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 Expressions-with-variables/186862: Dick is now seven times as old as harry. In six years Dick will be five times as old as Harry. How old will Harry be in five years?1 solutions Answer 140119 by ankor@dixie-net.com(15638)   on 2009-03-16 20:12:38 (Show Source): You can put this solution on YOUR website!Let d = Dick's present age Let h = Harry's present age ; Write an equation for each statement: : "Dick is now seven times as old as harry." d = 7h : " In six years Dick will be five times as old as Harry." d + 6 = 5(h + 6) : d + 6 = 5h + 30 ; d = 5h + 30 - 6 : d = 5h + 24 : How old will Harry be in five years? : Substitute 7h for d in the above equation 7h = 5h + 24 7h - 5h = 24 2h = 24 h = h = 12 is Harry's present then 12 + 5 = 17 yrs is Harry's age in 5 yrs
 Equations/186930: i am trying to figure out how to do this problem I know the answer is 150/x but need to know how to get to that answer if 300 jellybeans cost x dollars then how many jellybeans can you purchase for 50 cents at the same rate? I tried 300=x then j=50 but came up with 60x 300/x then 50j but can't come up with the answer they have for it I need the equation on how to get the answer thanks billie1 solutions Answer 140115 by ankor@dixie-net.com(15638)   on 2009-03-16 19:38:47 (Show Source): You can put this solution on YOUR website!if 300 jellybeans cost x dollars then how many jellybeans can you purchase for 50 cents at the same rate? : Use a ratio equation: = Cross multiply xj = 300 * .5 xj = 150 j =
 Miscellaneous_Word_Problems/186928: Mary lives 6 miles from the mall. She rides her bike to the mall. She rides 4 miles before she meets her friend. They drop off the bike and run together. It then takes them the same amount of time to run the rest of the way to the makk as it took Mary to ride the bike for the first 4 miles. She can bike 8 mph faster than she runs. How fast can she bike?1 solutions Answer 140113 by ankor@dixie-net.com(15638)   on 2009-03-16 19:33:41 (Show Source): You can put this solution on YOUR website!Mary lives 6 miles from the mall. She rides her bike to the mall. She rides 4 miles before she meets her friend. They drop off the bike and run together. It then takes them the same amount of time to run the rest of the way to the mall as it took Mary to ride the bike for the first 4 miles. She can bike 8 mph faster than she runs. How fast can she bike? : Let s = M's bike speed then (s-8) = M's running speed : Write time equation: time = : Bike time = Running time = : Cross multiply: 4(s-8) = 2s 4s - 32 = 2s 4s - 2s = 32 2s = 32 s = s = 16 mph is the bike speed : : Check solution, find the times of biking and running: 4/16 = .25 hr 2/8 = .25 hr
 Quadratic_Equations/186875: I need help please. How do you form a quadratic equation from this? If x=-3 and x=4, then form a quadratic equation.1 solutions Answer 140107 by ankor@dixie-net.com(15638)   on 2009-03-16 16:44:48 (Show Source): You can put this solution on YOUR website! How do you form a quadratic equation from this? If x=-3 and x=4, then form a quadratic equation. : If you know how to factor a quadratic equation, then reverse the process: x = -3 and x = 4, gives us factors of (x+3)(x-4) = 0 FOIL x^2 - 4x + 3x - 12 = 0 so we have: y = x^2 - x - 12
 Finance/186778: Rita, Brittany, and Maria can complete a jigsaw puzzle in 1 hour and 30 minutes if they work together. Working alone, it takes Rita 1 less hour to complete the jigsaw puzzle than it takes Brittany, and Brittany completes the jigsaw puzzle three times as fast as Maria. How much time would it take each to complete the jigsaw puzzle working alone aND Which rational function has a graph with the horizontal asymptote Y=-31 solutions Answer 140094 by ankor@dixie-net.com(15638)   on 2009-03-16 14:17:40 (Show Source): You can put this solution on YOUR website!Rita, Brittany, and Maria can complete a jigsaw puzzle in 1 hour and 30 minutes if they work together. Working alone, it takes Rita 1 less hour to complete the jigsaw puzzle than it takes Brittany, and Brittany completes the jigsaw puzzle three times as fast as Maria. How much time would it take each to complete the jigsaw puzzle working alone : Let r = time required Rita working alone Let b = Brittany alone Let m = Maria alone Let the completed puzzle = 1 ; + + = 1 : "it takes Rita 1 less hour to complete the jigsaw puzzle than it takes Brittany," r = (b-1) ; "Brittany completes the jigsaw puzzle three times as fast as Maria." m = 3b : Substitute for m and r: + + = 1 Multiply by 3b(b-1) to get rid of the denominators, results: 3b(1.5) + 3(b-1)*1.5 + 1.5(b-1) = 3b(b-1) : 4.5b + 4.5b - 4.5 + 1.5b - 1.5 = 3b^2 - 3b : 10.5b - 6 = 3b^2 - 3b : 0 = 3b^2 - 3b - 10.5b + 6 A quadratic equation: 3b^2 - 13.5b + 6 = 0 Simplify divide eq by 3 b^2 - 4.5b + 2 = 0 Factors to: (b-4)(b-.5) = 0 Two solutions b = .5 b = 4 hrs; this is the only solution that makes sense then r = 4 - 1 r = 3 hrs : m = 3(4) m = 12 hrs ; ; check solution in a calc using the original equation: + + = .5 + .375 + .125 = 1
 Numbers_Word_Problems/186852: the tens digit of a two-digit number exceeds twice the units digit by 1. if the digits are reversed, the sum of the new number and the original number is 143. find the original number.1 solutions Answer 140076 by ankor@dixie-net.com(15638)   on 2009-03-16 10:17:53 (Show Source): You can put this solution on YOUR website!the tens digit of a two-digit number exceeds twice the units digit by 1. if the digits are reversed, the sum of the new number and the original number is 143. find the original number. : Let x = the 10's digit Let y = the units then 10x + y = the number : "the tens digit of a two-digit number exceeds twice the units digit by 1." x = 2y + 1 or x - 2y = 1 : "if the digits are reversed, the sum of the new number and the original number is 143." (10y + x) + (10x + y) = 143 10y + x + 10x + y = 143 11x + 11y = 143 Simplify, divide equation by 11 x + y = 13 : Subtract the 1st equation x + y = 13 x - 2y = 1 -------------eliminates x 0x + 3y = 12 y = 4 then x = 2(4) + 1 x = 9 ; 94 = the number : : Check solution in the statement: if the digits are reversed, the sum of the new number and the original number is 143. 49 + 94 = 143
 Radicals/186829: 2/z+3 + 4/5z Can you walk me through this one, I do not understand what it is I am suppose to add1 solutions Answer 140046 by ankor@dixie-net.com(15638)   on 2009-03-15 21:42:01 (Show Source): You can put this solution on YOUR website! + The common denominator will be 5z(z+3), then you have: = = =
 Travel_Word_Problems/186698: A certain trip took 40 min to complete. If half the distance was 100 and the other half at 60, what's the distance traveled during the trip? a) 68 b) 50 1 solutions Answer 140045 by ankor@dixie-net.com(15638)   on 2009-03-15 21:26:33 (Show Source): You can put this solution on YOUR website!A certain trip took 40 min to complete. If half the distance was 100 and the other half at 60, what's the distance traveled during the trip? : Let d = half the distance : Write a time equation: (Time = dist/speed) Change 40 min to hr : + = Multiply equation by 300 300* + 300* = 300* Results: 3d + 5d = 100(2) 8d = 200 d = d = 25 mi is half the dist obviously 50 mi is the total distance ; ; Check solution; find the times at each speed: 25/100 = .25 hr 25/60 = .4167 hr ---------------- total = .667 hr which is 40 min
 Quadratic_Equations/186813: Translate the folowing into a quadratic equation, and solve it: The length of a rectangular garden is four times its width; if the area of the garden is 196 square meters, what are its dimensions?1 solutions Answer 140042 by ankor@dixie-net.com(15638)   on 2009-03-15 21:08:28 (Show Source): You can put this solution on YOUR website!Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is four times its width; if the area of the garden is 196 square meters, what are its dimensions? : See how easy this is: : Let x = the garden width and 4x = garden length then x(4x) = 4x^2 = garden area : Given the area as 196 sq/meters ; 4x^2 = 196 4x^2 - 196 = 0; a quadratic equation, also the difference of squares, so we have: (2x-14)(2x+14) Positive solution: 2x = +14 x = x = 7 m is the width and 4(7) = 28 m is length ; ; Check: 7 * 28 = 196
 Quadratic_Equations/186702: I am confused as to how an quadratic equation can be used in our every day lives? I need an example such as when cooking.1 solutions Answer 140039 by ankor@dixie-net.com(15638)   on 2009-03-15 20:10:05 (Show Source): You can put this solution on YOUR website!Here is one involving food that came up some time ago. Perhaps this will help : A restaurant sells about 330 sandwiches each day at a price of \$6 each. For each \$.25 decrease in price, 15 more sandwiches are sold per day. How much should the restaurant charge to maximize daily revenue? What is the maximum daily revenue? : Let x = amt (\$) decrease in price : Since there is an increase of 15 for each \$.25 decrease, \$1 decrease: 4*15 = 60 Let 60x = increase in sandwiches sold : Price = (6 - x) Number sold = (330 + 60x) : Revenue = price * number sold: Let y = Revenue: : y = (6-x)(330+60x) FOIL y = 1980 + 360x -330x - 60x^2 : A quadratic equation: y = -60x^2 + 30x + 1980 : Find the axis of symmetry: x = -b/(2a); a=-60; b=+30 x = -30/(2*-60) x = -30/-120 x = +.25 : Max revenue occurs at 6 - .25 = \$5.75 for the sandwich : Find Max revenue: The problem states that for every \$.25, they sell 15 more: (330+15) * 5.75 = \$1983.75 is the max revenue. :
 Quadratic_Equations/186740: When an arrow is shot in the air, the height of the arrow h(t),at time t, t>or equal to 0, is determined by the equation h(t)= -4tsquared +16t+1.For which interval of time is the height of the arrow greater than or equal to 11 meters? I figured out the vertex (2,17) and roots are in decimals-.0615528128 and 4.061552813. I believe the 4.061552813 is how long it takes to go up and down, reaching 17 meters going up, but I don't know how long for 11 meters. I missed on how to do this I was sick all week and have no one to explain it to me. Please help me. Chantal Laroche1 solutions Answer 140031 by ankor@dixie-net.com(15638)   on 2009-03-15 19:07:44 (Show Source): You can put this solution on YOUR website!When an arrow is shot in the air, the height of the arrow h(t), at time t, t>or equal to 0, is determined by the equation h(t)= -4tsquared + 16t + 1. For which interval of time is the height of the arrow greater than or equal to 11 meters : h(t) = -4t^2 + 16t + 1, where t = time in seconds, and h = height at t time. : There are three parts to the equation: -4t^2 is the effect of gravity (usually it's 4.9t^2) 16t is the upward velocity of the arrow 1 is the height above ground (0) that the arrow is launched : If you plot this equation, it would look like this: where height is on the y axis and time in sec on the x axis You can see the vertex is 2,17 as you stated the green line is at 11 meters : To calculate the time (t) that the arrow is at 11 meters; h(t) = 11 -4t^2 + 16t + 1 = 11 : -4t^2 + 16t + 1 - 11 = 0 : -4t^2 + 16t - 10 = 0 Use the quadratic formula: a=-4, b=16, c=-10 two solutions t = .775 sec on the way up and t = 3.225 sec on the way down therefore the arrow is => 11m between .775 sec to 3.225 sec or for 3.225-.775 = 2.45 sec : Did this help you understand what's going on here?
 Expressions-with-variables/186746: I typed the question incorrect the first time, SORRY... Together,it takes John and Deb 2 hr 55 min to sort recyclables. Alone, John would require 2 more hrs than Deb. How long would it take Deb to do the job alone?1 solutions Answer 139987 by ankor@dixie-net.com(15638)   on 2009-03-15 14:19:43 (Show Source): You can put this solution on YOUR website!Together,it takes John and Deb 2 hr 55 min to sort recyclables. Alone, John would require 2 more hrs than Deb. How long would it take Deb to do the job alone? : It might be easier to do this in minutes: Together: 2(60) + 55 = 175 min : Let t = time for D to do it alone then (t+120) = J's time alone: ; A typical shared work equation (let the completed job = 1): + = 1 Multiply equation by t(t+120) to get rid of the denominators 175(t+120) + 175t = t(t+120) : 175t + 21000 + 175t = t^2 + 120t ; 350t + 21000 = t^2 + 120t : 0 = t^2 + 120t - 350t - 21000 a quadratic equation: t^2 - 230t - 21000 = 0 Factor this to: (t-300)(t+70) = 0 the positive solution: t = 300 minutes or 5 hrs is D's time alone : : Check solution: (175/300) + (175/420) = 1
 Travel_Word_Problems/186720: Ali plans a road trip from Chicago to Detroit in his Honda Accord with an overnight stay in Hammond, Indiana. On Wednesday, he drove from Chicago to Hamond at an average speed of 47 mph. On Thursday, he continued to drive from Hamond to Detroit at an average speed of 69 mph. His driving time on Thursday is 2 hours longer that his driving time on Wednesday. If the total distance from Chicago to Detroit is 326 miles, then what is the total number of hours he drove on both days? How far is Detroit from Hamond, IN? 1 solutions Answer 139981 by ankor@dixie-net.com(15638)   on 2009-03-15 13:26:56 (Show Source): You can put this solution on YOUR website!On Wednesday, he drove from Chicago to Hammond at an average speed of 47 mph. On Thursday, he continued to drive from Hammond to Detroit at an average speed of 69 mph. His driving time on Thursday is 2 hours longer that his driving time on Wednesday. If the total distance from Chicago to Detroit is 326 miles, then what is the total number of hours he drove on both days? How far is Detroit from Hammond, IN? : Let t = time required to drive from Chi to Ham (Wednesday) then (t+2) = time to drive from Ham to Det (Thursday) ; Write a distance equation: Dist = speed * time ; 47t + 69(t+2) = 326 47t + 69t + 138 = 326 116t = 326 - 138 116t = 188 t = t = 1.62 hrs time from Chi to Ham and 1.62+2 = 3.62 hrs time from Ham to Det therefore: 1.62 + 3.62 = 5.24 hrs total two day drive time : : Check solution by finding the total distance: 47*1.62 + 3.62*69 = 76.14 + 249.48 = 325.92 ~ 326 mi
 Numbers_Word_Problems/186742: Bob was thinking of a number between 5 and 15 that when squared and added to 23 equals the next number's square. What is the number? x(x)+23 = (x+1)2 This should read as "x squared plus 23 equals the quantity x+1 squared. I couldn't type exponents, so my equation may not make sense as it was written! Thank you!1 solutions Answer 139980 by ankor@dixie-net.com(15638)   on 2009-03-15 12:51:39 (Show Source): You can put this solution on YOUR website!Bob was thinking of a number between 5 and 15 that when squared and added to 23 equals the next number's square. What is the number? : You can write it: x^2 + 23 = (x+1)^2 FOIL x^2 + 23 = x^2 + 2x + 1 : 23 - 1 = x^2 - x^2 + 2x : 22 = 2x : x = 11 ; : Check 11^2 + 23 = 144 12^2 = 144
 Geometric_formulas/186725: the height of a photo is 4 inches more than its width. After enlargement the height will increase by 18 inches and the width by 12 inches. If the ratio of the area of the original photo to the area of the enlarged photo is 4:25, then what will the new dimensions of the pgoto become? thank you 1 solutions Answer 139978 by ankor@dixie-net.com(15638)   on 2009-03-15 12:38:17 (Show Source): You can put this solution on YOUR website!the height of a photo is 4 inches more than its width. After enlargement the height will increase by 18 inches and the width by 12 inches. If the ratio of the area of the original photo to the area of the enlarged photo is 4:25, then what will the new dimensions of the photo become? : Let x = the width of the photo and (x+4) = the height then Area = x(x+4) = (x^2 + 4x) : "After enlargement the height will increase by 18 inches and the width by 12 inches." (x+4+18) = (x + 22) is the height after enlargement and (x+12) = width after enlargement then Area = (x+22) * (x+12) = (x^2 + 34x + 264) ; If the ratio of the area of the original photo to the area of the enlarged photo is 4:25, = Cross multiply 25(x^2 + 4x) = 4(x^2 + 34x + 264) : 25x^2 + 100x = 4x^2 + 136x + 1056 : 25x^2 - 4x^2 + 100x - 136x - 1056 = 0 : 21x^2 - 36x - 1056 = 0 : 7x^2 - 12x - 352 = 0 : use the quadratic formula: a=7, b=-12, c=-352 You should get a positive solution of x = 8 : The enlarged dimensions: 8 + 22 = 30" is the height 8 + 12 = 20" is the width ; : Check solution: = =
 Mixture_Word_Problems/186724: tank has three fill pipes and one drain pipe that are all controlled by levers located on a control board. The lenghts of time necessary to fill or empty the tank while working alone are listed below.P1 is started at noon and allowed to run for 10 minutes at which time p2 and p4 are opened. After some time has passed the operator realizes that he opened the drain pipe by mistake. In an attempt to rectify the situation, he accidently closes p2 and opens p3. The tank then fills in 15 minutes. At what time of the day the tank become full? FIll Drain Pipes p1 P2 P3 P4 Time(min) 20 60 90 30 1 solutions Answer 139973 by ankor@dixie-net.com(15638)   on 2009-03-15 10:57:15 (Show Source): You can put this solution on YOUR website!tank has three fill pipes and one drain pipe that are all controlled by levers located on a control board. The lenghts of time necessary to fill or empty the tank while working alone are listed below.P1 is started at noon and allowed to run for 10 minutes at which time p2 and p4 are opened. After some time has passed the operator realizes that he opened the drain pipe by mistake. In an attempt to rectify the situation, he accidently closes p2 and opens p3. The tank then fills in 15 minutes. At what time of the day the tank become full? FIll Drain Pipes p1 P2 P3 P4 Time(min) 20 60 90 30 : Let t = "some time passed" : P1 time = 10 + t + 15 P1 time = (t+25) : P2 time = t : P3 time = 15 : P4 time = t + 15 : Let the full tank = 1 : + + - = 1 reduce the fractions that we can + + - = 1 Multiply equation by 60, results: 3(t+25) + t + 10 - 2(t+15) = 60 3t + 75 + t + 10 - 2t - 30 = 60 3t + t - 2t + 75 + 10 - 30 = 60 2t + 55 = 60 2t = 60 - 55 2t = 5 t = 2.5 min is "some time has passed" therefore total time since noon: : 10 + 2.5 + 15 = 27.5 min, tank is full at 12:27:30 : : check solution on a calc; enter: + + - = 1
 Mixture_Word_Problems/186675: A grocer makes a natural breakfast cereal by mixing oat cereal that cost \$2 per pound with dried fruit and nuts that cost \$9 per pound. How many pounds of each are needed to make 60 pounds of the cereal if it will sell for \$ 7 per pound and yield a prifit of \$ 195 after the entire 60 pounds is sold.1 solutions Answer 139948 by ankor@dixie-net.com(15638)   on 2009-03-14 21:48:19 (Show Source): You can put this solution on YOUR website!A grocer makes a natural breakfast cereal by mixing oat cereal that cost \$2 per pound with dried fruit and nuts that cost \$9 per pound. How many pounds of each are needed to make 60 pounds of the cereal if it will sell for \$7 per pound and yields a profit of \$195 after the entire 60 pounds is sold. : Let x = amt of \$9 stuff The required total is 60 lb, therefore: (60-x) = amt of \$2 stuff : Find the original cost of the 60 lb mixture : (60*7) - 195 = \$225 is his cost for 60 lb which is: = \$3.75 cost per lb : The mixture equation: 9x + 2(60-x) = 3.75(60) : 9x + 120 - 2x = 225 : 9x - 2x = 225 - 120 : 7x = 105 x = x = 15 lb of \$9 stuff then 60 - 15 = 45 lb of \$2 stuff : ; Check solution: 9(15) + 2(45) = 135 + 90 = 225 : 60*7 = 420 - 225 = \$195 profit
 real-numbers/186673: sara and Bill live 13.5 miles apart . AT 10:00 AM they both leave their houses and start walking toward one another. THe ratio of Sara's speed to Bill's speed is 5:4. If they meet at 11:45 , how fast were they walking. Thanks 1 solutions Answer 139947 by ankor@dixie-net.com(15638)   on 2009-03-14 21:22:59 (Show Source): You can put this solution on YOUR website!sara and Bill live 13.5 miles apart . AT 10:00 AM they both leave their houses and start walking toward one another. THe ratio of Sara's speed to Bill's speed is 5:4. If they meet at 11:45 , how fast were they walking. : Let x = the multiplier of their speed 5x = Bill's speed 4x = Sara's speed : Their walking time 1.75 hrs : Write a distance equation: dist = time * speed B's dist + S's dist = 13.5 mi 1.75(5x) + 1.75(4x) = 13.5 8.75x + 7x = 13.5 15.75x = 13.5 x = B's speed = 5* = 4.2857 mph S's speed = 4* = 3.4286 mph ; ; Check solution by find the total distance 1.75*4.2857 = 7.5 mi 1.75*3.4286 = 6 mi -------------------- total dist = 13.5 mi
 Money_Word_Problems/186610: i need help with the following word problem: a museum charges \$10 for a regular admission ticket, but members recieve a discount of \$3 and students are admitted for \$5. Last saturday, 750 tickets were sold for a total of \$5400. if more 20 student tickets than regular tickets were sold, how many of each type of ticket were sold? thanks! 1 solutions Answer 139912 by ankor@dixie-net.com(15638)   on 2009-03-14 11:27:03 (Show Source): You can put this solution on YOUR website!museum charges \$10 for a regular admission ticket, but members receive a discount of \$3 and students are admitted for \$5. Last Saturday, 750 tickets were sold for a total of \$5400. if more 20 student tickets than regular tickets were sold, how many of each type of ticket were sold? : Let x = no. of reg tickets (\$10) Let y = no. of member ticket (\$7) Let z = no. of students (\$5) : No. of tickets equation: x + y + z = 750 : Total\$ equation 10x + 7y + 5z = 5400 : "20 student tickets than regular tickets were sold," z = (x+20) : We know y = 750 - x - z; substitute (x+20) for z y = 750 - x - (x+20) y = 750 - 2x - 20 y = (730 - 2x) : Substitute for y and z in the Total\$ equation, find x: 10x + 7(730-2x) + 5(x+20) = 5400 Get rid of the brackets 10x + 5110 - 14x + 5x + 100 = 5400 10x - 14x + 5x + 5210 = 5400 x = 5400 - 5210 x = 190 reg tickets : y = 730 - 2x y = 730 - 380 y = 350 member tickets : z = x + 20 z = 190 + 20 z = 210 students tickets ; : Check solutions in both equations 190 + 350 + 210 = 750 and 10(190) + 7(350) + 5(210) = 1900 + 2450 + 1050 = \$5400
 Miscellaneous_Word_Problems/186454: how wide a uniform border should be left on a plot of land 7m by 11m to have a rectangular area of 45m^2 available for flowers? Thank you!1 solutions Answer 139864 by ankor@dixie-net.com(15638)   on 2009-03-13 21:59:44 (Show Source): You can put this solution on YOUR website!how wide a uniform border should be left on a plot of land 7m by 11m to have a rectangular area of 45m^2 available for flowers? : Let x = width of the uniform border then the dimensions of the flower area will be: (7-2x) by (11-2x) : The area: (7 - 2x) * (11 - 2x) = 45 FOIL 77 - 14x - 22x + 4x^2 = 45 Arrange as a quadratic equation 4x^2 - 36x + 77 - 45 = 0 4x^2 - 36x + 32 = 0 Simplify, divide by 4 x^2 - 9x + 8 = 0 Factor (x-8)(x-1) = 0 Two solutions x = 8 and x = 1 meter; this is the solution that makes sense : : Check by finding the area (7-2) * (11-2) = 45
 Functions/186246: how do i find the 4th degree polynomial with real coefficients that has zeros of -2, 3, 1+4i, and 1-4i?1 solutions Answer 139854 by ankor@dixie-net.com(15638)   on 2009-03-13 19:49:19 (Show Source): You can put this solution on YOUR website!how do i find the 4th degree polynomial with real coefficients that has zeros of -2, 3, 1+4i, and 1-4i? ; Deal with (1 +/- 4i) fir4st ; x = 1 +/- 4i x - 1 = +/-4i Square both sides: (x-1)^2 = (4i)^2 x^2 - 2x + 1 = 16i^2 x^2 - 2x + 1 = 16(-1) x^2 - 2x + 1 = -16 x^2 - 2x + 1 + 16 = 0 x^2 - 2x + 17 : x = -2: (x^2 - 2x + 17) * (x+2) = x^3 + 13x + 34 : x = 3 (x^3 + 13x + 34) * (x-3) = (x^4 - 3x^3 + 13x^2 - 5x - 102) is the 4th degree polynomial
 Problems-with-consecutive-odd-even-integers/186401: If the first and third consecutive integers are added, the result is 63 less than five times the second integer. Find the third integer.1 solutions Answer 139837 by ankor@dixie-net.com(15638)   on 2009-03-13 17:49:44 (Show Source): You can put this solution on YOUR website!Let the three integers = x, x+1, x+2 : If the first and third consecutive integers are added, the result is 63 less than five times the second integer. x + (x+2) = 5(x+1) - 63 2x + 2 = 5x + 5 - 63 2x - 5x = 5 - 63 - 2 -3x = -60 x = x = +20 is the 1st integer : Find the third integer. 20 + 2 = 22 is the 3rd integer : : Check solution: first and third consecutive integers are added, the result is 63 less than five times the second integer. 20 + 22 = 5(21) - 63 42 = 105 - 63 42 = 42
 Complex_Numbers/186575: Perform the complex number operations and write the answer in the a + bi form. 2i + (3 - i) / (2 + 5i) 1 solutions Answer 139836 by ankor@dixie-net.com(15638)   on 2009-03-13 16:35:53 (Show Source): You can put this solution on YOUR website!Perform the complex number operations and write the answer in the a + bi form. 2i + (3 - i) / (2 + 5i) ; assume it's 2i + over a single denominator = = = = Multiply by the conjugate of the denominator over itself: * = = = =
 Length-and-distance/186466: Point P is 10 units from the origin. The slope of the line passing through P and the origin is 3. IF P is in the first quadrant, find its coordinates in simplified radical form. 1 solutions Answer 139833 by ankor@dixie-net.com(15638)   on 2009-03-13 15:59:16 (Show Source): You can put this solution on YOUR website!Point P is 10 units from the origin. The slope of the line passing through P and the origin is 3. IF P is in the first quadrant, find its coordinates in simplified radical form. : Solve this as right triangle, where x = horizontal leg; 3x = vertical leg; hypotenuse = 10 (slope = 3; rise/run) : x^2 + (3x)^2 = 10^2 x^2 + 9x^2 = 100 10x^2 = 100 x^2 = x^2 = 10 x = : Coordinates; x = ; y =
 Systems-of-equations/186542: Solve the System. 2x+3y+2z=1 2x-3y+2z=-1 4x+3y-2z=4 x= y= z=1 solutions Answer 139798 by ankor@dixie-net.com(15638)   on 2009-03-13 10:01:24 (Show Source): You can put this solution on YOUR website!2x + 3y + 2z = 1 2x - 3y + 2z =-1 4x + 3y - 2z = 4 : Use elimination with subtraction on 1st two equations 2x + 3y + 2z = 1 2x - 3y + 2z =-1 ------------------ 0x + 6y + 0z = 2 6y = 2 y = = : Add the last two equations, eliminate y & z, find x 2x - 3y + 2z =-1 4x + 3y - 2z = 4 ------------------ 6x + 0y + 0z = 3 6x = 3 x = = : Using the 1st equation, substitute for x & y, to find z 2() + 3() + 2z = 1 1 + 1 + 2z = 1 2z = 1 - 2 z = ; ; You can check the solutions in the 2nd and 3rd equation
 Length-and-distance/186316: The volume of a cube with an edge length of u units is u3 cubic units. If the length of each edge is doubled, how many times larger is the volume of the new cube than the volume of the original cube?1 solutions Answer 139765 by ankor@dixie-net.com(15638)   on 2009-03-12 21:40:55 (Show Source): You can put this solution on YOUR website!The volume of a cube with an edge length of u units is u^3 cubic units. If the length of each edge is doubled, how many times larger is the volume of the new cube than the volume of the original cube? : Doubling the edge = 2u Volume = (2u)^3 = 2^3 * u^3 = 8u^3 : Volume is 8 times original cube
 Travel_Word_Problems/186406: A car traveling 61 miles per hour passes a bus traveling 53 in the same direction on the highway. If they maintain their speeds, how long will it take them to be 28 miles apart?1 solutions Answer 139761 by ankor@dixie-net.com(15638)   on 2009-03-12 21:23:14 (Show Source): You can put this solution on YOUR website!A car traveling 61 miles per hour passes a bus traveling 53 in the same direction on the highway. If they maintain their speeds, how long will it take them to be 28 miles apart? : You can do this using relative speed, 61 - 53 = 8 mph relative speed : how long will it take to travel 28 mi at 8 mph : Time = = 3.5 hrs
 Age_Word_Problems/186499: The sum of 4 times Lottie's age and 7 times Eddie's age is 169. Eddie is one year more than twice as old ad Lottie. Find each of their ages.1 solutions Answer 139760 by ankor@dixie-net.com(15638)   on 2009-03-12 21:15:28 (Show Source): You can put this solution on YOUR website!Let L = Lottie's age now Let E = Eddie's age now : Write an equation for each statement: ; The sum of 4 times Lottie's age and 7 times Eddie's age is 169. 4L + 7E = 169 : Eddie is one year more than twice as old ad Lottie. E = 2L + 1 : Find each of their ages. : Substitute (2L+1) for E in the 1st equation: 4L + 7(2L+1) = 169 : 4L + 14L + 7 = 169 : 18L = 169 - 7 L = L = 9 yrs is Lottie's present age then E = 2(9) + 1 E = 19 yrs is Eddie's present age ; ; Check solution in the statement, "The sum of 4 times Lottie's age and 7 times Eddie's age is 169." 4(9) + 7(19) = 169, confirms our solution
 Geometric_formulas/186379: a farmer has 500 feet of fencing with which to build a rectangular livestock pen and wants to enclose the maximum area. use a variable to label length and width of the rectangle find a variable expression for the area of the pen this is totally killing me can someone please help??? thank you1 solutions Answer 139738 by ankor@dixie-net.com(15638)   on 2009-03-12 16:38:13 (Show Source): You can put this solution on YOUR website!a farmer has 500 feet of fencing with which to build a rectangular livestock pen and wants to enclose the maximum area. : use a variable to label length and width of the rectangle find a variable expression for the area of the pen : Let x = width of the pen Let L = length of the pen : write an equation for the total fencing available (the perimeter) 2L + 2x = 500 Simplify, divide equation by 2 L + x = 250 L = (250-x) : The area = L * x, substitute (250-x) for x A = x(250-x) : A = -x^2 + 250x; this is the variable expression for the area of the pen : You can calculate the max area using the axis of symmetry formula x=-b/(2a) In this problem: x = -250/(2*-1) x = -250/-2 x = 125 is the width for max area Note that would be a square: L = 250-x, right? L = 250 - 125 L = 125 also : To find the actual area: substitute 125 for x in the equation A = -(125^2) + 250(125) A = -15625 + 31250 A = + 15625 sq/ft is the max area : Note this corresponds to a square field: 125 * 125 = 15625 sq/ft : To graph this equation, area = y; write it: y = -x^2 = 250x On a TI83 or similar just enter y= -x^2 +25x, scale it x:-100,+300; y:-2000,+16000 ; it should look like this : : Note the max area (y) occurs when x = 125 : If you have to plot this on graph paper, you have to make up an x/y table and plot about a dozen points from x=0 to x=+250. let me know if you have to do that and don't know how to do it. Carl
 Equations/186403: If the formula R=-0.037x + 50.1 can be used to predict the world record in the 400-meter dash x years after 1925, for what years will the world records be 48.6 seconds or less?1 solutions Answer 139735 by ankor@dixie-net.com(15638)   on 2009-03-12 16:21:22 (Show Source): You can put this solution on YOUR website!If the formula R =-0.037x + 50.1 can be used to predict the world record in the 400-meter dash x years after 1925, for what years will the world records be 48.6 seconds or less? ; replace R with 48.6 and find x : -0.037x + 50.1 =< 48.6 : -.037x =< 48.6 - 50.1 : -.037x =< - 2.1 : .037x => 2.1; multiplied equation by -1, this reverses the inequality sign x => x => 56.8 ~ 57 yrs from 1925 : 1925 + 57 = 1982 and thereafter