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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
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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
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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):
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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) 4
1 solutions
Answer 73110 by Nate(3500) on 2007-09-25 20:02:49 (Show Source):
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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
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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
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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
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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 ...
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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%
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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%
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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
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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
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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
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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):
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