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 Miscellaneous_Word_Problems/560621: I am trying to simplify this. I don't actually have to solve, just set up in an algebraic expression. Below the problem is the work I did, but it's wrong. I can't figure out why. 1.In a certain triangle the measure of one angle is double the measure of a second angle but is 10 degrees less than the measure of the third angle. [The sum of the measures of three interior angles of a triangle is always 180 degrees.] What is the measure of each angle? 180 = 2x + x + 2x + 10 = 5x + 10 = 180 5x = 170 1 solutions Answer 363980 by ankor@dixie-net.com(15656)   on 2012-01-22 10:59:07 (Show Source): You can put this solution on YOUR website!1.In a certain triangle the measure of one angle is double the measure of a second angle but is 10 degrees less than the measure of the third angle. : Let x = "second angle" : "In a certain triangle the measure of one angle is double the measure of a second angle 2x = "one angle : "but is 10 degrees less than the measure of the third angle. " 2x + 10 = "a third angle : The sum of the 3 angles = 180; your equation seems right to me: 2x + x + (2x+10) = 180; 5x = 180 - 10 5x = 170 x = x = 34 degrees is the 2nd angle the 2(34) = 68 is the "one angle and 76 + 10 = 86 is the third angle : : Check: 68 + 34 + 86 = 180
 Angles/560524: An Angle is 12 degrees less than one half of its supplement. Find the supplement? i need help setting this up. Would it be x + 12 = 1/2(180-x) because i keep getting a decimal on that.1 solutions Answer 363979 by ankor@dixie-net.com(15656)   on 2012-01-22 10:36:19 (Show Source): You can put this solution on YOUR website!An Angle is 12 degrees less than one half of its supplement. : Your equation: x + 12 = 1/2(180-x) is correct to find the angle x x + 12 = 90 - .5x x + .5x = 90 - 12 1.5x = 78 x = x = 52 degrees is the angle : Find the supplement? 180 - 52 = 128 degrees : : We can confirm this 52 + 12 = .5(128) 64 = 64
 Travel_Word_Problems/560442: A cyclist leaves Las Vegas riding at the rate of 18 mph. One hour later, a car leaves Las Vegas going 45 mph in the same direction. How long will it take the car to overtake the cyclist? 1 solutions Answer 363931 by ankor@dixie-net.com(15656)   on 2012-01-21 21:56:18 (Show Source): You can put this solution on YOUR website!A cyclist leaves Las Vegas riding at the rate of 18 mph. One hour later, a car leaves Las Vegas going 45 mph in the same direction. How long will it take the car to overtake the cyclist? : Let t = travel time of the car then (t+1) = travel time of the bike : When car catches bike they will have traveled the same distance A simple distance equation : 45t = 18(t+1)
 Rational-functions/560441: please may you help me find the possible rational zeros of using the rational zero theorem for this problem f(x)=x to the fourth power+ 2x^-241 solutions Answer 363930 by ankor@dixie-net.com(15656)   on 2012-01-21 21:50:48 (Show Source): You can put this solution on YOUR website!f(x)= : = 0 Factors to = 0 Four solutions x = +/- therefore (irrational zeros) x = + x = - and x = +/- therefore (these are the rational zeros) x = +2 x = -2 : The
 �t�e�s�t/560361: Fred cycled from home to his friends house and back again. The distance from Fred's home to his friends house is 20km on his way from home to his friends house fred cycled at Xkm per hour on his way back freds speed had decreased by 2 km per hour it took fred 4 hours altogether to cycle to his friends house and back. Write down an equation for x. THEN SHow that the equation can be written as : x^2 - 12x + 10 = 0 and solve it. All i know is that it needs to be factorised somewhere? But im really unsure.1 solutions Answer 363916 by ankor@dixie-net.com(15656)   on 2012-01-21 20:44:27 (Show Source): You can put this solution on YOUR website!Fred cycled from home to his friends house and back again. The distance from Fred's home to his friends house is 20km on his way from home to his friends house fred cycled at Xkm per hour on his way back freds speed had decreased by 2 km per hour it took fred 4 hours altogether to cycle to his friends house and back. Write down an equation for x. : Let x = from home speed then (x-2) = return home speed : Write a time equation, time = dist/speed : from time + return time = 4 hrs + = 4 multiply by x(x-2) to clear the denominators, results: 20(x-2) + 20x = 4x(x-2) 20x - 40 + 20x = 4x^2 - 8x combine like terms on the right 0 = 4x^2 - 8x - 40x + 40 A quadratic equation 4x^2 - 48x + 40 = 0 simplify, divide by 4 and you have x^2 - 12x + 10 = 0 and solve it. Use the quadratic formula: a=1, b=-12; c=10 Only one solution will make sense, check it in the original time equation
 Travel_Word_Problems/560195: The local train is 25 miles down the track from central station when the express leaves the station. The local train travels at a rate of 50 mi/hr and the express travels at a rate of 80 mi/hr. Let N represent the number of hours since the express train left Central Station. Question 1.) Write at expression that represents the express train's distance from Central Station in N hours. Question 2.) When will the express train catch up with the local train?1 solutions Answer 363849 by ankor@dixie-net.com(15656)   on 2012-01-21 13:09:55 (Show Source): You can put this solution on YOUR website!The local train is 25 miles down the track from central station when the express leaves the station. The local train travels at a rate of 50 mi/hr and the express travels at a rate of 80 mi/hr. Let N represent the number of hours since the express train left Central Station. : Question 1.) Write at expression that represents the express train's distance from Central Station in N hours. 80n : Question 2.) When will the express train catch up with the local train? : When the express catches up with the local, they will have traveled the same distance write a distance equation: dist = = speed * time : 80n = 50(n + ) 80n = 50(n+.5) 80n = 50n + 25 80n - 50n = 25 30n = 25 n = n = hr or 50 minutes to catch up with the local : : Confirm this by finding the actual distances, they should be the same: Local took half hr longer; 8/6 hrs *80 = 66.67 mi *50 = 66,67 mi
 Problems-with-consecutive-odd-even-integers/560158: The first number of three consecutive even integers equals the sum of the second and third. Find the three numbers. If x represents the smallest integer, then which of the following equations could be used to solve the problem?1 solutions Answer 363820 by ankor@dixie-net.com(15656)   on 2012-01-21 10:00:44 (Show Source): You can put this solution on YOUR website!The first number of three consecutive even integers equals the sum of the second and third. Find the three numbers. : x = (x+2) + (x+4) x = 2x + 6 -6 = 2x - x x = -6
 Human-and-algebraic-language/559996: a motorboat has a constant speed of 14 miles per hour relative to the water going upstream for 33 miles and then returning. the total trip time was 7 hours. use this information to find the speed of the current.1 solutions Answer 363769 by ankor@dixie-net.com(15656)   on 2012-01-20 21:39:23 (Show Source): You can put this solution on YOUR website!a motorboat has a constant speed of 14 miles per hour relative to the water going upstream for 33 miles and then returning. the total trip time was 7 hours. use this information to find the speed of the current. : Let c = the rate of the current then (14-c) = effective speed upstream (in relation to the land) and (14+c) = effective speed downstream : Write a time equation; time = dist/speed : Time upstr + time downstr = 7 hrs + = 7 ; Multiply by (14-c)(14+c), results: 33(14+c) + 33(14-c) = 7(14-c)(14+c) : 462 + 33c + 462 - 33c = 7(196-c^2) : 924 = 1372 - 7c^2 : 7c^2 = 1372 - 924 : 7c^2 = 448 : c^2 = c^2 = 64 c = c = 8 mph is the speed of the current : : See if this checks out. Find the actual time of each trip. 33/(14-8) = 5.5 hrs 33/(14+8) = 1.5 hrs ------------------ total time: 7.0 hrs
 Average/560178: Say I have an 87.5 the first quarter and a 76.3 the second quarter and I got a 68 on my final exam which is worth 1/9th of my final grade, what would my final grade be?1 solutions Answer 363757 by ankor@dixie-net.com(15656)   on 2012-01-20 20:31:10 (Show Source): You can put this solution on YOUR website!Say I have an 87.5 the first quarter and a 76.3 the second quarter and I got a 68 on my final exam which is worth 1/9th of my final grade, what would my final grade be? : = = = 80.4
 Quadratic_Equations/560125: During the first part of a trip, a canoeist travels 34 miles at a certain speed. The canoeist travels 9 miles on the second part of the trip at a speed 5mph slower. The total time for the trip is 5hrs. What was the speed on each part of the trip? Type an integer or decimal and round to the nearest hundredth. 1 solutions Answer 363717 by ankor@dixie-net.com(15656)   on 2012-01-20 18:16:01 (Show Source): You can put this solution on YOUR website!During the first part of a trip, a canoeist travels 34 miles at a certain speed. The canoeist travels 9 miles on the second part of the trip at a speed 5mph slower. The total time for the trip is 5hrs. What was the speed on each part of the trip? : Let s = the speed on the 1st 34 mi then (s-5) = speed on the last 9 mi : Write a time equation, time = dist/speed : fast time + slow time = 5 hrs + = 5 multiply by s(s-5), results: 34(s-5) + 9s = 5s(s-5) 34s - 170 + 9s = 5s^2 - 25s 43s - 170 = 5s^2 - 25s 0 = 5s^2 - 25s - 43s + 170 A quadratic equation\ 5s^2 - 68s + 170 = 0 use the quadratic formula to find s: In this problem x=s; a=5; b=-68; c=170 : : I'll let you do the rest of the math here you will get two positive solutions, but only one will make sense Check it in the original time equation
 Money_Word_Problems/560131: I have story problems I have to get an equation for and solve. I try to draw out tables to help me figure out the equations but I have a rough time finding the right spot to put everything in. Can you help me? Here is the problem: A certain sum of money is invested at 6.35%, and \$4000 more than that amount is invested at 7.28%. If the annual interest from the two investments is \$972.70, how much was invested at 6.35%? My table I made using the formula I=P*R*T I = P * R * T INVEST 1 635X X 635 1 INVEST 2 728(4000-X) 4000-X 1 TOTAL 972.70 4000 Can you please explain what I did wrong and how to do it right and show me what the equation is? Thanks!! :) 1 solutions Answer 363703 by ankor@dixie-net.com(15656)   on 2012-01-20 17:09:02 (Show Source): You can put this solution on YOUR website!A certain sum of money is invested at 6.35%, and \$4000 more than that amount is invested at 7.28%. If the annual interest from the two investments is \$972.70, how much was invested at 6.35%? : Let's do it this way Let x = amt invested at 6.35% then it says,"\$4000 more than that amount, is invested at 7.28%." therefore (x+4000) = amt invested at 7.28% ; .0635x + .0728(x+4000) = 972.70; this is the equation you want .0635x + .0728x + 291.20 = 972.70 .0635x + .0728x = 972.70 - 291.20 .1363x = 681.50 x = x = \$5000 invested at 6.35% ; : Check the solution by finding the amt invested on each one .0635*5000 = 317.50 .0728*9000 = 655.20 =================== total int: = 972.70
 Geometry_Word_Problems/560080: A circular pool has a radius of 15 feet. It needs fencing that is 5 feet away at all points. What is the circumference of the fencing that will be need?1 solutions Answer 363696 by ankor@dixie-net.com(15656)   on 2012-01-20 16:42:57 (Show Source): You can put this solution on YOUR website!A circular pool has a radius of 15 feet. It needs fencing that is 5 feet away at all points. What is the circumference of the fencing that will be need? : This will increase the radius by 5ft and the diameter by 10 ft C = C = 78.54 ft
 logarithm/560081: The half-life of 234U, uranium-234, is 2.52 multiplied by 105 yr. If 97.9% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed? 1 solutions Answer 363680 by ankor@dixie-net.com(15656)   on 2012-01-20 15:45:33 (Show Source): You can put this solution on YOUR website!The half-life of 234U, uranium-234, is 2.52 multiplied by 105 yr. If 97.9% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed? : Assume you mean the half-life uranium 234 is 2.52(10^5) yrs : The radioactive decay formula: A = Ao*2^(-t/h), where A = resulting amt after t yrs Ao = initial amt, t=0 h = half-life of substance t = time : Assuming initial amt = 1 2^(-t/2.52(10^5) = .979 we will use nat logs *ln(2) = ln(.979) ; = ; = -.03062 : t = : t = 7,716 ~ 8,000 yrs
 Geometry_Word_Problems/559882: Two runners are to race one lap on a circular track.The radius to the inside lane is 40m. the radius to the outside lane is 41m. How much of a head start should the outside runner be given.1 solutions Answer 363672 by ankor@dixie-net.com(15656)   on 2012-01-20 15:18:56 (Show Source): You can put this solution on YOUR website!Two runners are to race one lap on a circular track.The radius to the inside lane is 40m. the radius to the outside lane is 41m. How much of a head start should the outside runner be given. : Find the circumference of each : = 257.6 = 251.3 ------------------- difference of: 6.3 head start
 Angles/559791: two angels are complementary. The sum measures of the first angel and half of the second angel is 64 degrees. find the measurments of angels.1 solutions Answer 363666 by ankor@dixie-net.com(15656)   on 2012-01-20 14:59:12 (Show Source): You can put this solution on YOUR website!two angels are complementary. A + B = 90 The sum measures of the first angel and half of the second angel is 64 degrees. A + .5B = 64 : Subtract the 2nd eq from the 1st eq: A + B = 90 A +.5B =64 ------------subtraction eliminates A, find B .5B = 26 B = 2*26 B = 52 degrees then A = 90 - 52 A = 38 degrees : : Check this 38 + .5(52) = 64
 Expressions-with-variables/559810: how do I solve for y if 1/3(y+3)+1/4(y+1)=31 solutions Answer 363649 by ankor@dixie-net.com(15656)   on 2012-01-20 13:40:07 (Show Source): You can put this solution on YOUR website!how do I solve for y if 1/3(y+3)+1/4(y+1)=3 : (y+3)+(y+1) = 3 get rid of the denominators, multiply by 12, results: 4(y+3) + 3(y+1) = 12(3) : 4y + 12 + 3y + 3 = 36 7y + 15 = 36 7y = 36 - 15 7y = 21 y = 21/7 y = 3 : : Check this by replacing y with 3 in the original equation
 Complex_Numbers/560058: Corrosion in the metal surface of an airplane can be difficult to detect visually. One test used to locate it involves passing an alternating current through a small area on the plane’s surface. If the current varies from one region to another, it may indicate that corrosion is occurring. The impedance Z (or opposition to the flow of electricity) of the metal is related to the voltage V and current I by the equation, where Z, V, and I are complex numbers. Calculate Z for the given values of V and I. V=10+20i I=3+7i 1 solutions Answer 363648 by ankor@dixie-net.com(15656)   on 2012-01-20 13:32:41 (Show Source): You can put this solution on YOUR website! The impedance Z (or opposition to the flow of electricity) of the metal is related to the voltage V and current I by the equation, where Z, V, and I are complex numbers. Calculate Z for the given values of V and I. V=10+20i I=3+7i : Z = V/I : Z = : multiply by the conjugate of the denominator over itself Z = * = = = =
 Travel_Word_Problems/560048: The distance from the Earth to the Moon is approximately 240,000 miles. If a rocket travels at a speed of 7.50 km/sec, it will take __________ days to travel between the Earth and Moon. 1 solutions Answer 363646 by ankor@dixie-net.com(15656)   on 2012-01-20 13:06:22 (Show Source): You can put this solution on YOUR website!The distance from the Earth to the Moon is approximately 240,000 miles. If a rocket travels at a speed of 7.50 km/sec, it will take __________ days to travel between the Earth and Moon. : Change 240,000 mi to km: 1.609 * 240000 = 386,160 km : Find the no. of sec in one day: 3600 * 24 = 86,400 sec in one day : = .596 days (14.3 hrs)
 Travel_Word_Problems/560030: An alien rocketship is traveling at a speed of 0.029 miles per second. At this speed, how many feet will it travel in 1 hour? Round to the nearest thousandth.1 solutions Answer 363645 by ankor@dixie-net.com(15656)   on 2012-01-20 12:56:14 (Show Source): You can put this solution on YOUR website!An alien rocketship is traveling at a speed of 0.029 miles per second. At this speed, how many feet will it travel in 1 hour? Round to the nearest thousandth. : There are 3600 sec in 1 hr, 5280 ft in 1 mile, therefore: : 3600 * .029 * 5280 = 551,232 ft in 1 hr
 Travel_Word_Problems/559895: A slow goods train starts from each city at 12.25 pm. One train travels at a constant speed of 60 km per hour and the other at 40 kilometres an hour. At what time (after passing one another) will they be 40 kilometres apart?1 solutions Answer 363643 by ankor@dixie-net.com(15656)   on 2012-01-20 12:51:05 (Show Source): You can put this solution on YOUR website!A slow goods train starts from each city at 12.25 pm. One train travels at a constant speed of 60 km per hour and the other at 40 kilometres an hour. At what time (after passing one another) will they be 40 kilometres apart? : I think we have to know how far apart the cities are.