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# Recent problems solved by 'mastermath'

 Sequences-and-series/187032: 6x + 3y – 2x – 5y 1 solutions Answer 140195 by mastermath(14)   on 2009-03-17 10:41:26 (Show Source): You can put this solution on YOUR website!6x + 3y – 2x – 5y Bring the terms containing x together Bring the terms containing y together = (6x-2x) + (3y-5y) = 4x + (-2y) = 4x - 2y
 Problems-with-consecutive-odd-even-integers/182365: This question is from textbook The product of two consecutive integers is 4 less than four times their sum. Find the integers.1 solutions Answer 136987 by mastermath(14)   on 2009-02-18 00:46:11 (Show Source): You can put this solution on YOUR website!Let the consecutive numbers be n and (n+1) respectively. Their sum is (n + n + 1) = (2n + 1) Four times their sum = 4(2n + 1) The product of the numbers = n(n + 1) The product of two consecutive integers is 4 less than four times their sum. ---------------------------------------------------------------------------- So, the equation becomes n(n + 1) = 4 (2n + 1) - 4 n^2 + n = 8n + 4 - 4 n^2 + n = 8n Subtract 8n on both the sides n^2 + n - 8n = 8n - 8n n^2 - 7n = 0 n (n - 7) = 0 Use the zero product rule n=0 or (n-7)=0 n=0 or n=7. ---------------------------------------------------- If n=0, n+1 = 0 + 1 = 1. So, one pair of consecutive integers is 0 and 1. If n=7, n+1 = 7 + 1 = 8. So, second pair of consecutive integers is 7 and 8. ----------------------------------------------------- Cheers, Mastermath.
 Exponential-and-logarithmic-functions/182324: (4p^2q)(p^2q^3) simplify thank you!1 solutions Answer 136855 by mastermath(14)   on 2009-02-17 12:09:44 (Show Source): You can put this solution on YOUR website!(4p^2q)(p^2q^3) = 4(p^2p^2)(q^3q) = 4(p^(2+2))(q^(3+1)) Ans:= 4p^4 q^4
 logarithm/182277: Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x. 1. f(x) = 2x – 5 2. f(x) = x2 - 4x + 3 3. f(x) = x3 + 4x2 - 2x - 3 4. f(x) = 7x 5. f(x) = log x 1 solutions Answer 136854 by mastermath(14)   on 2009-02-17 12:05:09 (Show Source): You can put this solution on YOUR website!1. f(x) = 2x – 5 So, put x=1,2,4,8,16 and find the value of f(x) f(1) = 2(1) - 5 = 2 - 5 = -3 f(2) = 2(2) - 5 = 4 - 5 = -1 f(4) = 2(4) - 5 = 8 - 5 = 3 f(8) = 2(8) - 5 = 16 - 5 = 11 f(16) = 2(16) - 5 = 32 - 5 = 27 So, as the value of x increases, f(x) also increases. ------------------------------------------------------------------- 2. f(x) = x2 - 4x + 3 So, put x=1,2,4,8,16 and find the value of f(x) f(1) = (1)^2 - 4(1) + 3 = 1 - 4 + 3 = 0 f(2) = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1 f(4) = (4)^2 - 4(4) + 3 = 16 - 16 + 3 = 3 f(8) = (8)^2 - 4(8) + 3 = 64 - 32 + 3 = 35 f(16) = (16)^2 - 4(16) + 3 = 256 - 64 + 3 = 195 So,initially as the value of x increases, f(x) initially decreases from f(1) to f(2), but after that, as x increases, f(x) increases drastically. -------------------------------------------------------------------------- 3. f(x) = x3 + 4x2 - 2x - 3 So, put x=1,2,4,8,16 and find the value of f(x) f(1) = (1)^3 - 4(1)^2 -2(1) - 3 = 1 - 4(1) -2 - 3 = 1 - 4 - 5 = -8 f(2) = (2)^3 - 4(2)^2 -2(2) - 3 = 8 - 4(4) -4 - 3 = 8 - 16 - 7 = -15 f(4) = (4)^3 - 4(4)^2 -2(4) - 3 = 64 - 4(16) -8 - 3 = 64 - 64 - 11= -11 f(8) = (8)^3 - 4(8)^2 -2(8) - 3 = 512 - 4(64) -16 - 3 = 512 - 256 - 19 = 237 f(16) = (16)^3 - 4(16)^2 -2(16) - 3 = 4096 - 4(256) -32 - 3 = 4096 - 1024 - 35 = 3037 So,initially as the value of x increases, f(x) initially decreases from f(1) to f(2), but after that, as x increases, f(x) increases drastically. ------------------------------------------------------------------------------ 4. f(x) = 7x So, put x=1,2,4,8,16 and find the value of f(x) f(1) = 7(1) = 7 f(2) = 7(2) = 14 f(4) = 7(4) = 28 f(8) = 7(8) = 56 f(16) = 7(16) = 112 So, as the value of x increases, f(x) also increases. ------------------------------------------------------------------- 5. f(x) = log x So, put x=1,2,4,8,16 and find the value of f(x) f(1) = log(1) = 0 f(2) = log(2) = 0.301 f(4) = log(4) = 0.602 f(8) = log(8) = 0.903 f(16) = log(16) = 1.204 So, as the value of x increases, f(x) also increases. But the increase is very less in value compared to the above functions. --------------------------------------------------------------------------------
 Linear_Equations_And_Systems_Word_Problems/182316: If f(x)=2x^2-7x+3, find: a) f(2) answer: show our work here? b) f(-3) answer: show your work here:1 solutions Answer 136849 by mastermath(14)   on 2009-02-17 11:32:15 (Show Source): You can put this solution on YOUR website!f(x)=2x^2-7x+3 (a) f(2) answer: -3 show your work here: To find f(2), substitute 2 in place of x f(2)=2(2)^2-7(2)+3 f(2)=2(4)-14+3 f(2)=8-14+3 f(2)=-3 ------------------------------------------ (b) f(-3) answer: 42 show your work here: To find f(-3), substitute -3 in place of x f(-3)=2(-3)^2-7(-3)+3 f(-3)=2(9)+21+3 f(-3)=18+21+3 f(-3)=42
 Square-cubic-other-roots/182248: 5x^4y-10x^2y^21 solutions Answer 136806 by mastermath(14)   on 2009-02-16 21:43:05 (Show Source): You can put this solution on YOUR website!5x^4y-10x^2y^2 We can take 5x^2y common from the two terms 5x^2y(x^2-2y)Ans:
 Problems-with-consecutive-odd-even-integers/182250: find three consective odd intergers such that three time the middle interger isseven more then the sum of the first and thrid interger. I know x= 1st, x+3 is 2nd and x+4 is thrird. I keep seting up as 3x=3(x+x+4)+71 solutions Answer 136782 by mastermath(14)   on 2009-02-16 20:04:40 (Show Source): You can put this solution on YOUR website!Let the three consecutive odd integers be: 1st number = x 2nd number = x+2 3rd number = x+4 three time the middle integer is seven more then the sum of the first and third integer. The sum of the first and the third integer is x+(x+4)= 2x+4. The three times the middle integer is 3(x+2). So, the equation becomes 3(x+2) = 7+ (2x+4) 3x + 6 = 7 + 2x + 4 3x + 6 = 11 + 2x now, subtract 2x on both the sides 3x + 6 - 2x = 11 + 2x - 2x x + 6 = 11 now, subtract 6 on both the sides x + 6 - 6 = 11 - 6 x = 5 So, 1st number = x = 5 2nd number = x+2 = 5 + 2 = 7 3rd number = x+4 = 5 + 4 = 9. Ans: So, the three consecutive odd integers are 5,7 and 9. ---------------------------------------------------------- Proof: Summation of 1st and 3rd number =5 + 9 = 14 Adding 7 to it we get 14 + 7 = 21. Three times second number = 7(3) = 21.
 Numbers_Word_Problems/182231: Q.(((The product of two consecutive even numbers is 12 more than the square of the smaller number. Form an equation and solve it to find the numbers))).1 solutions Answer 136777 by mastermath(14)   on 2009-02-16 19:48:24 (Show Source): You can put this solution on YOUR website!Let x and (x+2) be the two consecutive even numbers. Their product is x(x+2). The product of two consecutive odd numbers is 12 more than the square of the smaller number. The smaller number is x. so, the equation becomes x(x+2)= x²+ 12 x² + 2x = x² + 12 We can subtract x² on both the sides. 2x=12 now divide with 2 on both the sides x=6. x+2=6+2=8. So, the smaller odd number is 6. And the larger odd number is 8. Proof: The product of two consecutive even numbers is 12 more than the square of the smaller number. The product of the numbers is 6 and 8 is 48. Square of the smaller number (here 6) is 36. So, add 12 to 36 so, 12 + 36 = 48.
 Polynomials-and-rational-expressions/182245: This question is from textbook algebra II x2 + 9x = -201 solutions Answer 136775 by mastermath(14)   on 2009-02-16 19:37:06 (Show Source): You can put this solution on YOUR website!x²+ 9x = -20 First, add 20 on both the sides x²+ 9x + 20 = -20 + 20 x²+ 9x + 20 = 0 Now split 9x as sum of 4x and 5x x²+ 4x + 5x +20=0 Now, take x common from the first two terms. And take 5 common from the next two terms. x(x+4)+5(x+4)=0 (x+4)(x+5)=0 Using the zero-product rule If the product of two numbers is 0, then either of the numbers is 0 so, (x+4)=0 or (x+5)=0 thus, x=-4 or x=-5 Ans: x=-4,-5 Proof: Put x=-4 in the equation x²+ 9x= (-4)²+9(-4) = 16 - 36 = -20 now put x=-5 in the equation x²+ 9x= (-5)²+9(-5) = 25 - 45 = -20 Thus, both the values are satisfied.
 Numbers_Word_Problems/182112: Q. (((The product of two consecutive odd numbers is 10 more than the square of the smaller number))).1 solutions Answer 136742 by mastermath(14)   on 2009-02-16 15:28:22 (Show Source): You can put this solution on YOUR website!Let x and (x+2) be the two consecutive odd numbers. Their product is x(x+2). The product of two consecutive odd numbers is 10 more than the square of the smaller number. The smaller number is x. so, the equation becomes x(x+2)= x²+ 10 x² + 2x = x² + 10 We can subtract x² on both the sides. 2x=10 now divide with 2 on both the sides x=5. x+2=5+2=7. So, the smaller odd number is 5. And the larger odd number is 7.
 Graphs/182065: Two of the top grossing concert tours were by a jazz band and a rock band. Together the two tours visited 174 cities. The jazz band visited 96 cities more than the rock band. How many cities did each group visit. Jazz band _____ Rock band _____1 solutions Answer 136741 by mastermath(14)   on 2009-02-16 15:10:31 (Show Source): You can put this solution on YOUR website!Let the number of cities visited by Rock band be x. The jazz band visited 96 cities more than the rock band. So, the number of cities visited by Jazz band will be (x+96). Together the two tours visited 174 cities. So, add them together. Rock + Jazz = 174 x+(x+96)=174 2x+96=174 Now, subtract 96 on both the sides 2x+96-96=174-96 2x=78 Now, divide with 2 on both the sides x=39 Thus, x+96 = 39+96 =135. So, the number of cities visited by Rock band is 39. And the number of cities visited by Jazz band is 135.
 Linear-systems/182217: Please help, I'm not good at word problems. Two of the top grossing concert tours were by a jazz band and a rock band. Together, the two tours visited 174 cities. The jazz band visited 96 cities more than the rock band. How many cities did each group visit. Jazz Band Rock Band1 solutions Answer 136738 by mastermath(14)   on 2009-02-16 14:55:58 (Show Source): You can put this solution on YOUR website!Let the number of cities visited by Rock band be x. The jazz band visited 96 cities more than the rock band. So, the number of cities visited by Jazz band will be (x+96). Together, the two tours visited 174 cities. So, add both of them Rock + Jazz = 174 x+(x+96)=174 2x+96=174 subtract 96 on both the sides 2x+96-96=174-96 2x=78 Divide with 2 on both the sides x=39 so, x+96 = 39+96 = 135 Thus,the number of cities visited by Rock band is 39. And the number of cities visited by Jazz band is 135.
 Linear-systems/182160: Please help me to solve this equation: .1 solutions Answer 136735 by mastermath(14)   on 2009-02-16 14:41:05 (Show Source): You can put this solution on YOUR website!2(x+3)-5=x+7 First remove the brackets using distributive property 2x+2(3)-5 = x+7 2x+6-5=x+7 2x+1=x+7 Now subtract x on both the sides 2x+1-x= x+7-x x+1=7 Subtract 1 on both the sides x+1-1=7-1 x=6
 Signed-numbers/182074: (-w²-9w+4-(8w²-4)+(6w²-w+9)1 solutions Answer 136733 by mastermath(14)   on 2009-02-16 14:26:26 (Show Source): You can put this solution on YOUR website!(-w²-9w+4-(8w²-4)+(6w²-w+9) First remove the brackets -w²-9w+4-8w²+4+6w²-w+9 Now bring the like terms together The terms containing w and w² (-w²-8w²+6w²)-9w-w+9 (-9w²+6w²)-10w+9 -3w²-10w+9