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 Travel_Word_Problems/393400: Two vehicles, a car and a truck, leave an intersection at the same time. The car heads east at an average speed of 60 miles per hour, while the truck heads south at an average speed of 50 miles per hour. Find an expression for their distance apart d (in miles) at the end of t hours.1 solutions Answer 279258 by ankor@dixie-net.com(15652)   on 2011-01-11 21:13:23 (Show Source): You can put this solution on YOUR website!Two vehicles, a car and a truck, leave an intersection at the same time. The car heads east at an average speed of 60 miles per hour, while the truck heads south at an average speed of 50 miles per hour. Find an expression for their distance apart d (in miles) at the end of t hours. : Let t = the travel time of both vehicles then 60t = dist traveled by the car and 50t = dist traveled by the truck : Use pythag, d = the hypotenuse : d = We can simplify this d = : d = : d = extract the square root of 100 and t^2 : d = , is the simplified expression for this scenario
 Travel_Word_Problems/393348: Q: Bob and Bill both drive 60 miles to work. Bill drives an average of 10 miles per hous faster than Bob and it takes Bill 12 minutes less than Bob to get there. How fast are they driving? I just have no idea what kind of porportion I should be setting up. I've tried to think this through logically but I can't figure it out. Thank you for whatever help you can provide1 solutions Answer 279234 by ankor@dixie-net.com(15652)   on 2011-01-11 20:05:09 (Show Source): You can put this solution on YOUR website!Q: Bob and Bill both drive 60 miles to work. Bill drives an average of 10 miles per hrs faster than Bob and it takes Bill 12 minutes less than Bob to get there. How fast are they driving? : Lets do it this way. : Let s = Bob's speed then (s+10) = Bill's speed : Change 12 min to .2 hrs : Write a time equation: Time = dist/speed : Bob's time - Bills time = .2 hrs - = .2 Multiply by s(s+10); results: 60(s+10) - 60s = .2s(s+10) : 60s + 600 - 60s = .2s^2 + 2s An quadratic equation .2s^2 + 2s - 600 = 0 Multiply by 5 to get rid of the decimal s^2 + 10s - 3000 = 0 Factors to (s+60)(s-50) = 0 the positive solution: s = 50 mph is Bob's speed, then obviously 60 mph is Bill's speed : : See if this is true, find the travel time of each 60/50 = 1.2 hrs 60/60 = 1.0 hrs --------------- differs: .2 hrs
 Linear_Algebra/393273: Set up equation for problem and solve The volume of a box with square base and a height of 12 inches is 768 in3. Find the length of one side of the base.1 solutions Answer 279225 by ankor@dixie-net.com(15652)   on 2011-01-11 19:43:56 (Show Source): You can put this solution on YOUR website!Set up equation for problem and solve The volume of a box with square base and a height of 12 inches is 768 in3. Find the length of one side of the base. : Let x = one side of the square base then x^2 * 12 = 768 x^2 = x^2 = 64 x = x = 8 in is the side of the base : : Check this: 8 * 8 * 12 = 768
 Exponential-and-logarithmic-functions/393385: Exoponential Method 1.A biologist is researching a newly-discovered species of bacteria. at time t=0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Find an exponential equation thet approximates the information. 2. A \$1,000 deposit is made at a bank that pays 12% compound monthly. How much will you havein your account at the end of 10 years. 1 solutions Answer 279211 by ankor@dixie-net.com(15652)   on 2011-01-11 19:17:23 (Show Source): You can put this solution on YOUR website!1.A biologist is researching a newly-discovered species of bacteria. at time t=0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Find an exponential equation that approximates the information. : find k, the growth factor 100*(2^(6/k)) = 450 Divide both sides by 100 2^(6/k) = 4.5 use logs here log(2^(6/k)) = log(4.5) : log(2) = log(4.5) = = 2.17 k = k = 2.765 is the growth factor : A = Ao*2^(t/2.765), the exponential equation where Ao = initial amt A = amt after t hrs t = time in hrs : Check equation using Ao = 100: In a calc enter: 100*2^(6/2.765) results: 450.0 : : 2. A \$1,000 deposit is made at a bank that pays 12% compound monthly. How much will you have in your account at the end of 10 years. : Compound interest formula: A = where A = resulting amt after t years P = principal (\$1000) r = interest rate in decimals (.12) n = no. of time compounded per yr (12 times/yr) t = no. of yrs (10 yrs) : A = : A = : A = on a calc A = \$3300.39
 Mixture_Word_Problems/393206: ok so i have been sick and i have a test tomorrow on dry mixture word problem. i understand some but I am stuck on this one! please help: Trail Snax Corp mixes raisins that cost \$5 per kg with penuts that cost \$3.80 per kghow many kilograms of raisins should be mixed with 10 killograms of peanuts to obtain a mixture worth \$4.00! Thank you! :) 1 solutions Answer 279188 by ankor@dixie-net.com(15652)   on 2011-01-11 18:12:06 (Show Source): You can put this solution on YOUR website!Trail Snax Corp mixes raisins that cost \$5 per kg with penuts that cost \$3.80 per kg how many kilograms of raisins should be mixed with 10 killograms of peanuts to obtain a mixture worth \$4.00! : A typical mixture problem : Let x = amt of raisins required then (10-x) = amt of peanuts : 5x + 3.8(10-x) = 4(10) 5x + 38 - 3.8x = 40 5x - 3.8x = 40 - 38 1.2x = 2 x = x = 1 kg of raisin then 10 - 1 = 8 kg of peanuts : : Check solutions using decimals 5(1.67) + 3.8(8.33) = 4(10) 8.35 + 31.65 = 40 40 = 40; confirms our solution : Hope you are feeling better!
 Evaluation_Word_Problems/393228: 6. The denominator of a fraction exceeds the numerator by 4.When 3 is added to the booth numerator and the denominator, the fraction becomes 4/5. Find the fraction?1 solutions Answer 279162 by ankor@dixie-net.com(15652)   on 2011-01-11 17:00:47 (Show Source): You can put this solution on YOUR website!The denominator of a fraction exceeds the numerator by 4. d = n+4 : When 3 is added to the both numerator and the denominator, the fraction becomes 4/5. = Cross multiply 5(n+3) = 4(d+3) 5n + 15 = 4d + 12 5n = 4d + 12 - 15 5n = 4d - 3 Replace d with (n+4), find n 5n = 4(n+4) - 3 5n = 4n + 16 - 3 5n - 4n = 13 n = 13 is the numerator then d = 13 + 4 d = 17 is the denominator : is the fraction : : Check solution in original equation = =
 Finance/393182: A = P(1+r)t (t is as an exponent) In the formula A = P(1+r)t, P is the principal\, r is the annual rate of interest, and A is the amount after t years. An account earning interest at a rate of 4% has a principal of \$500,000. If no more deposits or withdrawls are made, about how much money will be in the account after five years? A \$705,200 B \$620,700 C \$608,300 D \$575,0001 solutions Answer 279161 by ankor@dixie-net.com(15652)   on 2011-01-11 16:43:40 (Show Source): You can put this solution on YOUR website!A = P(1+r)t (t is as an exponent) In the formula A = P(1+r)t, P is the principal\, r is the annual rate of interest, and A is the amount after t years. An account earning interest at a rate of 4% has a principal of \$500,000. If no more deposits or withdrawls are made, about how much money will be in the account after five years? : A = 500000(1.04)^5 A = 500000*1.2166529 A = \$608,326.45, so guess it's c
 Numbers_Word_Problems/393204: The average of the digit of a two digit number is 6 and the difference between the digits is also 6.find the number1 solutions Answer 279158 by ankor@dixie-net.com(15652)   on 2011-01-11 16:28:28 (Show Source): You can put this solution on YOUR website!Let 10x + y = a two digit number : The average of the digits of a two digit number is 6 = 6 x + y = 2(6) x + y = 12 : and the difference between the digits is also 6. x - y = 6 : Add to the 1st equation x + y = 12 x - y = 6 ------------adding eliminates y, find x 2x = 18 x = 9 then 9 - y = 6 y = 3 : find the number: 93 is the number
 Rate-of-work-word-problems/393202: Two pumps of different sizes working together can empty a tank in 3 hours. The larger pump can empty this tank in 5 hours. How long will it take the smaller one to do the job alone? Show the 4-step process.1 solutions Answer 279144 by ankor@dixie-net.com(15652)   on 2011-01-11 15:56:56 (Show Source): You can put this solution on YOUR website!Two pumps of different sizes working together can empty a tank in 3 hours. The larger pump can empty this tank in 5 hours. How long will it take the smaller one to do the job alone? : Let t = time required by the small pump alone : Let the completed job = 1 (an empty tank) : Each pump will do a fraction of the job, the two fractions add up to 1 : + = 1 Multiply by 5t, results 3t + 5(3) = 5t : 15 = 5t - 3t 15 = 2t t = t = 7.5 hrs, the small pump alone ; : Check the solution + = .6 + .4 = 1; confirms our solution
 Age_Word_Problems/393128: please help me with these problems: 1. Olan is 3 years older than his sister, Rose. One-half of Olan's age is 13 yrs. more than 1/4 his sister's age one year ago. Find their ages now. 2. Grace is 4 times as old as Vicky. Five years ago, Vicky was 30 years younger than Grace. Find their present ages. Thanks. I will appreciate your help in my daughter's homework.1 solutions Answer 279061 by ankor@dixie-net.com(15652)   on 2011-01-11 09:45:35 (Show Source): You can put this solution on YOUR website!Here is a method you can use on most of these age problems : Let L = Olan's present age Let R = Roses present age : Write an equation for each statement: " Olan is 3 years older than his sister, Rose." L = R + 3 : "One-half of Olan's age is 13 yrs. more than 1/4 his sister's age one year ago." L = 13 + (R-1) Get rid of those fractions multiply both sides by 4, results: 2L = 4(13) + R - 1 2L = 52 + R - 1 2L = R + 51 Substitute (R+3) for L (1st statement) 2(R+3) = R + 51 2R + 6 = R + 51 2R - R = 51 - 6 R = 45 yrs is Roses age then L = 45 + 3 L = 48 yrs is Olan's age : Check our solutions in the statement: "One-half of Olan's age is 13 yrs. more than 1/4 his sister's age one year ago." (48) = 13 + (45-1) 24 = 13 + 11 : : 2. "Grace is 4 times as old as Vicky." G = 4V : "Five years ago, Vicky was 30 years younger than Grace." V - 5 = (G - 5) - 30 V - 5 = G - 35 V = G - 35 + 5 V = G - 30 Replace G with 4V V = 4V - 30 +30 = 4V - V 30 = 3V V = 10 is Vicky's present age then G = 4(10) G = 40 is Grace's age : : Check this in the statement: "Five years ago, Vicky was 30 years younger than Grace." 10 - 5 = 40 - 5 - 30 5 = 40 - 35
 Numbers_Word_Problems/393090: A three digit number divisible by ten has a hundreds digit that is one less than its tens digit. The number is 52 times the sum of its digits. Find the number.1 solutions Answer 279047 by ankor@dixie-net.com(15652)   on 2011-01-11 08:57:10 (Show Source): You can put this solution on YOUR website!A three digit number divisible by ten has a hundreds digit that is one less than its tens digit. The number is 52 times the sum of its digits. Find the number. : We know the last digit = 0 : Let the number = 100x + 10y + 0 : " a hundreds digit that is one less than its tens digit." x = y - 1 : The number is 52 times the sum of its digits. 100x + 10y = 52(x+y) 100x + 10y = 52x + 5y 100x - 52x = 52y - 10y 48x = 42y Replace x with (y-1) 48(y-1) = 42y 48y - 48 = 42y 48y - 42y = 48 6y = 48 y = y = 8 then x = 7 : 780 is the number : : confirm this in the statement: "The number is 52 times the sum of its digits." 780 = 52(7+8) 780 = 52(15)
 Pythagorean-theorem/392996: how do i find the height and width of a tv screen with a diagnal length of 42" and a width: height ration of 4:31 solutions Answer 279045 by ankor@dixie-net.com(15652)   on 2011-01-11 08:09:36 (Show Source): You can put this solution on YOUR website!how do i find the height and width of a tv screen with a diagonal length of 42" and a width: height ration of 4:3 : Let x = the multiplier : Using pythag: (3x)^2 + (4x)^2 = 42^2 : 9x^2 + 16x^2 = 1764 25x^2 = 1764 Find the square root of both sides 5x = 42 x = x = 8.4 is the multiplier : Find the length and width 4*8.4 = 33.6 is the length 3*8.4 = 25.2 is the width : : Check the solution, find the hypotenuse on a calc, enter
 Square-cubic-other-roots/392962: We are solving for "p" Equation: 4 * sqrt (2p) + 1 = 241 solutions Answer 278951 by ankor@dixie-net.com(15652)   on 2011-01-10 21:08:21 (Show Source): You can put this solution on YOUR website!We are solving for "p" Equation: 4*sqrt(2p) + 1 = 24 ; 4*sqrt(2p) = 24 - 1 : 4*sqrt(2p) = 23 Divide both sides by 4 square both sides 2p = : 2p = divide both sides by 2 p = ///////////////////////////////////////////// Response to student comment : Check this using the decimal equiv in the original equation 529/32 = 16.53 = P : 4*sqrt(2p) + 1 = 24 4*sqrt(2(16.53)) + 1 = 24 4*sqrt(33.06) + 1 = 24 4*5.75 + 1 = 24 23 + 1 = 24; this checks out, all I can say is I interpreted the problem incorrectly. Please let me know what answer you have; Carl
 Polynomials-and-rational-expressions/392844: Is this equation correct: (x y)3 = x y3 ? Explain why. If it is correct, how can you prove this? If it is incorrect, what should be done to make it right? 1 solutions Answer 278950 by ankor@dixie-net.com(15652)   on 2011-01-10 21:00:38 (Show Source): You can put this solution on YOUR website!Is this equation correct: (x y)3 = x y3 : No
 Money_Word_Problems/392883: How do you calculate the amount of interest paid on a loan for \$4,000 for 2 years at 2.99%? 1 solutions Answer 278915 by ankor@dixie-net.com(15652)   on 2011-01-10 19:50:27 (Show Source): You can put this solution on YOUR website!How do you calculate the amount of interest paid on a loan for \$4,000 for 2 years at 2.99%? : If it's just simple interest calculate the total amt paid A = 4000(1.0299)^2 A = \$4242.77 - 4000 = 242.77 is the total interest
 Miscellaneous_Word_Problems/392684: The perimeter of a quadrilateral (four sided polygon) is 29 inches. The longest side is twice as long as the shortest side. The other two sides are equally long and are 2 inches longer than the shortest side. Find the length of all the sides. 1 solutions Answer 278831 by ankor@dixie-net.com(15652)   on 2011-01-10 17:02:40 (Show Source): You can put this solution on YOUR website!let the 4 sides be a, b, c, d; (a is the longest, d is the shortest) : Write an equation for each statement: : The perimeter of a quadrilateral (four sided polygon) is 29 inches. a + b + c + d = 29 : The longest side is twice as long as the shortest side. a = 2d : The other two sides are equally long b = c : and are 2 inches longer than the shortest side. b = d + 2 c = d + 2 : Substitute in the perimeter equation a + b + c + d = 29 2d + (d+2) + (d+2) + d = 29 5d + 4 = 29 5d = 29 - 4 d = d = 5 : You should be able to find the other 4 sides now, see that they add up to 29
 Miscellaneous_Word_Problems/392746: I hope someone can help me I do not know how to work this out I have to solve for x and simplify as much as possible -7-3x<5 Thank you so very much1 solutions Answer 278822 by ankor@dixie-net.com(15652)   on 2011-01-10 16:52:42 (Show Source): You can put this solution on YOUR website!-7 -3x < 5 Multiply by -1 to make the coefficient of x positive, this reverses the inequality sign 3x + 7 > -5 Subtract 7 from both sides 3x > -5 - 7 3x > -12 divide both sides by 3 x > x > -4
 Problems-with-consecutive-odd-even-integers/392609: "Find four consecutive odd integers such that the sum of the second and the fourth is 17 more than one-half the sum of the first and the third." 1 solutions Answer 278769 by ankor@dixie-net.com(15652)   on 2011-01-10 15:13:20 (Show Source): You can put this solution on YOUR website!"Find four consecutive odd integers such that the sum of the second and the fourth is 17 more than one-half the sum of the first and the third." : Four consecutive odd integers: x, (x+2), (x+4, (x+6) : (x+2) + (x+6) = .5(x + (x+4)) + 17 : 2x + 8 = .5(2x + 4) + 17 : 2x + 8 = x + 2 + 17 : 2x -x = 19 - 8 : x = 11, : : 11, 13, 15, 17 are the integers : : See if that is true in the original equation 13 + 17 = .5(11+15) + 17 30 = 13 + 17
 Miscellaneous_Word_Problems/392683: Twice one number plus a second number is 42, and the first number minus the second number is -6. Find the two numbers.1 solutions Answer 278758 by ankor@dixie-net.com(15652)   on 2011-01-10 14:49:31 (Show Source): You can put this solution on YOUR website!Twice one number plus a second number is 42, and the first number minus the second number is -6. Find the two numbers. : 2x + y = 42 x - y = -6 -------------adding eliminates y. find x 3x = 36 x = x = 12 : Find y 2(12) + y = 42 y = 42 - 24 y = 18 : Check solutions in the 2nd equation 12 - 18 = -6
 Square-cubic-other-roots/392611: Here is a question I was given on my √ test. On your own paper draw a right triangle. Label the vertical height as 12 cm and the hypotenuse as 20 cm. Please solve for the base x to the nearest 3 digit decimal answer. I know I am supposed to use the Pythagorean theory but I don't think I am doing it correctly. :/ Help!1 solutions Answer 278669 by ankor@dixie-net.com(15652)   on 2011-01-10 07:56:14 (Show Source): You can put this solution on YOUR website!On your own paper draw a right triangle. Label the vertical height as 12 cm and the hypotenuse as 20 cm. Please solve for the base x to the nearest 3 digit decimal answer. : Yes, let b = the length of the base : a^2 + b^2 = c^2 12^2 + b^2 = 20^2 144 + b^2 = 400 b^2 = 400 - 144 b^2 = 254 b + b = 16 : If you did this way, you did right
 Polynomials-and-rational-expressions/392493: So what I need to know is how to simplify this expression x^9+2x^8 by factoring and then check by multiplying?1 solutions Answer 278588 by ankor@dixie-net.com(15652)   on 2011-01-09 22:13:37 (Show Source): You can put this solution on YOUR website!expression x^9+2x^8 by factoring and then check by multiplying? : Just factor out x^8 and you have x^8(x + 2); : multiply x^8 * (x+2)