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Linear-systems/54707: A crate of grapefruit has a total mass of 4 kg. When 12 grapfruit are removed, the total mass is 3kg. Determine the mass of the crate and of the grapefruit.
I have an answer but i'm just making sure. Thx
1 solutions

Answer 36922 by Nate(3500) on 2006-10-04 19:29:52 (Show Source):

You can put this solution on YOUR website!
Well, you can easily understand that every 12 grapefruit gives us 1kg.
1/12 kg is the weight of one grapefruit

Money_Word_Problems/54549: Peanuts are selling for $2 per pound, and cashews are selling
for $5 per pound. How much of each type of nut would be needed to create
20 lb of a mixture that would sell for $2.75 per pound?
1 solutions

Answer 36805 by Nate(3500) on 2006-10-03 21:30:46 (Show Source):

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x = number of peanutes
y = number of cashews
(2x + 5y)/20 = 2.75 where x = 20 - y
(2(20 - y) + 5y)/20 = 2.75
40 - 2y + 5y = 55
3y = 15
y = 5
plug: x = 20 - y ~> x = 20 - 5 ~> x = 15
15lb of peanuts
5lb of cashews

Rational-functions/54544: This question is from textbook McDougal Littell Algebra 1 concepts and skills
this is really confusing.
arthur can wash a car in 30 minutes, Bonnie can wash a car in 40 minutes, and Claire can wash a car in 60 minutes. How will it take them to wash a car, working together?
so, i dont get how you organize all this and get an answer.
1 solutions

Answer 36803 by Nate(3500) on 2006-10-03 21:26:06 (Show Source):

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Work: t/30
Work: t/40
Work: t/60
t/30 + t/40 + t/60 = 1
120t/30 + 120t/40 + 120t/60 = 120
4t + 3t + 2t = 120
9t = 120
t = 40/3 or About 13.33 hours

Rational-functions/54537: This question is from textbook McDougal Littell Algebra 1 concepts and skills
i do not understand how to even start this problem. it says:
With your new lawn mower, you can mow a lawn in 4 hours. With an older mower, your friend can mow the same lawn in 5 hours. How long will it take you to mow the lawn, working together?
HELP!
1 solutions

Answer 36797 by Nate(3500) on 2006-10-03 21:13:17 (Show Source):

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Rate: 1/4
Time = t
Rate * Time = Work
t/4 = Work
Rate: 1/5
Time = t
Work = t/5
t/4 + t/5 = 1
20t/4 + 20t/5 = 20
5t + 4t + 20
9t = 20
t = 20/9
or 2 hours 13 minutes

testmodule/54538: Solve for n: L=a+(n-1)d
Thanks!
1 solutions

Answer 36796 by Nate(3500) on 2006-10-03 21:10:49 (Show Source):

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L = a + dn - d
L - a + d = dn
(L - a + d)/d = n

Distributive-associative-commutative-properties/54535: This question is from textbook Beginning Algebra
Hope I am in the right place with this question.
Factor each of the following trinomials completely.
2a^3-52a^2b+96ab^2.
I got as far as ...
2a(a^2-26ab+48b^2). Then I got completely lost.
1 solutions

Answer 36792 by Nate(3500) on 2006-10-03 21:05:28 (Show Source):

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2a(a^2 - 26ab + 48b^2) factors of 48 that sum to -26 ~> -2 and -24
2a(a - 2b)(a - 24b)

Distributive-associative-commutative-properties/54519: This question is from textbook Algebra Structure and Method
(7-2x)subtracted from (11-2x).
1 solutions

Answer 36791 by Nate(3500) on 2006-10-03 21:02:31 (Show Source):

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11 - 2x - 7 + 2x
Answer: 4

Rectangles/54536: This question is from textbook Beginning Algebra
Word problem;
The area of a rectangle of length x is given by 3x^2+5x. Find the width of the rectangle.
1 solutions

Answer 36789 by Nate(3500) on 2006-10-03 20:57:31 (Show Source):

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area/length = width
(3x^2 + 5x)/x = 3x + 5

Complex_Numbers/54529: Not sure if I did this right...
√-3 - √-75
I came up with √3i - 5√3i
Thanks!
1 solutions

Answer 36788 by Nate(3500) on 2006-10-03 20:56:33 (Show Source):

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sqrt(-3) - sqrt(-75)
i*sqrt(3) - i*sqrt(3*5*5)
i*sqrt(3) - 5i*sqrt(3)
sqrt(3)(i - 5i)
sqrt(3)(-4i)
-4i*sqrt(3)

Radicals/54534: √(6x+1)= x-1 Solve.
I got 6x+1=x^2-2x+1
Subtracted 6x and 1 and got 0=x^2-8x+0
x(x-8)
x=0
x=8
What did I do wrong?
Thanks
1 solutions

Answer 36787 by Nate(3500) on 2006-10-03 20:54:40 (Show Source):

You can put this solution on YOUR website!
You need to check your answers with square root values.
sqrt(6 * 0 + 1) = 0 - 1
sqrt(1) = -1 Wrong *even though sqrt(1) = +- 1
sqrt(6 * 8 + 1) = 8 - 1
sqrt(49) = 7 True

Quadratic_Equations/54474: 1. A baseball hit straight up in the air is at height h feet above the ground, whre h is given by h(t)= 4+50t-16t², t seconds after being hit.
A)State a reasonable domain for this function
B)What is the y -intercept? Interpret the y-intercept relative to this situation
C)When does the baseball hit the ground?
D)When, if ever, is it 30 feet high? 90 feet high?
E)What is the maximum height that the baseball reaches? When does it reach that height?
P.S. I have been sick for like a week and returning to school tom. i have to turn in this worksheet, i was not there so i am freaking out how to do this. I think the y-intercept is 4, would the domain be all real numbers. Please help If you can, thanks
1 solutions

Answer 36785 by Nate(3500) on 2006-10-03 20:52:38 (Show Source):

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A)
Well, for a vertical parabola, the domain is always all real numbers (unless acted upon by a different source - not a parabola.) The domain is all real values.
B) Y - Intercept
y = -16(0)^2 + 50(0) + 4
y = 4
(0,4)
C)
0 = -16t^2 + 50t + 4
0 = 8t^2 - 25t - 2
x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%2825+%2B-+sqrt%28+-25%5E2+-+4%2A8%2A-2+%29%29%2F%282%2A8%29+

x+=+%2825+%2B-+sqrt%28+625+%2B+64+%29%29%2F%2816%29+

x+=+%2825+%2B-+sqrt%28+689+%29%29%2F%2816%29+

about 3.2 seconds
D)
f(x) = -16t^2 + 50t + 4
v(1.5625,68.56640625)
The highest the ball will go is about 68 feet.
30 = -16t^2 + 50t + 4
0 = -16t^2 + 50t - 26
0 = 8t^2 - 25t + 13
x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%2825+%2B-+sqrt%28+-25%5E2+-+4%2A8%2A13+%29%29%2F%282%2A8%29+

x+=+%2825+%2B-+sqrt%28+625+-+416+%29%29%2F%2816%29+

x+=+%2825+%2B-+sqrt%28+209+%29%29%2F%2816%29+

About 2.5 seconds
E)
v(1.5625,68.56640625) Vertex explains it all.
You might have to check if that is right (the vertex).

Rational-functions/54469: I need help in finding the real and imaginary zeros to:
U(x)= x^4-4x^3+x^2-12x-12
Am I correct in that the possible zeros would be +-1,+-2,+-3,+-12?
Thanks.
1 solutions

Answer 36781 by Nate(3500) on 2006-10-03 20:21:36 (Show Source):

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a = factors of constant
a = 1, 2, 3, 4, 6, 12
b = factors of leading coefficient
b = 1
+- a/b = possible zeroes
+-1, +-2, +-3, +-4, +-6, +-12

Geometry_proofs/54487: Factor:
(a+b)^3+8
1 solutions

Answer 36780 by Nate(3500) on 2006-10-03 20:19:51 (Show Source):

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C(3,0)a^3b^0 + C(3,1)a^2b^1 + C(3,2)a^1b^2 + C(3,3)a^0b^3 + 8
a^3 + 3a^2b + 3ab^2 + b^3 + 8
That is a speedy way.

Human-and-algebraic-language/54525: the sum of three consecutivee numbers is 27. what are the numbers?
1 solutions

Answer 36779 by Nate(3500) on 2006-10-03 20:17:34 (Show Source):

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First Number = i
Second Number = i + 1
Third Number = i + 2
i + i + 1 + i + 2 = 27
3i + 3 = 27
3i = 24
i = 8
The numbers are: 8,9, and 10

Human-and-algebraic-language/54524: andy is 6 years older than tom. the sum of thier ages is 26. how old are they?
1 solutions

Answer 36778 by Nate(3500) on 2006-10-03 20:16:21 (Show Source):

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Andy = x + 6
Tom = x
x + x + 6 = 26
2x = 20
x = 10
Tom is 10 years old. Andy is 16 years old.

Geometry_proofs/54488: x^9-y^9
1 solutions

Answer 36777 by Nate(3500) on 2006-10-03 20:15:24 (Show Source):

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(x^3)^3 - (y^3)^3 = (x^3 - y^3)(x^6 + x^3y^3 + y^6)
(x)^3 - (y)^3 = (x - y)(x^2 + xy + y^2)
(x - y)(x^2 + xy + y^2)(x^6 + x^3y^3 + y^6) And so on....

Functions/54491: Solve the equation
a + b + c = 5
4a + 2b + c = 11
9a + 3b + c = -3

1 solutions

Answer 36776 by Nate(3500) on 2006-10-03 20:11:43 (Show Source):

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-a - b - c = -5
4a + 2b + c = 11
~> 3a + b = 6 or as: b = 6 - 3a
4a + 2b + c = 11
-9a - 3b - c = 3
~> -5a - b = 14
Plug:
-5a - (6 - 3a) = 14
-5a - 6 + 3a = 14
-2a = 20
a = -10
Plug:
b = 6 - 3a
b = 6 + 30 = 36
Plug:
a + b + c = 5
-10 + 36 + c = 5
c = -21

Functions/54493: Evaluate
f(x)=3x^2-4x-3 at f(x-1)
am i posting this question in the right place?
1 solutions

Answer 36775 by Nate(3500) on 2006-10-03 20:07:46 (Show Source):

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f(x) = 3x^2 - 4x - 3
f(x - 1) = 3(x - 1)^2 - 4(x - 1) - 3
f(x - 1) = 3(x^2 - 2x + 1) - 4x + 4 - 3
f(x - 1) = 3x^2 - 6x + 3 - 4x + 1 = 3x^2 - 10x + 4

Square-cubic-other-roots/54498: I am stuck on correct answer for:
(y^2 - 4y + 3) - (4y^2 + 5Y - 2) =

I am not using any specific book. I am just practicing...
1 solutions

Answer 36774 by Nate(3500) on 2006-10-03 20:05:09 (Show Source):

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y^2 - 4y + 3 - 4y^2 - 5y + 2
-3y^2 - 9y + 5

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ay%5E2%2Bby%2Bc=0

(in our case -3y%5E2%2B-9y%2B5+=+0

) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

Discriminant d=141 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+141+%29%29%2F2%5Ca

y%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+141+%29%29%2F2%5C-3+=+-3.47905701450632

y%5B2%5D+=+%28-%28-9%29-sqrt%28+141+%29%29%2F2%5C-3+=+0.479057014506319

Quadratic expression -3y%5E2%2B-9y%2B5

can be factored:
-3y%5E2%2B-9y%2B5+=+-3%28y--3.47905701450632%29%2A%28y-0.479057014506319%29

Again, the answer is: -3.47905701450632, 0.479057014506319. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B-9%2Ax%2B5+%29

Human-and-algebraic-language/54521: 3 times a number plus 8 is equal to five times the number. how do you solve this proublem
1 solutions

Answer 36773 by Nate(3500) on 2006-10-03 20:03:15 (Show Source):

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3x + 8 = 5x
3x - 3x + 8 = 5x - 3x
8 = 2x
4 = x

Square-cubic-other-roots/54497: I am stuck on correct answer for:
if 7 - sq. root of x = 4, then x =

I am not using any specific book. I am just practicing...
1 solutions

Answer 36772 by Nate(3500) on 2006-10-03 20:02:22 (Show Source):

You can put this solution on YOUR website!
7 - sqrt(x) = 4
- sqrt(x) = -3
sqrt(x) = 3
x = 9

Square-cubic-other-roots/54501: I am stuck on correct answer for:
X-1 over 2X TIMES X over X^2 - 1 =

I am not using any specific book. I am just practicing...
1 solutions

Answer 36771 by Nate(3500) on 2006-10-03 20:01:25 (Show Source):

You can put this solution on YOUR website!
(x - 1)/2x * x/(x^2 - 1)
(x(x - 1))/(2x(x - 1)(x + 1))
1/(2(x + 1))
1/(2x + 2)

Human-and-algebraic-language/54520: the sum of 20 and a number is 30
1 solutions

Answer 36770 by Nate(3500) on 2006-10-03 19:59:52 (Show Source):

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x + 20 = 30
x = 10

Square-cubic-other-roots/54505: I am stuck on correct answer for:
(3 x 10^2) x (2 x 10^-3) = =

I am not using any specific book. I am just practicing...
1 solutions

Answer 36769 by Nate(3500) on 2006-10-03 19:59:17 (Show Source):

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3 x 10^2 x 2 x 10^-3 = ?
3 x 2 x 10^2 x 10^-3 = ?
6 x 10^-1 = 0.6

Distributive-associative-commutative-properties/54516: This question is from textbook Algebra Structure and Method
The opposite of the difference between x and 4.
1 solutions

Answer 36768 by Nate(3500) on 2006-10-03 19:57:48 (Show Source):

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-(x - 4)
-x + 4

percentage/54518: The price of a swimming pool has been discounted 20%. The sale price is 1210.75. What is the orignial list price of the pool?
Similar problem already solved but don't know how!-Discounted 16.5%, Sale price 1210.75. Find original price.
x-.165x=1210.75
.835x=1210.75 But Where did I get .835 from?!?
.835 .835
x=1450.
1 solutions

Answer 36767 by Nate(3500) on 2006-10-03 19:57:19 (Show Source):

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x - .165x = 1210.75
x(1 - .165) = 1210.75
x(.835) = 1210.75
x = 1450

Volume/54367: This question is from textbook Algebra 1
Problem:
A right circular cylinder has a radius of 10 inches and a height of 20 inches. Find the volume of the right circular cylinder.
Radius=10 inches
Height= 20 inches
Formula (guess) : (pi x r)h

This is how i worked it out:
10 x 3.14=31.4 x 20= 628 in.

I miss these kind of problems everytime on homework and on test. I really need help.
1 solutions

Answer 36673 by Nate(3500) on 2006-10-02 22:07:07 (Show Source):

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I think a right circular cylinder is just a normal cylinder, right?
Volume = (pi)r^2 * h = (pi)(100)(20) = 6,283.19 in^3

Graphs/54388: This question is from textbook College Algebra
Write the standard from of the equation and the general form of the equation of each circle of radius r and center (h,k);graph each circle.

The problem says: r=4; (h,k)=(2,-3)
1 solutions

Answer 36672 by Nate(3500) on 2006-10-02 22:04:09 (Show Source):

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(x - 2)^2 + (y + 3)^2 = 16

Surface-area/54380: I hope this is the right topic! I am not sure where to start with this....
The volume of the box is represented by (x^2+5x+6)(x+5). Find the polynomial that represents the area of the bottom of the box.
Thank you in advance!
ac
1 solutions

Answer 36669 by Nate(3500) on 2006-10-02 21:56:33 (Show Source):

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Volume = Area * Height
Area = x^2 + 5x + 6 or (x + 2)(x + 3)

Geometry_proofs/54378: factor completely.
512x^3-1
1 solutions

Answer 36668 by Nate(3500) on 2006-10-02 21:55:01 (Show Source):

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(8x)^3 - (1)^3
(8x - 1)(64x^2 + 8x + 1)

Pythagorean-theorem/54413: This question is from textbook TRIGONOMETRY
PLEASE HELP ME WITH THIS PROBLEM:
Let f(x)=x^3-8x^2+17x-9. Use the factor theorem to find other solutions to f(x)-f(1)=0, besides x=1.
1 solutions

Answer 36667 by Nate(3500) on 2006-10-02 21:51:54 (Show Source):

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f(x) = x^3 - 8x^2 + 17x - 9
f(1) = 1 - 8 + 17 - 9 = -7 + 8 = 1
f(x) - f(1) = 0
x^3 - 8x^2 + 17x - 9 - 1 = 0
x^3 - 8x^2 + 17x - 10 = 0
(x - 1)(x^2 - 7x + 10) = 0 use Descarte's Rule of Signs and all that stuff
(x - 1)(x - 5)(x - 2) = 0
x = 1 and x = 5 and x = 2
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E3+-+8x%5E2+%2B+17x+-+10%29

graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E3+-+8x%5E2+%2B+17x+-+10%29

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Recent problems solved by 'Nate'