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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 provide 1 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 $575,000 1 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 number 1 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 4:3 1 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

Rational-functions/392897: Please help me solve this equation. (3+2 sqrt 2)(1+ sqrt 2) Thank you(: 1 solutions Answer 278953 by ankor@dixie-net.com(15652)   on 2011-01-10 21:13:49 (Show Source): You can put this solution on YOUR website! Please help me solve this equation. (3+2 sqrt 2)(1+ sqrt 2) but this is not an equation, perhaps they want you to FOIL this and simplify 3 + 3sqrt(2) + 2sqrt(2) + 2(2) which is 7 + 5sqrt(2) : Comment: "Thank you, do you mind showing me how you got that answer." I am ashamed to see I made a mistake here, although I got the correct answer will try to correct it step-by-step : To multiply these two factors we use the FOIL method which stands for First; Outer, Inner, Last : Multiply First terms: 3 * 1 = 3 Outer terms: 3 * sqrt(2) = 3sqrt(2) Inner terms: 2sqrt(2) * 1 = 2sqrt(2) Last terms: sqrt(2) * 2sqrt(2) = 2(2) Which gives us 3 + 3sqrt(2) + 2sqrt(2) + 4 Combine like terms 3sqrt2) + 2sqrt(2) = 5sqrt(2) 3 + 4 = 7 so we have 7 + 5sqrt(2)

Square-cubic-other-roots/392962: We are solving for "p" Equation: 4 * sqrt (2p) + 1 = 24 1 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 much 1 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)

Linear_Algebra/392483: You must buy 100 pets and spend $100. You may buy dogs, cats and mice, and you must buy at least one of each pet. Dogs cost $15, cats cost $1 and mice are 25 cents each. How many of each pet will you buy if you spend exactly $100 and buy exactly 100 pets? 1 solutions Answer 278586 by ankor@dixie-net.com(15652)   on 2011-01-09 22:10:02 (Show Source): You can put this solution on YOUR website! You must buy 100 pets and spend $100. You may buy dogs, cats and mice, and you must buy at least one of each pet. Dogs cost $15, cats cost $1 and mice are 25 cents each. How many of each pet will you buy if you spend exactly $100 and buy exactly 100 pets? : Let no. of each animal be, d, c, m : Total animal equation d + c + m = 100 Total cost equation 15d + 1c + .25m = 100 : We got three unknowns and two equations, but we know the solutions are integers Eliminate the cats 15d + 1c + .25m = 100 1d + 1c + 1m = 100 ---------------------- Subtraction eliminates c 14d - .75m = 0 or .75m = 14d m = d substitute values for d, until you get an integer value for m when you get to d = 3 m = *3 m = m = 56 mice : We have 3 dogs and 56 mice, then 100 - 59 = 41 cats : : Check that in the cost equation 15(3) + 1(41) .25(56) = 45 + 41 + 14 = 100

Numbers_Word_Problems/392407: if five times a number is increased by four less than three times the number , the result is 44 . Find the number . 1 solutions Answer 278559 by ankor@dixie-net.com(15652)   on 2011-01-09 20:46:57 (Show Source): You can put this solution on YOUR website! if five times a number is increased by four less than three times the number , the result is 44 . Find the number. : 5x + 3x - 4 = 44 8x = 44 + 4 8x = 48 x = 6

Linear-systems/392306: A two digit number is 6 times its units digit. Find the number if the sum of its digits is 6. 1 solutions Answer 278548 by ankor@dixie-net.com(15652)   on 2011-01-09 20:33:56 (Show Source): You can put this solution on YOUR website! Let x = the 10's digit Let y = the units (10x + y) is the two digit number : Write an equation for each phrase "A two digit number is 6 times its units digit." 10x + y = 6y 10x = 6y - y 10x = 5y simplify, divide by 5 2x = y : "the sum of its digits is 6." x + y = 6 replace y with 2x x + 2x = 6 3x = 6 x = 2 therefore y = 4 : 24 is the number : : Check 24 = 6*4

Miscellaneous_Word_Problems/392213: 19. A motorist travelled 115 km on an expressway at an average speed of 92 km/h and another 45 minutes on the other roads. If the average speed for his whole journey was 80 km/h, how far did he travel on the other road? 1 solutions Answer 278542 by ankor@dixie-net.com(15652)   on 2011-01-09 20:24:07 (Show Source): You can put this solution on YOUR website! 19. A motorist traveled 115 km on an expressway at an average speed of 92 km/h and another 45 minutes on the other roads. If the average speed for his whole journey was 80 km/h, how far did he travel on the other road? : Let d = distance on the other roads : Change 45 min to .75 hrs : Write a time equation: time = dist/speed : express time + road time = total time + .75 = Find least common multiple 92: 2*2*23 80: 2*2*2*2*5 LCM: 2*2*2*2*5*23 = 1840 : Multiply equation by 1840, results: 20(115) + .75(1840) = 23(d+115) : 2300 + 1380 = 23d + 2645 : 3680 - 2645 = 23d : 1035 = 23d d = d = 45 miles on other roads : : Check solution by finding the times (total dist 115 + 45 = 160 mi) 115/92 = 1.25 hrs other rd= .75 hrs ------------------- 160/80 = 2.00 hrs

Angles/392057: (9x + 3) + (7x + 1) 9x + 3 + 7x + 1= 180 16x + 4= 180 16x + 4 - 4= 180 - 4 16x= 176 x= 11 I not sure how to work 9x + 3 AND 7x + 1= measure of the larger angle and measure of the smaller angle= too get the answer correct. 1 solutions Answer 278274 by ankor@dixie-net.com(15652)   on 2011-01-08 21:50:06 (Show Source): You can put this solution on YOUR website! (9x + 3) + (7x + 1) 9x + 3 + 7x + 1= 180 16x + 4= 180 16x + 4 - 4= 180 - 4 16x= 176 x= 11 : You've done the main part, just substitute 11 for x in the two original expressions 9(11) + 3 = 102 degrees 7(11) + 1 = 78 degrees ----------------------- totals to 180 degrees which is what it should do

Linear_Equations_And_Systems_Word_Problems/392072: A collection of 90 coins, pennies, nickels, and dimes, has a value of $2.85. If there are twice as may pennies as there are nickels and dimes combined, how many pennies, dimes, and nickels are there? 1 solutions Answer 278272 by ankor@dixie-net.com(15652)   on 2011-01-08 21:43:00 (Show Source): You can put this solution on YOUR website! A collection of 90 coins, pennies, nickels, and dimes, has a value of $2.85. If there are twice as may pennies as there are nickels and dimes combined, how many pennies, dimes, and nickels are there? : p + n + d = 90 : .01p + .05n + .10d = 2.85 : "there are twice as may pennies as there are nickels and dimes combined," p = 2(n + d) divide both sides by 2 .5p = n + d .5p - n - d = 0; add to the 1st equation p + n + d = 90 ----------------------eliminates n and d find p 1.5p = 90 p = p = 60 pennies : Rewrite the two equation using p=60 n + d = 30 n = (30-d) and .05n + .10d = 2.25 Substitute (30-d) for n .05(30-d) + .10d = 2.25 1.5 - .05d + .10d = 2.25 .05d = 2.25 - 1.50 d = d = 15 dimes then obviously n = 15 nickels : : Check solutions by finding the total$ .01(60) + .05(15) + .10(15) = .60 + .75 + 1.5 = 2.85, confirms our solution p=60; n=15; d=15

Linear_Equations_And_Systems_Word_Problems/392083: Nathan's monthly electric bill includes a fixed service charge and an additional charge for the number of kilowatt-hours (kwh) of electricity used. One bill, including a charge for 595 kwh of electricity, is $61.72. Another bill, including a charge for 650 kwh, is $67.11. Find the fixed cahrge and the cost per kilowatt-hour. 1 solutions Answer 278264 by ankor@dixie-net.com(15652)   on 2011-01-08 20:54:52 (Show Source): You can put this solution on YOUR website! Nathan's monthly electric bill includes a fixed service charge and an additional charge for the number of kilowatt-hours (kwh) of electricity used. One bill, including a charge for 595 kwh of electricity, is $61.72. Another bill, including a charge for 650 kwh, is $67.11. Find the fixed charge and the cost per kilowatt-hour. : Let x = the fixed charge Let y = the cost/kwh : An equation for each month x + 650y = 67.11 x + 595y = 61.72 --------------------subtracting eliminate x find y 55y = 5.39 y = y = $.098 per kwh : Find the fixed cost (x) x + 650(.098) = 67.11 x + 63.70 = 67.11 x = 67.11 - 63.70 x = $3.41 : Check this solution in the 2nd equation 3.41 + 595(.098) = 3.41 + 58.31 = 61.72 :

Trigonometry-basics/392084: an arc of length 32 in is found in a circle with a radius of 8 in. find the measure of the central angle which intrcepts this arc 1 solutions Answer 278259 by ankor@dixie-net.com(15652)   on 2011-01-08 20:43:34 (Show Source): You can put this solution on YOUR website! an arc of length 32 in is found in a circle with a radius of 8 in. find the measure of the central angle which intercepts this arc : Find the circumference of the circle C = C = 50.2655 : Find the angle * 360 = 229.18 degrees

Equations/391955: 1. A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have traveled only 1315 miles in the same length of time. Find the speeds of the plane and ship. 2. A person invested $10,000. The greater part is invested at 6% and the remainder at 5%. The annual income from the greater part is $160 more than the annual income from the smaller part. What is the smaller part of investment? 3. What amount of mixture, one 95% alcohol and the other 15% alcohol, must be used to make 10 liters of mixture which is 45% alcohol? What equation will express this problem? 1 solutions Answer 278213 by ankor@dixie-net.com(15652)   on 2011-01-08 16:37:23 (Show Source): You can put this solution on YOUR website! 1. A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have traveled only 1315 miles in the same length of time. Find the speeds of the plane and ship. : Let x = speed of plane and Let y = speed of ship : Two distance equations; dist = time * speed : 4x + 25y = 1580 and 4(.5x) + 25(1.25y) = 1315 2x + 31.25y = 1315 : Multiply above equation by 2. Subtract the first equation 4x + 62.5y = 2630 4x + 25y = 1580 ---------------------subtraction eliminates x, find y: 37.5y = 1050 y = y = 28 mph speed of the ship : Find x using the 1st equation 4x + 25(28) = 1580 4x + 700 = 1580 4x = 1580 - 700 4x = 880 x = x = 220 mph speed of the plane : Check solution in 2nd equation: 4(110) + 25(35) = 440 + 875 = 1315 : : 2. A person invested $10,000. The greater part is invested at 6% and the remainder at 5% The annual income from the greater part is $160 more than the annual income from the smaller part. What is the smaller part of investment? : Let x = the smaller part of the investment then (10000-x) = the larger part : .06(10000-x) - .05x = 160 : : 3. What amount of mixture, one 95% alcohol and the other 15% alcohol, must be used to make 10 liters of mixture which is 45% alcohol? What equation will express this problem? : Let x = amt of 95% solution then (10-x) = amt of 15% solution : .95x + .15(10-x) = .45(10)