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 Quadratic_Equations/443312: What is the quadratic equation?1 solutions Answer 305784 by ankor@dixie-net.com(15624)   on 2011-05-01 15:21:05 (Show Source): You can put this solution on YOUR website!A quadratic equation is an equation involving the 2nd power, but no higher power, of an unknown. The general form a^2 + bx + c = 0 (a, b, and c are known; x is unknown) (a does not = 0). There are three ways to solve this kind of equation for x. One way is to factor the left hand side, one is completing the square, and the third is using the quadratic formula:
 Trigonometry-basics/443124: If one root of a quadratic equation is 1/2-2i, what is the equation? 1 solutions Answer 305782 by ankor@dixie-net.com(15624)   on 2011-05-01 15:12:15 (Show Source): You can put this solution on YOUR website!If one root of a quadratic equation is 1/2-2i, what is the equation? x = - 2i We can write it x = .5 - 2i x - .5 = -2i Square both sides, FOIL the left side x^2 - 1x + .25 = 4i^2 we know i^2 = -1, therefore x^2 - x + .25 = 4(-1) x^2 - x + .25 = -4 x^2 - x + .25 + 4 = 0 x^2 - x + 4.25 = 0; the equation
 Linear-equations/443184: Find x and y intercepts and graph the equation plotting the intercepts, show me how you do this step by step please. Create graph. 5x -6y = -451 solutions Answer 305777 by ankor@dixie-net.com(15624)   on 2011-05-01 14:42:06 (Show Source): You can put this solution on YOUR website!Find x and y intercepts and graph the equation plotting the intercepts, show me how you do this step by step please. Create graph. : 5x -6y = -45 : The x intercept occurs when y = 0, replace y with 0 in the above equation 5x - 6(0) = -45 5x = -45 x = x = -9 is the x intercept : The y intercept occurs when x = 0, replace x with 0 in the same equation 5(0) -6y = -45 -6y = -45 y has to be positive, multiply both sides by -1 6y = 45 y = reduces to , therefore: y = 7.5 is the y intercept : we can confirm this with a graph, put equation in to slope/intercept form y = mx + b 5x - 6y = -45 subtract 5x from both sides -6y = -5x - 45 get rid of the negative y, multiply both sides by -1 6y = 5x + 45 divide by 6 y = x - reduce fraction y = x - y = x + 7.5 : Plot this using x=-3 and x=+3 When x= -3 y = (-3) + 7.5 y = + 7.5 y = -2.5 + 7.5 y = 5 Ordered pair -3, 5 : when x = +3 y = (3) + 7.5 y = + 7.5 y = +2.5 + 7.5 y = 10 ordered pair 3, 10 : Plot a straight line thru these to points should look like this You can see the intercepts are what we calculated them to be
 Age_Word_Problems/443266: Beth is two years older than Julio. Gerald is twice as old as Beth. Debra is twice as old as Gerald. The sum of their ages is 38. How old is Beth?1 solutions Answer 305771 by ankor@dixie-net.com(15624)   on 2011-05-01 14:16:59 (Show Source): You can put this solution on YOUR website!Beth is two years older than Julio. Gerald is twice as old as Beth. Debra is twice as old as Gerald. The sum of their ages is 38. How old is Beth? : write an equation for each statement, get everything in terms of b: : Beth is two years older than Julio. b = j+2 or j = (b-2) : Gerald is twice as old as Beth. g = 2b : Debra is twice as old as Gerald. d = 2g Replace g with 2b d = 2(2b) d = 4b : The sum of their ages is 38. b + j + g + d = 38 Replace j, g, d b +(b-2) + 2b + 4b = 38 8b = 38 + 2 b = b = 5 yrs is Beth's age : : Check solution by finding the total 5 + 3 + 10 + 20 = 38, confirms our solution of b=5 :
 Travel_Word_Problems/443214: The Smith family and the Jones family are next-door neighbors and are driving to Las Vegas in separate cars for vacation. They are traveling on the same road in the same direction. The Smith family leaves at 8:00am and drives 70mph. Because of a luggage malfunction, the Jones family leaves at 10:00 am and drives 20% faster than the Smith family in an attempt to catch them. A. How long will it take the Jones family to catch the Smith family? 12 hrs B.At what time of day will this occur? 8 pm C. How far from the starting point will they be when the Jones family catches the Smith Family? 840 miles I cannot figure out how to write the equation I figured out the answers on a bar graph1 solutions Answer 305744 by ankor@dixie-net.com(15624)   on 2011-05-01 12:53:08 (Show Source): You can put this solution on YOUR website!The Smith family and the Jones family are next-door neighbors and are driving to Las Vegas in separate cars for vacation. They are traveling on the same road in the same direction. The Smith family leaves at 8:00am and drives 70mph. Because of a luggage malfunction, the Jones family leaves at 10:00 am and drives 20% faster than the Smith family in an attempt to catch them. ; A. How long will it take the Jones family to catch the Smith family? Let t = travel time of Jones then (t+2) = travel time of Smith : Find Jones' speed: 1.2(70) = 84 mph : When J catches S, they will have traveled the same distance write a distance equation Dist = speed * time : 84t = 70(t+2) 84t = 70t + 140 84t - 70t = 140 14t = 140 t = t = 10 hrs is Jones travel time : B.At what time of day will this occur? 10 Am + 10 hrs = 8 Pm : C. How far from the starting point will they be when the Jones family catches the Smith Family? 84 * 10 = 840 mi : Confirm this by finding the dist of the Smiths 70 * 12 = 840 mi
 Rectangles/443128: a rectangle has its length increased by a factor of three and its width increased by a factor of two. what is the ratio of the area of the original rectangle to the area of the larger rectangle? 1:6, 1:5, 1:3, 2:3... can you please explain the equation of how to work this out?1 solutions Answer 305739 by ankor@dixie-net.com(15624)   on 2011-05-01 12:25:45 (Show Source): You can put this solution on YOUR website!a rectangle has its length increased by a factor of three and its width increased by a factor of two. what is the ratio of the area of the original rectangle to the area of the larger rectangle? : Let L = original Length then 3L = increased length : Let W = original width then 2W = increased width : LW = original area then 3L*2W = 6LW increased area : Areas, Ratio Cancel LW or 1:6 is the ratio of the areas
 Quadratic_Equations/443135: Please help me with this problem I am having a diffcult time with it, Than you so much. The population P in 1999 for a state given along with r, its annual percentage rate of continuous growth P= 21 millions, r= 1.9% (a) Write the formula f(x) = P e^yx, where r is in the decimal notation, that models the population in millions x years after 1999. (b) Estimate the population in 2020 F(x) = ? The population in 2020 will be approximately how many million? (round to the nearest tenth as needed) Any help is greatly appreciated!!!1 solutions Answer 305709 by ankor@dixie-net.com(15624)   on 2011-05-01 10:48:48 (Show Source): You can put this solution on YOUR website!The population P in 1999 for a state given along with r, its annual percentage rate of continuous growth P = 21 millions, r= 1.9% (a) Write the formula f(x) = P e^rx, where r is in the decimal notation, that models the population in millions x years after 1999. f(x) = 21*e^.019x : (b) Estimate the population in 2020, (that's 21 yrs after 1999) F(x) = 21*e^(.019*21) f(x) = 21*e^.399 Find e^.399 on a calc f(x) = 21 *1.4903 f(x) = 31.3 million in 2020
 Divisibility_and_Prime_Numbers/442923: Formula x2 - x + 41 substitute the x in the formula with 0, then two even numbers, then two odd numbers and see if a prime number occurs. Try to find a number for x that when substituted in the formula yields a composite number1 solutions Answer 305599 by ankor@dixie-net.com(15624)   on 2011-04-30 21:48:38 (Show Source): You can put this solution on YOUR website!Formula x^2 - x + 41 substitute the x in the formula with 0, then two even numbers, then two odd numbers and see if a prime number occurs. : This is an equation used to generate prime numbers. : Try to find a number for x that when substituted in the formula yields a composite number. Obviously, when x = 41, we have 41^2 = 1681 has to be a composite number
 Miscellaneous_Word_Problems/442880: One more I am stuck on, I feel like there is something missing. A person who must meet the requirements of a nutritional program is considering a combination of two foods which are in tubes. Each tube of A contains 4 units of protein, 2 units of carbs, and 2 units of fat and weighs 3 pounds. The requirement is 42 units of protein, 30 units of carbs, and 18 units of fat. How many tubes of each should be used?1 solutions Answer 305589 by ankor@dixie-net.com(15624)   on 2011-04-30 21:36:51 (Show Source): You can put this solution on YOUR website! There is something missing, only tube A is given here, there probably should be tube B and tube C
 Quadratic_Equations/442639: Solve the following equation by using the quadratic formula. (Enter solutions from smallest to largest. If there is one solution with a multiplicity of two, enter it in both answer boxes.) 3x^2=-4x+2 x = ? x = ? Please show me the steps to get the answer. Thanks1 solutions Answer 305584 by ankor@dixie-net.com(15624)   on 2011-04-30 21:27:48 (Show Source): You can put this solution on YOUR website!3x^2 = -4x + 2 put equation into the standard form 3x^2 + 4x - 2 = 0 The quadratic equation In this equation: a=3, b=4, c=-2 : Minus a minus is a plus : : Find the square root. Two solutions x = x = .387 and x = x = -1.721
 Miscellaneous_Word_Problems/442797: Please help me solve this equation: If the surface area of a cube is increased by a factor of 64, what is the change in the length if the sides of the cube?1 solutions Answer 305576 by ankor@dixie-net.com(15624)   on 2011-04-30 21:14:03 (Show Source): You can put this solution on YOUR website!If the surface area of a cube is increased by a factor of 64, what is the change in the length if the sides of the cube? : Let 6x^2 = surface area of original cube Let 6y^2 = surface area of larger cube : 6y^2 = 64(6x^2) divide both sides by 6 y^2 = 64x^2 Find the square root of both sides y = 8x : We can say the new cube side is 8 times the original cube side
 Quadratic_Equations/442559: solving by elimination method. 5x+5y=-11 7x-3y=13 1 solutions Answer 305549 by ankor@dixie-net.com(15624)   on 2011-04-30 19:39:00 (Show Source): You can put this solution on YOUR website!solving by elimination method. 5x+5y=-11 7x-3y=13 : Multiply the 1st equation by 3, multiply the 2nd equation by 5, results: 15x + 15y = -33 35x - 15y = 65 -----------------addition eliminates y, find x 50x = 32 x = simplify, divide by 2 x = or x = .64 : Find y using the 1st equation: 5() + 5y = -11 + 5y = -11 same as 3.2 + 5y = -11 5y = -11 - 3.2 5y = -14.2 y = y = -2.84 : : Check solutions in the 2nd original equation: 7x - 3y = 13 7(.64) - 3(-2.84) = 13 4.48 + 8.52 = 13 13 = 13; confirms our solutions
 Average/442917: A teacher told Melinda that she has a course average of 78 based on her six math tests. When she got home, she found 5 of her tests with scores of 87, 63, 79, 71, and 96. She couldn't find the sixth test. What score did she obtain on that test?1 solutions Answer 305538 by ankor@dixie-net.com(15624)   on 2011-04-30 18:49:53 (Show Source): You can put this solution on YOUR website!A teacher told Melinda that she has a course average of 78 based on her six math tests. When she got home, she found 5 of her tests with scores of 87, 63, 79, 71, and 96. She couldn't find the sixth test. What score did she obtain on that test? ; Let x = score on the lost test : = 78 : = 78 Multiply both sides by 6 x + 396 = 6(78) x + 396 = 468 x = 468 - 396 x = 72 is the score of the lost test
 Linear-systems/442756: A labourer is engaged for 20 days on the condition that he will receive for Rs. 60 for each day he works and will be fined Rs. 5 for each day he is absent. If he receives Rs. 745 in all, for how many days did he remain absent1 solutions Answer 305535 by ankor@dixie-net.com(15624)   on 2011-04-30 18:39:56 (Show Source): You can put this solution on YOUR website!A labourer is engaged for 20 days on the condition that he will receive for Rs. 60 for each day he works and will be fined Rs. 5 for each day he is absent. If he receives Rs. 745 in all, for how many days did he remain absent. : Let a = number of days absent then (20-a) = number of days worked : Pay amt - fine amt = 745 60(20-a) - 5a = 745 1200 - 60a - 5a = 745 -65a = 745 - 1200 -65a = -455 a = a = 7 days absent : : Check this, he worked 13 days so we have: 13(60) - 7(5) = 780 - 35 = 745; confirms our solution
 Proportions/442768: a) A locomotive is 10 m long and weighs 72 tonnes. A similar model, made of the same material, is 40 cm long, find the mass of the model. b) Suppose the tank of the model locomotive contains 0.85 liters of water when full, find the capacity of the tank of the locomotive. 1 solutions Answer 305521 by ankor@dixie-net.com(15624)   on 2011-04-30 16:49:20 (Show Source): You can put this solution on YOUR website!a) A locomotive is 10 m long and weighs 72 tonnes. A similar model, made of the same material, is 40 cm long, find the mass of the model. : Convert 40 cm to .4 m : Use a volume proportion equation, let x = mass of the 40 cm engine = = Cross multiply: 1000x = 72 * .064 1000x = 4.608 x = x = .004608 tonnes change to kilograms .004608*1000 = 4.61 kg : : b) Suppose the tank of the model locomotive contains 0.85 liters of water when full, find the capacity of the tank of the locomotive. = .064x = 1000*.85 .064x = 850 x = x = 13,281.25 liters of water
 Polynomials-and-rational-expressions/442414: Please use the laws of exponents to simplify: 3.7^(7/4)/ 3.7^(4/7) **Please note that the squared portion is a fraction**1 solutions Answer 305315 by ankor@dixie-net.com(15624)   on 2011-04-29 20:50:47 (Show Source): You can put this solution on YOUR website!Please use the laws of exponents to simplify: = Use a common denominator : , numerators are 49 and 16 : ; numerator is 33
 real-numbers/442155: Simplify . I don't know if this is written right. on the problem in front of me the 3 is tiny1 solutions Answer 305307 by ankor@dixie-net.com(15624)   on 2011-04-29 20:39:19 (Show Source): You can put this solution on YOUR website! Factor inside the radical to reveal the cubes, extract the cube roots: =