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# Recent problems solved by 'Nate'

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 Travel_Word_Problems/100961: This question is from textbook Algebra I Please help.... May rides her bike the same distance Leah walks. May rides her bike 10km/h faster than Leah walks. If it takes May 1 h and Leah 3h to travel that distance, how fast does each travel?1 solutions Answer 73473 by Nate(3500)   on 2007-09-27 21:23:35 (Show Source): You can put this solution on YOUR website!distance = rate * time Leah: rate = r time = 3 distance = 3r May: rate = r + 10 time = 1 distance = r + 10 The distances were equal: 3r = r + 10 2r = 10 r = 5
 Linear_Equations_And_Systems_Word_Problems/100963: Jimmy caught a big fish, its head was 5 inches long. The tail was as long as the head plus hlf of the body. Its body was as long as the head plus the tail. How long is the fish? This is not from a textbook, but from a worksheet given by the teacher.1 solutions Answer 73470 by Nate(3500)   on 2007-09-27 21:21:28 (Show Source): You can put this solution on YOUR website!h = length of head b = length of body t = length of tail h = 5 t = h + b/2 or t = 5 + b/2 b = h + t or b = 5 + t Plug: b = 5 + t b = 5 + 5 + b/2 b/2 = 10 b = 20 Plug: t = 5 + b/2 t = 5 + 20/2 = 5 + 10 = 15 5 + 20 + 15 = 40 inches
 Mixture_Word_Problems/100790: Paint costing \$18 per gallon is to be mixed with \$2 per gallon thinner to make 48 gallons of a paint that can be sold for \$14 per gallon. How much paint thinner should be used?1 solutions Answer 73390 by Nate(3500)   on 2007-09-27 08:59:29 (Show Source): You can put this solution on YOUR website!(18(x) + 2(48 - x))/(48) = 14 18x + 2(48 - x) = 672 18x + 96 - 2x = 672 16x = 576 x = 36 48 - 36 = 12 gallons of thinner
 Rational-functions/100442: I need some help with this exquation could someone please help me. Solve for x 1 solutions Answer 73119 by Nate(3500)   on 2007-09-25 20:19:23 (Show Source): You can put this solution on YOUR website! . . . . .
 Rational-functions/100440: Could someone please help me with this equation? I cant seem to solve it. Solve for x 1 solutions Answer 73118 by Nate(3500)   on 2007-09-25 20:17:30 (Show Source): You can put this solution on YOUR website! . . . . . which is positive and negative
 Graphs/100403: The square of a number is six more than the number. Find the number1 solutions Answer 73117 by Nate(3500)   on 2007-09-25 20:15:49 (Show Source): You can put this solution on YOUR website!x^2 = x + 6 x^2 - x - 6 = 0 (x - 3)(x + 2) = 0 Either 3 or -2
 logarithm/100433: Solve for X 10^(x+3)= 5e^(7-x) I have only gotton to here: 2^(x+3)= e^(7-x)1 solutions Answer 73114 by Nate(3500)   on 2007-09-25 20:08:46 (Show Source): You can put this solution on YOUR website! . . . . . . . . .
 Graphs/100431: Dear Tutor- I am having trouble graphing these functions. Can you please explain how I should do it? Thanks! "Graph a function with the following domain and range" Domain: -4(less than)x(less than or equal to)7 Range: -2(less than)y(lessthan or equal to) 41 solutions Answer 73110 by Nate(3500)   on 2007-09-25 20:02:49 (Show Source): You can put this solution on YOUR website!f(x) = 6x/11 + 2/11 would be an example
 Expressions-with-variables/100205: This question is from textbook Algebra structure and Method My last tough problem of the night is done but I would feel much better knowing I AM DOING THEM RIGHT SO I am checking 2 of them on this site (which is AWESOME!) -50+(-2)(3(1-F)-3(-2+F)) simplify..thanks!1 solutions Answer 72974 by Nate(3500)   on 2007-09-24 22:34:53 (Show Source): You can put this solution on YOUR website! . . . . . . . .
 Quadratic_Equations/100208: Let α and β be the two roots of a quadratic equation ax^2 + 2b^x + c = 0, where a, b and c are constants. Obtain the quadratic equation whose two roots are λ and δ such that λ = α^2 + β^2 and δ = α^2 - β^2. 1 solutions Answer 72973 by Nate(3500)   on 2007-09-24 22:30:02 (Show Source): You can put this solution on YOUR website!α = (-2b + sqrt(4b^2 - 4ac))/2a and β = (-2b - sqrt(4b^2 - 4ac))/2a . (x - λ)(x - δ) = 0 . (x - α^2 - β^2)(x - α^2 + β^2) = 0 . (x - ((-2b + sqrt(4b^2 - 4ac))/2a)^2 - ((-2b - sqrt(4b^2 - 4ac))/2a)^2)(x - α^2 + β^2) = 0 . (x - (-2b + sqrt(4b^2 - 4ac))^2/4a^2 - (-2b - sqrt(4b^2 - 4ac))^2/4a^2)(x - α^2 + β^2) = 0 . (x - (4b^2 - 4b*sqrt(4b^2 - 4ac) + 4b^2 - 4ac)/4a^2 - (4b^2 + 4b*sqrt(4b^2 - 4ac) + 4b^2 - 4ac)/4a^2)(x - α^2 + β^2) = 0 . (x - (8b^2 - 8b*sqrt(b^2 - ac) - 4ac)/4a^2 - (8b^2 + 8b*sqrt(b^2 - ac) - 4ac)/4a^2)(x - α^2 + β^2) = 0 . (x - (2b^2 - 2b*sqrt(b^2 - ac) - ac)/a^2 - (2b^2 + 2b*sqrt(b^2 - ac) - ac)/a^2)(x - α^2 + β^2) = 0 . (x + (-2b^2 + 2b*sqrt(b^2 - ac) + ac)/a^2 + (-2b^2 - 2b*sqrt(b^2 - ac) + ac)/a^2)(x - α^2 + β^2) = 0 . (x + (-4b^2 + 2ac)/a^2)(x - α^2 + β^2) = 0 . (x + (-4b^2 + 2ac)/a^2)(x - ((-2b + sqrt(4b^2 - 4ac))/2a)^2 + ((-2b - sqrt(4b^2 - 4ac))/2a)^2) = 0 . (x + (-4b^2 + 2ac)/a^2)(x - (2b^2 - 2b*sqrt(b^2 - ac) - ac)/a^2 + (2b^2 + 2b*sqrt(b^2 - ac) - ac)/a^2) = 0 . (x + (-4b^2 + 2ac)/a^2)(x + (-2b^2 + 2b*sqrt(b^2 - ac) + ac)/a^2 + (2b^2 + 2b*sqrt(b^2 - ac) - ac)/a^2) = 0 . (x + (-4b^2 + 2ac)/a^2)(x + 4b*sqrt(b^2 - ac)/a^2) = 0 . x^2 + x(-4b^2 + 2ac)/a^2 + x*4b*sqrt(b^2 - ac)/a^2 + (-4b^2 + 2ac)4b*sqrt(b^2 - ac)/a^4 = 0
 Rational-functions/100072: Find the domain f(x)=7+sqrt(3x+21) and express it using interval notation1 solutions Answer 72868 by Nate(3500)   on 2007-09-24 14:13:34 (Show Source): You can put this solution on YOUR website!f(x) = 7 + sqrt(3x + 21) The only limitation to this function is the root. 3x + 21 >= 0 3x >= -21 x >= -7
 expressions/100019: Can someone please help? (–2a^2 b^3)^2 / (2a^2 b)^31 solutions Answer 72835 by Nate(3500)   on 2007-09-23 22:46:48 (Show Source): You can put this solution on YOUR website! . . . .
 absolute-value/100018: |1/2X-3|-4=61 solutions Answer 72834 by Nate(3500)   on 2007-09-23 22:43:42 (Show Source): You can put this solution on YOUR website!|1/2x - 3| - 4 = 6 |1/2x - 3| = 10 1/2x - 3 = 10 and 1/2x - 3 = -10 1/2x = 13 and 1/2x = -7 x = 26 and x = -14
 Linear-systems/100016: a no. consist of two digit whose sum is 9. if 9 is subtacted from the no.the digit interchange their places.find the no.1 solutions Answer 72833 by Nate(3500)   on 2007-09-23 22:42:00 (Show Source): You can put this solution on YOUR website!Number: 10a + b a + b = 9 or b = 9 - a 10a + b - 9 = 10b + a Plug: 10a + b - 9 = 10b + a 10a + 9 - a - 9 = 10(9 - a) + a 10a + 9 - a - 9 = 90 - 10a + a 9a = 90 - 9a 18a = 90 a = 5 b = 9 - a = 9 - 5 = 4 Number: 10a + b = 10*5 + 4 = 54
 Linear-systems/100015: the sum of the digit of a two digit no. is 15if the no. formed by reversing the digit is less than the original no. by 27.find the original no. 1 solutions Answer 72832 by Nate(3500)   on 2007-09-23 22:37:48 (Show Source): You can put this solution on YOUR website!Number: 10a + b or a,b a + b = 15 or b = 15 - a and 10b + a = 10a + b - 27 Plug: 10b + a = 10a + b - 27 10(15 - a) + a = 10a + 15 - a - 27 150 - 10a + a = 10a + 15 - a - 27 150 - 9a = 9a - 12 162 = 18a 9 = a b = 15 - a = 15 - 9 = 6 Number: 10a + b = 10(9) + 6 = 96
 Human-and-algebraic-language/99998: The sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21. What are the numbers?1 solutions Answer 72831 by Nate(3500)   on 2007-09-23 22:34:38 (Show Source): You can put this solution on YOUR website!Define the digit as: 10a + b or as a,b where a and b are interchangeable a + b = 9 or b = 9 - a and a^2 - ab + b^2 = 21 a^2 - a(9 - a) + (9 - a)^2 = 21 a^2 - 9a + a^2 + 81 - 18a + a^2 = 21 3a^2 - 27a + 60 = 0 3a^2 - 12a - 15a + 60 = 0 (3a^2 - 12a) + (-15a + 60) = 0 3a(a - 4) - 15(a - 4) = 0 (3a - 15)(a - 4) = 0 a = 4 or a = 15/3 a = 4 ... b = 9 - a = 9 - 4 = 5 45 ... or 54 because a and b are interchangeable a = 15/3 = 5 ...
 Percentage-and-ratio-word-problems/100006: how many milileters of a 20% acis solution must be mixed with 30ml of an 80% acid solution to make a 32% acid solution? i have to show a chart and fill it out 1 solutions Answer 72829 by Nate(3500)   on 2007-09-23 22:23:36 (Show Source): You can put this solution on YOUR website![80%(30) + 20%(x)]/[30 + x] = 32% [0.8(30) + 0.2x]/[30 + x] = 0.32 [24 + 0.2x]/[30 + x] = 0.32 24 + 0.2x = 0.32[30 + x] 24 + 0.2x = 9.6 + 0.32x 14.4 = 0.12x 120 = x Maybe implement different values for your chart. Use different situations to find the solution. 120mL of 20%
 Miscellaneous_Word_Problems/100007: a 16 yard fishing line is cut ino two pieces. express the longer piece in terms of the shorter1 solutions Answer 72828 by Nate(3500)   on 2007-09-23 22:19:49 (Show Source): You can put this solution on YOUR website!The longer piece is the smaller piece from the whole. l = 16 - s
 Geometric_formulas/100008: How much of a liquid with a 30% alchohol content and how much of a liquid with a 100% alcohol content should be added to end up with 42 milliiters of with a 50% alcohol content? 1 solutions Answer 72826 by Nate(3500)   on 2007-09-23 22:17:56 (Show Source): You can put this solution on YOUR website![ 100%(x) + 30%(42 - x) ]/[42] = 50% [ x + 0.3(42 - x) ]/42 = 0.5 [ x + 12.6 - 0.3x ]/42 = 0.5 [ 0.7x + 12.6 ]/42 = 0.5 0.7x + 12.6 = 21 0.7x = 8.4 x = 12 42 - x = 30 12mL of 100% and 30mL of 30%
 Miscellaneous_Word_Problems/100009: a board that is 12 feet long is cut into two pieces. one part is four more than twice the other. Find the length of each parts.1 solutions Answer 72824 by Nate(3500)   on 2007-09-23 22:14:37 (Show Source): You can put this solution on YOUR website!s = smaller board piece l = larger board piece s + l = 12 and l = 2s + 4 Plug: s + 2s + 4 = 12 3s = 8 s = 8/3 ft Plug: s + l = 12 8/3 + l = 36/3 l = 28/3 ft
 logarithm/99196: Solve: log base 2 (3x+6)- log base 2 (x-5)= log base 2 (6)1 solutions Answer 72187 by Nate(3500)   on 2007-09-19 17:50:46 (Show Source):
 Equations/99200: Solve for "d" : ax+df=r(d+e)1 solutions Answer 72186 by Nate(3500)   on 2007-09-19 17:48:20 (Show Source): You can put this solution on YOUR website!ax + df = r(d + e) ax + df = rd + re df - rd = re - ax d(f - r) = re - ax d = (re - ax)/(f - r)
 Distributive-associative-commutative-properties/99207: Okay,I totally don't get distributive,associative OR commutative properties. And I have a major test next week!! could someone PLEASE explain it? like how do you know which to use? and what's the first step? Thanks!1 solutions Answer 72183 by Nate(3500)   on 2007-09-19 17:46:26 (Show Source): You can put this solution on YOUR website!Associative Property ~> it doesn't matter how you "associate" paranthesis (2 + 3) + 4 = 2 + (3 + 4) (2*3)*4 = 2*(3*4) Communitive Property ~> it doesn't matter how the elements are moved 2 + 3 = 3 + 2 2*3 = 3*2 Distributive Property ~> done by distributing a value a(1 + 2) = 1a + 2a 4(b + c) = 4b + 4c
 Distributive-associative-commutative-properties/99217: is 7+4=4+7 a commutative properties or a associative properties?1 solutions Answer 72181 by Nate(3500)   on 2007-09-19 17:41:56 (Show Source): You can put this solution on YOUR website!additive communitive
 Polynomials-and-rational-expressions/99133: Evaluate sqrt(-121) 1 solutions Answer 72146 by Nate(3500)   on 2007-09-19 13:51:03 (Show Source): You can put this solution on YOUR website!isqrt(121) 11i
 expressions/99145: How do I set up and solve this word problem? There are 5 times as many 1\$ bills as 5\$ bills. The entire number of bills is 48. How many 1\$ bills are there? 1 solutions Answer 72145 by Nate(3500)   on 2007-09-19 13:49:49 (Show Source): You can put this solution on YOUR website!x = amount of ones y = amount of fives x = 5y and x + y = 48 Plug: x + y = 48 5y + y = 48 6y = 48 y = 8 8 five dollar bills 40 one dollar bills
 Geometry_Word_Problems/99147: Geometry. The length of a rectangular playing field is 5 ft less than twice its width.If the perimeter of the playing field is 230 ft, find the length and width of the field?1 solutions Answer 72144 by Nate(3500)   on 2007-09-19 13:47:15 (Show Source): You can put this solution on YOUR website!width = x length = 2x - 5 2*width + 2*length = 230 2(x) + 2(2x - 5) = 230 2x + 4x - 10 = 230 6x = 240 x = 40 width = x or 40 feet length = 2x - 5 or 75 feet
 Polynomials-and-rational-expressions/99146: Perform the indicated multiplication. Then simplify each radical expression sqrt7(2sqrt3+3sqrt7)1 solutions Answer 72143 by Nate(3500)   on 2007-09-19 13:43:34 (Show Source):
 Linear-equations/99138: what is the slope intercept for;2x +3y=90 ? I have m=2/3 b=30 is that correct?1 solutions Answer 72142 by Nate(3500)   on 2007-09-19 13:11:46 (Show Source): You can put this solution on YOUR website!2x + 3y = 90 3y = -2x + 90 y = -2x/3 + 30 slope = -2/3 b = 30
 Radicals/99140: The problem is to simplify and the answer said I got it wrong. Problem: My answer 5a^2b sqrt(b^3)1 solutions Answer 72141 by Nate(3500)   on 2007-09-19 13:09:50 (Show Source):
 real-numbers/98726: How many ordered pairs (x,y) of integers satisfy… (1/X)+(1/Y)=(1/2)1 solutions Answer 71855 by Nate(3500)   on 2007-09-17 16:59:19 (Show Source): You can put this solution on YOUR website!1/x + 1/y = 1/2 xy/x + xy/y = xy/2 y - xy/2 + x = 0 y(1 - x/2) + x = 0 y(2 - x)/2 = -x y = -2x/(2 - x) Infinite ordered pairs ... excluding x = 2 and x = 0