280* = 280(.25) cancel the denominators: 8d - 7d = 70 d = 70 km is the length of the journey : : Check this, find the time at each speed 70/35 = 2.00 hr 70/40 = 1.75 hr ---------------- time dif: .25 hrs which is 15 min
 Rate-of-work-word-problems/522873: 6 chairs are made by 8 workers in 12 days. 50 chairs are made by 15 workers in how many days? 1 solutions Answer 347081 by ankor@dixie-net.com(15745)   on 2011-10-28 19:51:52 (Show Source): You can put this solution on YOUR website!6 chairs are made by 8 workers in 12 days. Find no. of man-day required for each chair = 16 man-days per chair : 50 chairs are made by 15 workers in how many days? Let d = no. of days to accomplish this 15d = 50(16) 15d = 800 d = d = 53 days
 Travel_Word_Problems/522570: A person travels by car from one city to another with different constant speeds between the cities. She drives 30 min at 80 km/hr, 12 min at 100 km/hr and 45 min at 40 km/hr. Determine the average speed for the trip and determine the distance between the initial and final cities along the trip.1 solutions Answer 347072 by ankor@dixie-net.com(15745)   on 2011-10-28 18:42:36 (Show Source): You can put this solution on YOUR website!A person travels by car from one city to another with different constant speeds between the cities. She drives 30 min at 80 km/hr, 12 min at 100 km/hr and 45 min at 40 km/hr. Determine the average speed for the trip and determine the distance between the initial and final cities along the trip. : Change minutes to hrs, divide by 60: 30 min = .50 hrs 45 min = .75 hrs 12 min = .20 hrs ---------------- total + 1.45 hrs, total travel time : let a = average speed for the trip : Write a dist equation, dist = speed * time : 80(.5) + 100(.20) + 40(.75) = 1.45a 40 + 20 + 30 = 1.45a 90 = 1.45a a = a = 62.069 km/h, for the entire trip and 90 km is the total distance
 Travel_Word_Problems/522714: two cars are leaving a city, one traveling east and the other traveling west. the car going east is traveling at 66 mph and the cargoing west is traveling at 60 mph. how long before they are 441 miles apart? write an algebraic expression for the distance traveled by the car going east write an algebraic expression for the distance traveled by the car going west write an algebraic expression for the total distance traveled by the two cars write an equation to answer the question 1 solutions Answer 347027 by ankor@dixie-net.com(15745)   on 2011-10-28 15:30:30 (Show Source): You can put this solution on YOUR website!two cars are leaving a city, one traveling east and the other traveling west. the car going east is traveling at 66 mph and the car going west is traveling at 60 mph. how long before they are 441 miles apart? : write an algebraic expression for the distance traveled by the car going east 66t : write an algebraic expression for the distance traveled by the car going west 60t ; write an algebraic expression for the total distance traveled by the two cars 66t + 60t : write an equation to answer the question 66t + 60t = 441 126t = 441 t = t = 3.5 hrs
 Travel_Word_Problems/522686: If a train travels at the speed of 45 km/hr, it is late by 48 minutes. If it travels 50 km/hr it arrives exactly on time. What is distance the train is traveling (in km)?1 solutions Answer 347018 by ankor@dixie-net.com(15745)   on 2011-10-28 15:05:37 (Show Source): You can put this solution on YOUR website!If a train travels at the speed of 45 km/hr, it is late by 48 minutes. If it travels 50 km/hr it arrives exactly on time. What is distance the train is traveling (in km)? : let d = the distance traveled then = the time to arrive on time and = the time to be 48 min late : Convert 48 min: = .8hrs : slower time - ideal time = .8 hrs - = .8 multiply by 450 450* - 450* = 450(.8) cancel the denominators, results: 10d - 9d = 360 d = 360 miles is the distance ; : : Check this by finding the times 360/45 = 8.0 hrs, late 360/50 = 7.2 hrs. on time ----------------- differs: .8 hrs which is 48 min
 Numeric_Fractions/522687: what does 1 1/3 multiplyed by 2/3 is simplest form?1 solutions Answer 347015 by ankor@dixie-net.com(15745)   on 2011-10-28 14:51:30 (Show Source): You can put this solution on YOUR website!what does 1 1/3 multiplyed by 2/3 is simplest form? : Convert 1 1/3 to an improper fraction : * =
 Linear_Equations_And_Systems_Word_Problems/522670: Doreen and Irena plan to leave their houses at the same time, roller blade towards each other, and meet fo rlunch after 4 hours on the road. Doreen can maintain a speed of 7 mph, which is 70% of Irena's speed. If they meet exactly as planned, what is the distance between their houses. 1 solutions Answer 347014 by ankor@dixie-net.com(15745)   on 2011-10-28 14:24:59 (Show Source): You can put this solution on YOUR website!meet for lunch after 4 hours on the road. Doreen can maintain a speed of 7 mph, which is 70% of Irena's speed. If they meet exactly as planned, what is the distance between their houses. : let s = Irene's speed Find d's speed .7s = 7 s = 7/.7 s = 10 mph is Irene's speed : Write a distance equation; dist = speed * time 4(10) + 4(7) = 68 miles
 Rate-of-work-word-problems/522778: A certain tank can be filled by pipe A in 12 minutes. Pipe B can empty the tank in 18 minutes. If both pipes are open, how long will it take to fill or empty the tank?1 solutions Answer 347013 by ankor@dixie-net.com(15745)   on 2011-10-28 14:10:13 (Show Source): You can put this solution on YOUR website!A certain tank can be filled by pipe A in 12 minutes. Pipe B can empty the tank in 18 minutes. If both pipes are open, how long will it take to fill or empty the tank? : It takes less time to fill it than to empty it, therefore with both valves open the tank will be filled eventually : Let t = time to fill the tank with both valves open Let a full tank = 1 - = 1 multiply by 36 36* - 36* = 36(1) Cancel the denominators, results 3t - 2t = 36 t = 36 hrs to fill the tank with both valves left open
 Travel_Word_Problems/522681: A truck driver began driving at 8 am,drove 570 miles,and arrived at his destination at 6 pm. His stops along the route added up to exactly 1 hour. While he was driving, he averaged 65 mph for the first part of the trip and 60 mph for the rest of the trip. How long did he travel at each rate?1 solutions Answer 347011 by ankor@dixie-net.com(15745)   on 2011-10-28 13:58:00 (Show Source): You can put this solution on YOUR website!A truck driver began driving at 8 am,drove 570 miles,and arrived at his destination at 6 pm. His stops along the route added up to exactly 1 hour. While he was driving, he averaged 65 mph for the first part of the trip and 60 mph for the rest of the trip. How long did he travel at each rate? : From the information given, we know the trip took 10 hrs Stops added up to 1 hr, so travel time = 9 hrs : Let t = travel time at 65 mph then (9-t) = travel time at 60 mph : Write a distance equation, dist = speed * time 65t + 60(9-t) = 570 65t + 540 - 60t = 570 65t - 60t = 570 - 540 5t = 30 t = 30/5 t = 6 hrs at 65 mph then 9-6 = 3 hrs at 60 mph : : Check this by finding the dist at each speed 65(6) = 390 60(3) = 180 ----------- total = 570