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 Travel_Word_Problems/315527: How fast would you have to travel to drive 150 miles in an hour. Thank you1 solutions Answer 225726 by ankor@dixie-net.com(15746)   on 2010-06-18 12:22:51 (Show Source): You can put this solution on YOUR website!Surprisingly, you would have to drive 150 mph
 Mixture_Word_Problems/315378: If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix 20 drinks?1 solutions Answer 225656 by ankor@dixie-net.com(15746)   on 2010-06-17 21:14:00 (Show Source): You can put this solution on YOUR website!If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix 20 drinks? : let t = time required when they all worked together : Let the completed job = 1 (the mixing of 20 drinks) : + + = 1 Multiply by 30, results 6t + 3t + 2t = 30 : 11t = 30 t = t = 2.73 minutes, or 2 min 44 sec : : Check solution using a calc + + = .546 + .273 + .182 = 1.00
 Exponential-and-logarithmic-functions/315266: evaluate the exponential equation for three positive values of x, three negative values of x and at x=0; transform the second expression into the equivalent lagarithmic equation; and evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. show your work. use the resulting ordered pairs to plot the graph of each function; y= 2^x+2 x= 4^y+2 1 solutions Answer 225586 by ankor@dixie-net.com(15746)   on 2010-06-17 16:33:35 (Show Source): You can put this solution on YOUR website!: evaluate the exponential equation for three positive values of x, three negative values of x and at x=0; y = 2^x + 2 : Three positive values for x x=2 y = 2^2 + 2 y = 5 : x=3 y = 2^3 + 2 y = 8 + 2 y = 10 : x=4 y = 2^4 + 2 y = 16 + 2 y = 18 : Three negative values for x x=-2 y = 2^-2 + 2 y = .25 + 2 y = 2.25 : x=-3 y = 2^-3 + 2 y = .125 + 2 y = 2.125 : x=-4 y = 2^4 + 2 y = .0625 + 2 y = 2.0625 : Chart x | y ------ -4 | 2.0625 -3 | 2.125 -2 | 2.25 2 | 5 3 | 10 4 | 18 The graph : : transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. show your work. use the resulting ordered pairs to plot the graph of each function; x = 4^y+2 4^y = x - 2 ln(4^y) = ln(x-2) y*ln(4) = ln(x-2) y = : For 3 values greater than 1 x=3 y = y = y = y = 0 : x=4 y = y = y = .5 : x=6 y = y = y = 1 : You cannot evaluate any values 2 or below (log of a negative number) : Chart x | y ------ 3 | 0 4 | .5 6 | 1 The graph
 Age_Word_Problems/314878: FIVE YEARS AGO GEMMA WAS TWICE AS OLD AS TONY IS NOW, IN SEVEN YEARS SHE WILL BE FIVE TIMES AS OLD TONY IS NOW WHAT ARE THEIR CURRENT AGES?1 solutions Answer 225560 by ankor@dixie-net.com(15746)   on 2010-06-17 15:35:34 (Show Source): You can put this solution on YOUR website!FIVE YEARS AGO GEMMA WAS TWICE AS OLD AS TONY IS NOW, IN SEVEN YEARS SHE WILL BE FIVE TIMES AS OLD TONY IS NOW WHAT ARE THEIR CURRENT AGES? : let g = G's present age let t = T's present age : Write an equation for each statement: : "FIVE YEARS AGO GEMMA WAS TWICE AS OLD AS TONY IS NOW," g - 5 = 2t g = 2t + 5 : "IN SEVEN YEARS SHE WILL BE FIVE TIMES AS OLD TONY IS NOW" g + 7 = 5t Replace g with (2t+5) (2t + 5) + 7 = 5t 2t + 12 = 5t 12 = 5t - 2t 12 = 3t t = t = 4 yrs is T's present age then g = 2(4) + 5 g = 13 yrs is G's present age : : You can check solution in the 1st equation
 Polynomials-and-rational-expressions/315244: Please help me set up and solve this problem. The reciprocal of twice an integer added to the reciprocal of two more than twice the integer is 7/24. What is the integer? 1 solutions Answer 225559 by ankor@dixie-net.com(15746)   on 2010-06-17 15:25:05 (Show Source): You can put this solution on YOUR website! The reciprocal of twice an integer added to the reciprocal of two more than twice the integer is 7/24. What is the integer? : Let x = the integer + = multiply equation by 24x(2x+2) 24x(2x+2)* + 24x(2x+2)* = 24x(2x+2)* cancel the denominators, results: 12(2x+2) + 24x = 7x(2x+2) : 24x + 24 + 24x = 14x^2 + 14x : 48x + 24 = 14x^2 + 14x : Combine on the right 0 = 14x^2 + 14x - 48x - 24 : A quadratic equation 14x^2 - 34x - 24 = 0 : simplify, divide by 2 7x^2 - 17x - 12 = 0 : factor this to (7x+4)(x-3) = 0 : The positive solution is all we want here x = 3 is the integer, that everyone is waiting for! : : See if this is true + = + = + =
 Equations/315202: Three numbers add up to 60.The first number is 1/3 of the second number. The third number is twice the second number. What are the three numbers?1 solutions Answer 225547 by ankor@dixie-net.com(15746)   on 2010-06-17 15:01:43 (Show Source): You can put this solution on YOUR website!Write an equation for each statement : Three numbers add up to 60. x + y + z = 60 : The first number is 1/3 of the second number. x = y : The third number is twice the second number. z = 2y : What are the three numbers? x + y + z = 60 replace x and z y + y + 2y = 60 : y + 3y = 60 Multiply eq by 3, results y + 3(3y) + 3(60) : y + 9y = 180 y = y = 18 then z = 2(18) z = 36 and x = *18 x = 6 : : Check by finding the sum of these three numbers 6 + 18 + 36 = 60
 Length-and-distance/315171: A bird is flying around the world at a rate of 4.1 meters/sec. How many days will it take to complete his journey? (circumference of earth=25, 000 miles)1 solutions Answer 225545 by ankor@dixie-net.com(15746)   on 2010-06-17 14:51:50 (Show Source): You can put this solution on YOUR website!A bird is flying around the world at a rate of 4.1 meters/sec. How many days will it take to complete his journey? (circumference of earth=25, 000 miles) : 1 mi = 1609.35 meters : time (days) = t = 113.58 days
 Polynomials-and-rational-expressions/315249: Maria bicycles 8km per hour faste than Praedup. In the same time it takes Praedup to bicycle 42 km, maria can bicycle 66km. How fast are each bicyclist traveling?1 solutions Answer 225541 by ankor@dixie-net.com(15746)   on 2010-06-17 14:37:21 (Show Source): You can put this solution on YOUR website!Maria bicycles 8km per hour faste than Praedup. In the same time it takes Praedup to bicycle 42 km, maria can bicycle 66km. How fast are each bicyclist traveling? : let s = P's biking speed "Maria bicycles 8 km per hour faster than P"; therefore: (s+8) = M's biking speed : Write a time equation; time = dist/speed : M's time = P's time = Cross multiply 66s = 42(s+8) : 66s = 42s + 336 : 66s - 42s = 336 : 24s = 336 s = s = 14 km/h is P's speed then 14 + 8 = 22 km/hr is M's speed : : check solution by finding the times, (should be equal) 66/22 = 3 hrs 42/14 = 3 hrs; confirms our solutions
 Matrices-and-determiminant/315059: 1.If dan makes 20 drinks in 5 minutes and Sue makes 20 drinks in 10 minutes and Jack makes 20 drinks in 15 minutes How much time will it take all 3 of them working together to mix the 20 drinks? 1 solutions Answer 225539 by ankor@dixie-net.com(15746)   on 2010-06-17 14:27:40 (Show Source): You can put this solution on YOUR website!1.If dan makes 20 drinks in 5 minutes and Sue makes 20 drinks in 10 minutes and Jack makes 20 drinks in 15 minutes. How much time will it take all 3 of them working together to mix the 20 drinks? : let t = time required when they all worked together : Let the completed job = 1 (the mixing of 20 drinks) : + + = 1 Multiply by 30, results 6t + 3t + 2t = 30 : 11t = 30 t = t = 2.73 minutes, or 2 min 44 sec : : Check solution using a calc + + = .546 + .273 + .182 = 1.00
 Length-and-distance/315172: A turtle is crossing a field, going 1 mile in 5 days. What is his speed in ft/sec?1 solutions Answer 225473 by ankor@dixie-net.com(15746)   on 2010-06-17 09:54:35 (Show Source): You can put this solution on YOUR website!A turtle is crossing a field, going 1 mile in 5 days. What is his speed in ft/sec? : = .0122 ft/sec : (assuming the turtle does not stop to sleep or eat, rather unrealistic, but there it is!)
 Travel_Word_Problems/315037: at noon a private plane left Austin for Los Angeles,2300km away,flying at 500km/h. one hour later a jet left Los Angeles for Austin at 700km/h. at what time did they pass each other?1 solutions Answer 225374 by ankor@dixie-net.com(15746)   on 2010-06-16 21:53:34 (Show Source): You can put this solution on YOUR website!at noon a private plane left Austin for Los Angeles, 2300km away, flying at 500km/h. one hour later a jet left Los Angeles for Austin at 700km/h. at what time did they pass each other? : Let t = travel time of the private plane then (t-1) = travel time of the jet : When the aircraft meet, the sum of their distances will be 2300 km Write a dist equation; dist = speed * time : jet dist + private dist = 2300 km 700(t-1) + 500t = 2300 : 700t - 700 + 500t = 2300 : 1200t = 2300 + 700 : 1200t = 3000 t = t = 2.5 hrs : 12:00 + 2:30 = 2:30 PM the planes will meet : : Confirm solution by finding the distance 2.5(500) = 1250 1.5(700) = 1050 --------------- total dist 2300
 Travel_Word_Problems/315058: Joseph watch the roadside mile markers during a long car trip on an interstate highway. He notices that at 10:45 a.m. they are passing a marker labeled 101, and at 11:00 a.m. the car reaches marker 119. What is the car's speed?1 solutions Answer 225365 by ankor@dixie-net.com(15746)   on 2010-06-16 21:36:22 (Show Source): You can put this solution on YOUR website!Joseph watch the roadside mile markers during a long car trip on an interstate highway. He notices that at 10:45 a.m. they are passing a marker labeled 101, and at 11:00 a.m. the car reaches marker 119. What is the car's speed? : From the given information we can say, the car went 18 mi in 15 min : S = * 18 S = 72 mph
 Matrices-and-determiminant/315060: 2. Two cyclists start biking from a trial and start 3 hours apart. The 2nd cyclist travels at 10 mph and starts 3 hours after the 1st cyclist who is traveling at 6 mph. How much time will pass before the 2nd cyclist catches up with the 1st from the time the 2nd cyclist started biking? Please help me with this one i got stuck Thank you1 solutions Answer 225362 by ankor@dixie-net.com(15746)   on 2010-06-16 21:26:25 (Show Source): You can put this solution on YOUR website!The 2nd cyclist travels at 10 mph and starts 3 hours after the 1st cyclist who is traveling at 6 mph. How much time will pass before the 2nd cyclist catches up with the 1st from the time the 2nd cyclist started biking? : Let t = travel time of the 2nd cyclist then (t+3) = travel time of the 1st cyclist : When the 2nd overtakes the 1st, they will have traveled the same distance ; Write distance equation; dist = speed * time 2nd dist = 1st dist 10t = 6(t+3) 10t = 6t + 18 10t - 6t = 18 4t = 18 t = t = 4.5 hrs for the 2nd cyclist to catch the first ; : Check solution by finding distance of each, should be equal: 10*4.5 = 45 mi 6 *7.5 = 45 mi
 Numbers_Word_Problems/314941: Jackie is twice as old as John. Ten years ago, Jackie was three times as old as John was ten years ago. How old is each one new? Is there a certain format to use when doing these type of word problems? I get lost on this. Thank you for any help you provide. 1 solutions Answer 225265 by ankor@dixie-net.com(15746)   on 2010-06-16 15:20:10 (Show Source): You can put this solution on YOUR website!Jackie is twice as old as John. Ten years ago, Jackie was three times as old as John was ten years ago. How old is each one now? : Here is one method, that's pretty easy : Let x = Jackie's present age Let y = John's present age : Write an equation for each statement: : "Jackie is twice as old as John." x = 2y : Ten years ago, Jackie was three times as old as John was ten years ago. x - 10 = 3(y - 10) x - 10 = 3y - 30 x = 3y - 30 + 10 x = 3y - 20 : From the 1st equation, replace x with 2y 2y = 3y - 20 +20 = 3y - 2y y = 20 yrs is John's present age then x = 2(20) x = 40 is Jackie's present age : : Check solutions in the statement: "Ten years ago, Jackie was three times as old as John was ten years ago." 40 - 10 = 3(20 - 10) 30 = 3(10), confirms our solutions
 Miscellaneous_Word_Problems/314932: Tracy, Stacy, and Fred assembled a very large puzzle together in 40 hours. If Stacy worked twice as fast as Fred and Tracy worked just as fast as Stacy, then how long would it have taken Fred to assemble the puzzle alone? 1 solutions Answer 225260 by ankor@dixie-net.com(15746)   on 2010-06-16 15:11:20 (Show Source): You can put this solution on YOUR website!Tracy, Stacy, and Fred assembled a very large puzzle together in 40 hours. If Stacy worked twice as fast as Fred and Tracy worked just as fast as Stacy, then how long would it have taken Fred to assemble the puzzle alone? : Let x = time required by Fred then .5x = time required by Stacy, and time required by Tracy : Let the completed puzzle = 1 : A shared work equation + + = 1 multiply by .5x, results 40 + 40 + .5(40) = .5x : 40 + 40 + 20 = .5x : .5x = 100 hrs, Mult by 2 x = 200 hrs Fred alone : : Check solution in shared work equation + + = .4 + .4 + .2 = 1
 test/314267: Solve for the indicated letter. Solve the formula. S= 1/3 nr^2h + 4nrh for r.1 solutions Answer 225254 by ankor@dixie-net.com(15746)   on 2010-06-16 14:19:51 (Show Source): You can put this solution on YOUR website!Solve for the indicated letter. Solve the formula. S = for r. : = S Multiply by 3 = 3S : = 3S Factor out nh nh(r^2 + 12r) = 3S divide both sides by nh r^2 + 12r = Arrange as a quadratic equation r^2 + 12r - = 0 Solve for r using the quadratic formula In this equation: x = r a=1; b=12; c=- : :
 Evaluation_Word_Problems/314635: 4.at the beginning of a walk, bill and nancy are 8.8 miles apart. it they oleave at the same time and walk in the same direction, bill overtakes nancy in 11 hours. if they walk towards each other they meet in 1 hour. what are their speeds? 1 solutions Answer 225118 by ankor@dixie-net.com(15746)   on 2010-06-15 21:54:04 (Show Source): You can put this solution on YOUR website!4.at the beginning of a walk, bill and nancy are 8.8 miles apart. if they leave at the same time and walk in the same direction, bill overtakes nancy in 11 hours. if they walk towards each other they meet in 1 hour. what are their speeds?: : let b = Bill's walking speed let n = Nancy's walking speed : walking the same direction they're effective speed is the difference walking towards each other they're effective speed is the sum : "Same direction" equation Write a time equation: Time = dist/speed = 11 8.8 = 11(b-n) 8.8 = 11b - 11n Simplify, divide by 11 .8 = b - n Or b - n = .8 : "Toward equation" = 1 8.8 = 1(b + n) b + n = 8.8 : Use elimination b - n = .8 b + n = 8.8 ---------------addition eliminates n, find b 2b = 9.6 b = 4.8 mph is Bill's walking speed : Find n 4.8 + n = 8.8 n = 8.8 - 4.8 n = 4 mph is Nancy's walking speed
 Equations/314273: 2/17 = x-6/x+9 If I have to use LCD 17 is a prime number and 9 is 3X3 meaning that I need to multiply by 51 to get rid of denominators then 51(2/17) = 51(x-6/x+9) then I got stuck can you please help me understand what will follow?1 solutions Answer 224744 by ankor@dixie-net.com(15746)   on 2010-06-14 21:42:31 (Show Source): You can put this solution on YOUR website!Assume the problem is: = The LCD is 17(x+9), but with this problem you can cross multiply 17(x-6) = 2(x+9) : 17x - 102 = 2x + 18 : 17x - 2x = 18 + 102 : 15x = 120 x = x = 8 : : Check solution in the original equation: = =
 Numeric_Fractions/314367: I dont get how to do algabra atttt alllllllllllll!!! Please hlp ! Ill give you an ecasion and can you answer it and tell me how you got the answer W/3 + 6 = 21 solutions Answer 224733 by ankor@dixie-net.com(15746)   on 2010-06-14 21:25:38 (Show Source): You can put this solution on YOUR website!Assume the problem is: + 6 = 2 remember whatever you do to one side, do also to the other side Subtract 6 from both sides + 6 - 6 = 2 - 6 which is = -4 Multiply both sides by 3 3* = 3 * -4 cancels the denominator and you have W = -12 : Now check the solution in the original equation + 6 = 2 -4 + 6 = 2, 2 = 2, confirms our solution
 Rate-of-work-word-problems/314096: 1.Some work is done by two people in 24 minutes. One of them can do this work alone in 40 minutes. How much time does the second person take to do the same work ? 2.A car is filled with four and half gallons of fuel for a round trip.If the amount of fuel taken while going is 1/4 more than the amount taken for coming, what is the amount of fuel consumed while coming back? 3.The lowest temperature in the night in a city A is 1/3 more than 1/2 the highest during the day. Sum of the lowest temperature and the highest temperature is 100 degrees. Then what is the low temp? 1 solutions Answer 224727 by ankor@dixie-net.com(15746)   on 2010-06-14 21:13:49 (Show Source): You can put this solution on YOUR website!Some work is done by two people in 24 minutes. One of them can do this work alone in 40 minutes. How much time does the second person take to do the same work ? : Let t = time for 2nd person to do the job Let the completed job = 1 A shared work equation + = 1 reduce the fraction + = 1 multiply eq by 5t, results 3t + 5(24) = 5t 120 = 5t - 3t 120 = 2t t = 60 min alone : : 2.A car is filled with four and half gallons of fuel for a round trip. If the amount of fuel taken while going is 1/4 more than the amount taken for coming, what is the amount of fuel consumed while coming back? : let x = amt of fuel consumed on the way back then 1.25x = amt of fuel consumed going : x + 1.25x = 4.5 2.25x = 4.5 x = x = 2 gal consumed coming back : : 3.The lowest temperature in the night in a city A is 1/3 more than 1/2 the highest during the day. L = H + H L = H + H L = H : Sum of the lowest temperature and the highest temperature is 100 degrees. L + H = 100 Then what is the low temp? : Replace L with H H + H = 100 H = 100 11H = 6(100) h = h = 54.54 degrees is the high then 100 - 54.54 = 45.45 degrees is the low
 Human-and-algebraic-language/314258: A manufacturer produces two models of the same toy: Model A and Model B. Model A takes 4 hours to produce and costs \$8/each. Model B takes 3 hours to produce and costs \$7/each. If the manufacturer allots a total of 5800 hours and \$12,600 for production each week, how many of each model will be produced? Thanks in advance for any assistance!1 solutions Answer 224664 by ankor@dixie-net.com(15746)   on 2010-06-14 17:39:33 (Show Source): You can put this solution on YOUR website!A manufacturer produces two models of the same toy: Model A and Model B. Model A takes 4 hours to produce and costs \$8/each. Model B takes 3 hours to produce and costs \$7/each. If the manufacturer allots a total of 5800 hours and \$12,600 for production each week, how many of each model will be produced? : Let a = no. of A models Let b = no. of B models : the labor equation 4a + 3b = 5800 : the cost equation 8a + 7b = 12600 : Multiply the labor equation by 2, subtract from the cost equation 8a + 7b = 12600 8a + 6b = 11600 ------------------subtraction eliminates a, find b b = 1000 ea B model toys : find a using the labor equation 4a + 3(1000) = 5800 4a = 5800 - 3000 4a = 2800 a = a = 700 ea A model toys : : Check solutions in the cost equation 700(8) + 1000(7) = 5600 + 7000 = 12,600; confirms our solutions
 Numbers_Word_Problems/314084: 1)Suppose that Q is jointly proportional to R and the Square of S. If Q=24 when R=3 and S=4. Find Q when R=2 and S=3. 2)When and anvil is dropped into a gorge, the speed with which it strikes the ground is directly proportional to the square root of the distance it falls. An anvil that falls 400 feet hits the ground at a speed of 160 feet per second. Find the height of a cliff over the gorge is a dropped anvil hits the ground ata speed of 128 feet per second. 1 solutions Answer 224653 by ankor@dixie-net.com(15746)   on 2010-06-14 16:45:48 (Show Source): You can put this solution on YOUR website!1)Suppose that Q is jointly proportional to R and the Square of S. Q:(R*S^2) ; If Q=24 when R=3 and S=4. Find Q when R=2 and S=3. = = Q = 9 : : 2)When and anvil is dropped into a gorge, the speed with which it strikes the ground is directly proportional to the square root of the distance it falls. s: An anvil that falls 400 feet hits the ground at a speed of 160 feet per second. Find the height of a cliff over the gorge is a dropped anvil hits the ground at a speed of 128 feet per second. let h = height of the cliff A ratio equation = same as = Cross multiply = 20 * 128 = 2560 = = 16 Square both sides h = 16^2 h = 256 ft
 Rectangles/314212: Hi, I cant even get started on this problem after reviewing my textbook all day. Any help is greatly appreciated! 14 Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. A rectangular cabinet door has a 20 inch by 38 inch glass panel in the center with a uniform wooden edge around the glass. If the area of the wooden edge is 248 square inches, how wide is the wooden edge? Thank you, Daniel 1 solutions Answer 224639 by ankor@dixie-net.com(15746)   on 2010-06-14 16:05:03 (Show Source): You can put this solution on YOUR website!Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. A rectangular cabinet door has a 20 inch by 38 inch glass panel in the center with a uniform wooden edge around the glass. If the area of the wooden edge is 248 square inches, how wide is the wooden edge? : Let x = the width of the wooden edge : Find the total area of the glass and the edge (20*38) + 248 = 1008 sq/in : The dimensions of the total area, which include the wooden edge, will be: (2x+20) by (2x+38) : The total area equation (2x+20) * (2x+38) = 1008 FOIL 4x^2 + 76x + 40x + 760 = 1008 Arrange as a quadratic equation 4x^2 + 116x + 760 - 1008 = 0 : 4x^2 + 116x - 248 = 0 Simplify, divide by 4, resulting in x^2 + 29x - 62 = 0 Factors to (x+31)(x-2) = 0 positive solution only is what we want here x = 2 in is the width of the wooden edge : : Check solution finding the difference in area 24 * 42 = 1008, overall area 20 * 38 = 760, glass area ------------------- differ: = 348, given area of wooden edge
 Money_Word_Problems/314183: A group of students agreed that each would chip in the same amount of money to pay for a party that cost \$100.00. Then they found 5 more student interested in the party and in sharing the cost. This decreased the amount each had to pay by \$1.00. How many students were involved in the party and how much did each student have to pay? 1 solutions Answer 224632 by ankor@dixie-net.com(15746)   on 2010-06-14 15:41:24 (Show Source): You can put this solution on YOUR website!A group of students agreed that each would chip in the same amount of money to pay for a party that cost \$100.00. Then they found 5 more student interested in the party and in sharing the cost. This decreased the amount each had to pay by \$1.00. How many students were involved in the party and how much did each student have to pay? : Let x = no. of students finally involved then (x-5) = no. of students before 5 more joined : = amt each had to pay : Before = after + \$1 = + 1 multiply equation by x(x-5), results 100x = 100(x-5) + x(x-5) : 100x = 100x - 500 + x^2 - 5x combine on the right 0 = 100x - 100x + x^2 - 5x - 500 a quadratic equation x^2 - 5x - 500 = 0 Factors to: (x - 25)(x + 20) = 0 positive solution x = 25 students finally involved ; Find the cost: = \$4.00 per student : Check solution find the cost before 100/20 = \$5, one dollar more
 test/314188: One number is three times another. The sum of their reciprocals is four over nine. Find the numbers.1 solutions Answer 224603 by ankor@dixie-net.com(15746)   on 2010-06-14 14:06:18 (Show Source): You can put this solution on YOUR website!One number is three times another. x = 3y : The sum of their reciprocals is four over nine. + = : Find the numbers. Replace x with (3y) + = multiply each term by 9y, results 3 + 9 = 4y 12 = 4y y = y = 3 find x x = 3(3) x = 9 : : Check solution + = + = :
 Quadratic_Equations/314018: ) Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 9 miles, the distance between the cars was 3 miles more than the distance traveled by the car heading east. How far had the eastbound car traveled?1 solutions Answer 224566 by ankor@dixie-net.com(15746)   on 2010-06-14 09:42:13 (Show Source): You can put this solution on YOUR website! Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 9 miles, the distance between the cars was 3 miles more than the distance traveled by the car heading east. How far had the eastbound car traveled? : Let x = distance traveled by the eastbound car then (x+3) = distance between the cars when the northbound car had traveled 9 mi : A pythag problem a^2 + b^2 = c^2 where a = x b = 9 c = (x+3) : x^2 + 9^2 = (x+3)^2 x^2 + 81 = x^2 + 6x + 9 Combine on the left x^2 - x^2 - 6x + 81 - 9 = 0 -6x + 72 = 0 -6x = -72 x = x = +12 mi traveled by the eastbound car : : Check: 12^2 + 9^2 = 15^2
 Geometry_Word_Problems/313783: if the area of a circle is equal to the area of an equilateral triangle , then the ratio of the side of the triangle to the radius of the circle is closest to which number ? a 3 b 4 c 5 d 6 e 71 solutions Answer 224509 by ankor@dixie-net.com(15746)   on 2010-06-13 21:46:33 (Show Source): You can put this solution on YOUR website!if the area of a circle is equal to the area of an equilateral triangle, then the ratio of the side of the triangle to the radius of the circle is closest to which number? : Choose a value for the area; A = 60 = 60 r^2 = r = r = 4.37 is the radius : The triangle (s=side) *s*h = 60 Find the height of the triangle in terms of s h = h = h = Area of the triangle *s*h = 60 s * h = 120; mult both sides by 2 Replace h with s * = 120 Square both sides s^2 * .75s^2 = 14400 .75s^4 = 14400 s^4 = s^4 = 19200 Find the 4th root of both sides s = 19200^(1/4) s = 11.77 is the side of triangle : ~ 2.7, closest to 3 : : seems like there should be a more elegant way to do this, but I can't come up with it.
 Linear-systems/313929: Hello, I am trying to figure out how to find the solution for this equation. 2x-y+3z=1 -x+2y-z=-2 x+y+2z=-1 Can anybody help me solve this problem? thanks1 solutions Answer 224437 by ankor@dixie-net.com(15746)   on 2010-06-13 16:58:29 (Show Source): You can put this solution on YOUR website!2x - y + 3z = 1 -x +2y - z =-2 x + y + 2z = -1 : No Multiply the last equation by -1 and add and see what happens 2x - y + 3z = 1 -x +2y - z = -2 -x - y - 2z = 1 --------------------adding eliminates all three variables
 Complex_Numbers/313899: How do you solve this problem step by step? For i = square root of -1, if 3i(2 + 5i)= x + 6i, then x = ? 1 solutions Answer 224435 by ankor@dixie-net.com(15746)   on 2010-06-13 16:48:54 (Show Source): You can put this solution on YOUR website!3i(2 + 5i)= x + 6i, : Multiply inside the brackets 6i + 15(i^2) = x + 6i : We know i^2 = -1 6i + 15(-1) = x + 6i 6i - 15 = x + 6i : Subtract 6i from both sides -15 = x
 Miscellaneous_Word_Problems/313793: Julie sells 3 ducks and 4 chickens for \$70.30. One chicken and one duck together are sold for \$20.70. What is the price of a chicken?1 solutions Answer 224430 by ankor@dixie-net.com(15746)   on 2010-06-13 16:08:57 (Show Source): You can put this solution on YOUR website!Julie sells 3 ducks and 4 chickens for \$70.30. 3d + 4c = 70.30 : One chicken and one duck together are sold for \$20.70. d + c = 20.70 d = (20.70-c) : What is the price of a chicken? : Replace d with (20.7-c) in the 1st equation 3(20.7-c) + 4c = 70.30 : 62.10 - 3c + 4c = 70.30 c = 70.30 - 62.10 c = \$8.20 price of a chicken : : Check, find the price of duck 20.70 - 8.20 = 12.50 3(12.50) + 4(8.20) = 70.30; confirms our solution of c = 8.2
 Money_Word_Problems/313872: Can anyone help me figure the interest earned for a word problem, please? A money market fund pays 14% annual interest compounded daily. What is the value of \$10,000 invested in this fund after 15 years? Any help would be appreciated!1 solutions Answer 224426 by ankor@dixie-net.com(15746)   on 2010-06-13 15:55:03 (Show Source): You can put this solution on YOUR website!A money market fund pays 14% annual interest compounded daily. What is the value of \$10,000 invested in this fund after 15 years? : The compound interest equation A = P(1+)^nt where A = amt after t years P = initial amt (10000) r = interest rate in decimals, (.14) n = time compounded per year, (365) t = time in yrs, (15) : A = 10000(1+)^(365*15) : A = 10000*(1.00038356)^5475 : A = 10000*8.1628825 : A = \$81,628.83