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 Polynomials-and-rational-expressions/587727: I was wondering if (-13g^2h^5k^2)^0 would be -13g^2h^5k^2 or would it be something else. Can you please explain your answer. Thanks1 solutions Answer 374268 by ankor@dixie-net.com(15664)   on 2012-03-16 18:49:16 (Show Source): You can put this solution on YOUR website!I was wondering if (-13g^2h^5k^2)^0 would be -13g^2h^5k^2 or would it be something else. Can you please explain your answer. : Any expression or term that has an exponent of 0, is equal to 1
 Travel_Word_Problems/587782: A bicycle's wheel has a radius of 325 mm. what distance (in km)will the bicycle travel if the wheel turns 100,000 times? Please help!(: remember, this is a circle problem!1 solutions Answer 374266 by ankor@dixie-net.com(15664)   on 2012-03-16 18:41:47 (Show Source): You can put this solution on YOUR website!A bicycle's wheel has a radius of 325 mm. what distance (in km)will the bicycle travel if the wheel turns 100,000 times? : Change 325 mm to .325 meters : Mult the circumference by 100000 revolutions, divide by 1000 to get km = 204.2 km
 real-numbers/587737: what is the solution to the equation 2/3X + 1/6 = 1?1 solutions Answer 374265 by ankor@dixie-net.com(15664)   on 2012-03-16 18:24:59 (Show Source): You can put this solution on YOUR website!what is the solution to the equation X + = 1 Multiply by 6 to get rid of the denominators 6*X + 6* = 6*1 cancel out the denominators 2(2x) + 1 = 6 4x = 6 - 1 4x = 5 x = x = 1.25
 Travel_Word_Problems/587842: A rectangular plot measures 12m by 5m.A path of width constant width runs along one side and one end.if the total area of the plot and path is physics 120m find the width of the path.1 solutions Answer 374258 by ankor@dixie-net.com(15664)   on 2012-03-16 17:42:12 (Show Source): You can put this solution on YOUR website!A rectangular plot measures 12m by 5m. A path of width constant width runs along one side and one end. if the total area of the plot and path is physics 120m find the width of the path. : Let x = the width of the path with a path on one side and one end the overall dimensions will be: (x+12) by (x+5) : Area: (x+12)*(x+5) = 120 FOIL x^2 + 5x + 12x + 60 = 120 x^2 + 17x + 60 - 120 = 0 x^2 + 17x - 60 = 0 Factors to (x+20)(x-3) = 0 Positive solution x = 3 meters is the width of the path ;
 Travel_Word_Problems/587725: It took 4 seconds to travel 384 m. What is the average speed?1 solutions Answer 374255 by ankor@dixie-net.com(15664)   on 2012-03-16 17:35:24 (Show Source): You can put this solution on YOUR website!It took 4 seconds to travel 384 m. What is the average speed? : find the no. of meters traveled in 1 sec find how far in 1 hr (3600 sec) Convert to km/hr * = 345.6 km/hr
 Coordinate-system/587724: How do I solve for y with M=1/2 and b=3 using y=mx+b1 solutions Answer 374251 by ankor@dixie-net.com(15664)   on 2012-03-16 16:55:20 (Show Source): You can put this solution on YOUR website!How do I solve for y with M=1/2 and b=3 using y=mx+b : Just replace m with 1/2 and replace b with 3 y = x + 3
 Travel_Word_Problems/587747: jake is on a 24-mile bike trip. He wants to average 10 miles per hour. He is halfway to his distination and has averaged 8 miles per hour. What must his average speed be on the last part to complete on time1 solutions Answer 374250 by ankor@dixie-net.com(15664)   on 2012-03-16 16:46:36 (Show Source): You can put this solution on YOUR website!Jake is on a 24-mile bike trip. He wants to average 10 miles per hour. He is halfway to his destination and has averaged 8 miles per hour. What must his average speed be on the last part to complete on time ; Let s = the required speed to average 10 mph for the trip : write a time equation, time = dist/speed : + = Multiply by 40s 40s* + 40s* = 40s* cancel the denominators 5s(12) + 40(12) = 4s(24) 60s + 480 = 96s 480 = 96s - 60s 480 = 36s s = 480/36 s = 13 mph on the last half of the trip : : Check, find the times. + = 1.5 + .9 = 2.4
 Equations/587583: Could someone please help me with this problem? 3x - 2(x-4)= 5x + 81 solutions Answer 374195 by ankor@dixie-net.com(15664)   on 2012-03-16 10:03:35 (Show Source): You can put this solution on YOUR website!3x - 2(x-4)= 5x + 8 This is not going be solved, multiply what's inside the brackets (distribute) 3x - 2x + 8 = 5x + 8 subtract 8 from both sides x = 5x + 8 - 8 x = 5x, obviously makes no sense,
 Radicals/587572: 10r2+20r-88=-8 Could not figure out how to factor this radical out. Is it possible to have no solution?1 solutions Answer 374178 by ankor@dixie-net.com(15664)   on 2012-03-16 07:21:55 (Show Source): You can put this solution on YOUR website!10r2+20r-88=-8 : 10r^2 + 20r - 88 + 8 = 0 10r^2 + 20r - 80 = 0 simplify, divide both sides by 10 r^2 + 2r - 8 = 0 Factors easily to (r+4)(r-2) = 0 Two solutions r = -4 r = 2 : : Check solutions in original equation r= -4 10(-4^2) + 20(-4) - 88 = -8 10(16) - 80 - 88 = -8 : You can check the r=2 solution
 Miscellaneous_Word_Problems/587424: For most flying creatures, the length of the wing varies inversely as the number of wingbeats per second. A dragonfly has a winglength of 1.6 inches and a wingspeed of 45 times per second. If a bee has a wingspeed of 200 beats per second, what is the length of a bee's wing?1 solutions Answer 374159 by ankor@dixie-net.com(15664)   on 2012-03-15 21:53:30 (Show Source): You can put this solution on YOUR website!For most flying creatures, the length of the wing varies inversely as the number of wingbeats per second. A dragonfly has a winglength of 1.6 inches and a wingspeed of 45 times per second. If a bee has a wingspeed of 200 beats per second, what is the length of a bee's wing? : = ; varies inversely Cross multiply 200b = 1.6 * 45 200b = 72 b = b = .36 inch is the bee's wing
 Travel_Word_Problems/587417: Eddie is flying a jet against the wind on a 330 mile trip. Flying with the same wind speed, Eddie could fly a 550 mile trip in the same amount of time. If Eddie's jet flies 220 miles per hour in still air, what is the speed of the wind? Solve problem algebraically please...1 solutions Answer 374154 by ankor@dixie-net.com(15664)   on 2012-03-15 19:58:28 (Show Source): You can put this solution on YOUR website!Eddie is flying a jet against the wind on a 330 mile trip. Flying with the same wind speed, Eddie could fly a 550 mile trip in the same amount of time. If Eddie's jet flies 220 miles per hour in still air, what is the speed of the wind? : Let w = speed of the wind then (220+w) = effective speed with the wind and (220-w) = effective speed against the wind : Write a time equation: time = dist/speed : = Cross multiply 330(220+w) = 550(220-w) 72600 + 330w = 121000 - 550w 330w + 550w = 121000 - 72600 880w = 48400 w = w = 55 mph is the wind ; : Check this by finding the times, they should be equal 550/275 = 2 hrs 330/165 = 2 hrs
 Polynomials-and-rational-expressions/587153: Please help me solve this problem: If the area of a rectangle is given by 81g^2 - 180gw + 100w^2 square feet, what are possible expressions for the length and width?1 solutions Answer 374037 by ankor@dixie-net.com(15664)   on 2012-03-15 08:19:11 (Show Source): You can put this solution on YOUR website!If the area of a rectangle is given by 81g^2 - 180gw + 100w^2 square feet : You should recognize this is a perfect square; (9g-10w)(9g-10w), therefore The rectangle could be a square (9g-10w) on each side
 Quadratic_Equations/587211: use the height as a function of time in motion equation: h(t) = -16t squared + vt + c A baseball player hits a pitched ball when it is 4 ft above ground. The initial upward velocity is 80 ft/sec. How long will it take for the ball to hit the ground?1 solutions Answer 374032 by ankor@dixie-net.com(15664)   on 2012-03-15 07:33:47 (Show Source): You can put this solution on YOUR website!use the height as a function of time in motion equation: h(t) = -16t squared + vt + c A baseball player hits a pitched ball when it is 4 ft above ground. The initial upward velocity is 80 ft/sec. How long will it take for the ball to hit the ground? : h(t) = -16t^2 + vt + c from the information given we know v = 80 c = 4 : h(t) = -16t^2 + 80t + 4 When the ball hits the ground we have h(t) = 0, therefore: -16t^2 + 80t + 4 = 0 simplify divide by -4 4t^2 - 20t - 1 = 0 Use the quadratic formula to find t x = t; b=-20, c=-1 Do the math, the positive solution t = 5.0495 seconds : You should check this in the original problem
 Rate-of-work-word-problems/587005: Jane takes 4 hours to do a job that Alice can do in 3 hours. If Jane works 1/2 hour before Alice joins her, how long will it take the two of them to finish the job?1 solutions Answer 373972 by ankor@dixie-net.com(15664)   on 2012-03-14 21:39:30 (Show Source): You can put this solution on YOUR website!Jane takes 4 hours to do a job that Alice can do in 3 hours. If Jane works 1/2 hour before Alice joins her, how long will it take the two of them to finish the job? : Let t = time required to finish the job together then (t+.5) = total time worked by Jane : Let the completed job = 1 : Each girl will do a fraction of the job, the two fractions add up to 1 + = 1 multiply by 12 12* + 12* = 12 Cancel the denominators 4t + 3(t+.5) = 12 3t + 4t + 1.5 = 12 7t = 12 - 1.5 7t = 10.5 t = t = 1.5 hrs to finish the job together : : Check (J works 2 hrs) + = 1 .5 + .5 = 1
 Travel_Word_Problems/586678: Andrew rode 14 miles on his bike in 1 hour 45 minutes what is Andrews average speed?1 solutions Answer 373898 by ankor@dixie-net.com(15664)   on 2012-03-14 13:02:50 (Show Source): You can put this solution on YOUR website!Andrew rode 14 miles on his bike in 1 hour 45 minutes what is Andrews average speed? : Speed = dist/time : change 1 hr 45 min to 1.75 hrs : = 8 mph : : Check this by finding the dist: 8 * 1.75 = 14
 Linear-systems/586667: 1: twice the numerator of a fraction exceeds the denominator by 2. if 1 is added to both the numerator and the denominator, the resulting fraction is equal to 2/3. find the orginal fraction1 solutions Answer 373894 by ankor@dixie-net.com(15664)   on 2012-03-14 12:50:21 (Show Source): You can put this solution on YOUR website!1: twice the numerator of a fraction exceeds the denominator by 2. if 1 is added to both the numerator and the denominator, the resulting fraction is equal to 2/3. find the original fraction. : Write an equation for each statement : "twice the numerator of a fraction exceeds the denominator by 2" 2n = d + 2 or d = (2n-2) : "if 1 is added to both the numerator and the denominator, the resulting fraction is equal to 2/3" = Cross multiply 2(d+1) = 3(n+1) 2d + 2 = 3n + 3 2d = 3n + 3 - 2 2d = 3n + 1 Replace d with (2n-2) 2(2n-2) = 3n + 1 4n - 4 = 3n + 1 4n - 3n = 1 + 4 n = 5 is the numerator and d = 2(5) - 2 d = 8 is the denominator : is the original fraction : : Check this; add 1 to the the numerator and the denominator reduces to
 test/586564: I need help on this problem please help: You are solving ax^2+bx+c=0(where a doesn't=0) by completing the square as shown below. How should you proceed to step 3? Step 1- ax^2+bx=-c Step 2- x^2+b/a x=-c/a. Thank you!1 solutions Answer 373869 by ankor@dixie-net.com(15664)   on 2012-03-14 09:48:06 (Show Source): You can put this solution on YOUR website!How should you proceed to step 3? Step 1- ax^2 + bx =-c Step 2- x^2 + b/a x =-c/a Find the 3rd term to complete the square, half the coefficient of x, squared Step 3: x^2 + (b/a)x + (b/2a)^2 = -c/a + (b/2a)^2
 Rate-of-work-word-problems/586466: if 6 roofers take 2 days to put on a new roof, how long would it take 4 roofers to do the same job, assuming they each work at the same rate?1 solutions Answer 373817 by ankor@dixie-net.com(15664)   on 2012-03-13 21:57:41 (Show Source): You can put this solution on YOUR website!if 6 roofers take 2 days to put on a new roof, how long would it take 4 roofers to do the same job, assuming they each work at the same rate? : Find the number of man-days to do the job 6 * 2 = 12 man-days : "how long would it take 4 roofers to do the same job," let d = no. of days for 4 men to do it 4d = 12 d = 12/4 d = 3 days
 Travel_Word_Problems/586589: A motorcycle traveling at 60mph overtakes a car traveling at 30mph that had a three-hour head start. How far from the starting point are the two vehicles? How do I put this into an algebraic equation and solve it? Thanks1 solutions Answer 373815 by ankor@dixie-net.com(15664)   on 2012-03-13 21:51:12 (Show Source): You can put this solution on YOUR website!A motorcycle traveling at 60mph overtakes a car traveling at 30mph that had a three-hour head start. How far from the starting point are the two vehicles? How do I put this into an algebraic equation and solve it? : Let t = travel time of motorcycle then (t+3) = travel time of the car : Write a distance equation, dist = speed * time 60t = 30(t+3) 60t = 30t + 90 60t - 30t = 90 t = 90/30 t = 3 hrs for the motorcycle to overtake the car ; Find this dist: 3 * 60 = 180 mi Check the dist: 6 * 30 = 180 mi
 Exponential-and-logarithmic-functions/586189: 4e^x+2=32 ln(5x-3)^1/3=2 2x^(3x-2)+4=16 2e^(x-2)=e^x+7 1/3lnx+ln2-ln3=3 ln(x+2)-ln4=3 Hello. Thank you for your time. I have a test and Im practicing on these problems, but I keep getting something wrong. Can you work them out please? Thank you sooo much!!! =)1 solutions Answer 373811 by ankor@dixie-net.com(15664)   on 2012-03-13 21:44:12 (Show Source): You can put this solution on YOUR website!4e^x + 2 = 32 4e^x = 32 - 2 4e^x = /4 e^x = 7.5 use nat logs here ln(e^x) = ln(7.5) the log equiv of exponents x*ln(e) = ln(7.5) ln of e is 1 therefore x = ln(7.5} x = 2.015 : : ln(5x-3)^1/3 = 2 Cube both sides ln(5x-3) = 2^3 ln(5x-3) = 8 find the anti-log of both sides () 5x - 3 = 2981 5x = 2981 + 3 x = 2984/5 x = 596.8 : : 2x^(3x-2) + 4 = 16 2x^(3x-2) = 16 - 4 2x^(3x-2) = 12 x^(3x-2) = 12/2 x^(3x-2) = 6 use common logs log(x^(3x-2)) = log(6) (3x-2)log(x) = .778 log(x) = That's about all I can do with this : : 2e^(x-2) = e^x + 7 2e^(x-2) - e^x = 7 I don't think there is a solution here : : ln(x) + ln(2) - ln(3) = 3 ln(x^(1/3)) + ln(2) - ln(3) = 3 combine as a single log : = 3 find the antilog (e^10) of 3, gets rid of ln = 20.0855 : = 3(20.0855) : = 60.2566 : = ; = 30.1283 Cube both sides: x = 30.1283^3 x ~ 27348
 Travel_Word_Problems/586561: What is the speed of a car traveling 144 km in 90 minutes in kilometers per hour1 solutions Answer 373799 by ankor@dixie-net.com(15664)   on 2012-03-13 21:08:15 (Show Source): You can put this solution on YOUR website!What is the speed of a car traveling 144 km in 90 minutes in kilometers per hour : Speed = dist/time change 90 min to 1.5 hr s = s = 96 km/hr
 Numbers_Word_Problems/586293: Bill, Joe & Cindy each have money. Together Bill and Joe have \$18. Together Joe and Cindy have \$21. Finally, together Bill and Cindy have a total of \$23. How much money does each individual have?1 solutions Answer 373798 by ankor@dixie-net.com(15664)   on 2012-03-13 21:05:21 (Show Source): You can put this solution on YOUR website!Bill, Joe & Cindy each have money. Together Bill and Joe have \$18. b + j = 18 : Together Joe and Cindy have \$21. j + c = 21 j = (21-c) : together Bill and Cindy have a total of \$23. b + c = 23 b = (23-c) ; How much money does each individual have? Replace b and j in the 1st equation (23-c) + (21-c) = 18 -2c + 44 = 18 44 - 18 = 2c 26 = 3c c = 26/2 c = 13 then j = 21 - 13 j = 8 and b = 23 - 13 b = 10
 Rate-of-work-word-problems/586059: Together Leonard and Donte can do a job in 4 hours and 16 minutes. If it takes Leonard 8 hours to do the job alone how long would it take Donte to do the job alone ?1 solutions Answer 373655 by ankor@dixie-net.com(15664)   on 2012-03-13 08:46:06 (Show Source): You can put this solution on YOUR website! Together Leonard and Donte can do a job in 4 hours and 16 minutes. If it takes Leonard 8 hours to do the job alone how long would it take Donte to do the job alone ? : Let d = time required by D to do the job alone Let the completed job = 1 : Do the problem in minutes 4 hr 16 min = 256 min 8 hrs = 480 min : + = 1 multiply by 480d 480d* + 480d* = 480d Cancel the denominators 256d + 480(256) = 480d 122880 = 480d - 256d 122880 = 224d d = d = 548.57 minutes converts to 9 hrs 8.57 min
 Travel_Word_Problems/585804: an airplane is traveling 550 miles per hour. It is carrying 80 passengers. How many miles per minute? How many feet per second? How many passenger-miles on a 400 mile trip? How many passenger-miles per minute?1 solutions Answer 373624 by ankor@dixie-net.com(15664)   on 2012-03-12 21:31:00 (Show Source): You can put this solution on YOUR website!an airplane is traveling 550 miles per hour. It is carrying 80 passengers. : How many miles per minute? = 9.167 mi/min : How many feet per second? = 806.67 ft/sec : How many passenger-miles on a 400 mile trip? 80 * 400 = 32000 pass-mi : How many passenger-miles per minute? find the no. of minutes to make the trip: * 60 = 43.64 minutes = 738 pass-mi/min
 Age_Word_Problems/585809: The average weight of a group of 10 people increases by 1 kg when one of them weighing 58kgs is replaced by a new person. The weight of the new person is : 1 solutions Answer 373587 by ankor@dixie-net.com(15664)   on 2012-03-12 19:45:17 (Show Source): You can put this solution on YOUR website!The average weight of a group of 10 people increases by 1 kg when one of them weighing 58kgs is replaced by a new person. The weight of the new person is: : Let x = the total weight of the 9 people that remain the same Let y = weight of the new person : New group av - Old group av = 1 - = 1 mult by 10, gets rid of the denominators (x + y) - (x + 58) = 10 Remove the brackets x + y - x - 58 = 10 x - x + y = 10 + 58 y = 68 lb is the weight of the new guy
 Numbers_Word_Problems/585951: How old is Fatma now if her age in seven years is one more than twice her age five years ago1 solutions Answer 373574 by ankor@dixie-net.com(15664)   on 2012-03-12 19:15:59 (Show Source): You can put this solution on YOUR website!How old is Fatma now if her age in seven years is one more than twice her age five years ago : Let f = F's age now : f + 7 = 2(f-5) + 1 f + 7 = 2f - 10 + 1 f + 7 = 2f - 9 7 + 9 = 2f - f f = 16 yrs now : : Check this 16 + 7 = 2(16-5) + 1 23 = 2(11) + 1
 Polynomials-and-rational-expressions/585833: I need help on how do I work this problem out m^2-10m+25 a line underneath the problem and underneath the line m^2-251 solutions Answer 373553 by ankor@dixie-net.com(15664)   on 2012-03-12 17:27:46 (Show Source): You can put this solution on YOUR website! Both numerator and denominator will factor Cancel (m-5)'s results
 Age_Word_Problems/585757: a man is 37 years old and his child is 8 years old. How many years ago was the product of their ages 96?1 solutions Answer 373518 by ankor@dixie-net.com(15664)   on 2012-03-12 14:16:09 (Show Source): You can put this solution on YOUR website!a man is 37 years old and his child is 8 years old. How many years ago was the product of their ages 96? : Let y = no. of yrs ago that this was true : (37-y)(8-y) = 96 FOIL 296 - 37y - 8y + y^2 = 96 : y^2 - 45y + 296 - 96 = 0 y^2 - 45y + 200 = 0 Factors to (y-5)(y-40) = 0 Two solutions y = 40 and y = 5 yrs, is the only reasonable answer : 5 yrs ago: 32 * 3 = 96
 Travel_Word_Problems/585763: What is the distance in meters traveled by an object if the time spent traveling is 2 hours and the object's velocity is .29m/s?1 solutions Answer 373479 by ankor@dixie-net.com(15664)   on 2012-03-12 08:53:46 (Show Source): You can put this solution on YOUR website!What is the distance in meters traveled by an object if the time spent traveling is 2 hours and the object's velocity is .29m/s? : change 2hrs to seconds, 2 * 3600 = 7200 : 7200 * .29 = 2,088 meters
 Exponential-and-logarithmic-functions/585645: Okay so for a car project I have this problem and I need to find out how long it would take for me to pay for the car to pay less than 125% of what it is worth.- A=P(1+r/12)^t. A= amount of money total i paid for the car,P= amount of loan i needed) r= interest rate and t= length of loan(in months) For my particular case, I have: A= 26641.12, P= 21000, r= .0349 (3.49%), and t= 48. I know I have to use logarithms to get T down to find the time, but I'm stuck1 solutions Answer 373478 by ankor@dixie-net.com(15664)   on 2012-03-12 08:50:58 (Show Source): You can put this solution on YOUR website!A=P(1+r/12)^t. A= amount of money total i paid for the car, P= amount of loan i needed) r= interest rate and t= length of loan(in months) : For my particular case, I have: A= 26641.12, P= 21000, r= .0349 (3.49%), and t= 48. : you give t=48, but isn't that what we are trying to find here? And 1.25 * 21000 = 26250 : 21000[1+(.0349/12))^t] = 26250 : = Using common logs = The log equiv of exponents = find the logs t * .00126 = .09691 t = t = 76.9, pay it off in 76 months to pay less that \$26250 : : Check this, enter in you calc: 21000(1+(.0349/12))^76 results: \$26,186.26 is what you'll pay in 76 months