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33_1/3 = 33.33
1/3 = 0.33
Are they the same?
You tell me.

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Solve 4/n - 1/2 = -6/3n.

Multiply each fraction by 6n.
This is done to remove the fractions.
After doing the math, we get 24 - 3n = -12.
We now solve for n.
-3n = -12 - 24
-2n = -36
n = -36/-2
n = 18

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This question is incomplete.
Where's the rest of the question?

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12a^5/6a
Just divide the top by the bottom.
12/6 = 2
a^5/a = a^4
Final answer: 2a^4

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(2x-3)(3x-2)
Just multiply using FOIL.
2x times 3x = 3x^2
2x times -2 = -4x
-3 times 3x = -9x
-3 times -2 = 6
We now have 3x^2 - 4x - 9x + 6.
Combine like terms and you're done.
Final answer: 3x^2 - 13x + 6

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x = -2y
This is a linear function.
All you need is two points to graph it.
Linear functions make straight lines. The word linear means line.
There are many ways to find points.
Let x = 0
0 = -2y
0/-2 = y
0 = y
One point to graph is (0,0). This particular point is called the origin.
It's where the x and y axis meet.
Solving for y, we get the equation y = x/-2.
If we let x = 2, y = -1.
This makes the point (0, -1).
Plot these two points on the xy-plane and connect the points with a straight line going from quadrant 2 down through the origin into quadrant 4.

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To find the y-intercept, set x = 0 and solve for y.
To find the x-intercept, set y = 0 and solve for x.
Sample:
Given the function f(x) = -2x^2 - 5x + 4, find the intercepts.
Let x = 0 and solve for y.
f(0) = -2(0)^2 - 5(0) + 4
f(0) = 0 + 0 + 4
f(0) = 4
The y-intercept is the point (0,4).
==================================
Now, let y = 0 and solve for x.
Keep in mind that y = f(x). So, set f(x) = 0 and solve for x.
0 = -2x^2 - 5x + 4
2x^2 + 5x - 4 = 0
This quadratic only factors using the quadratic formula.
After doing the math, I got:
x = (-5 ± √57)/4
So, the x-intercepts are the points ((-5 +√57)/4), 0) and ((-5 -√57)/4), 0).
The reason I got this odd-looking x value is because the function I selected did not factor other than using the quadratic formula.

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60 - 3 = 57
1188/57 = $20.84
If you're looking for the original purchase price, you'd just divide by 2.
Each cassette was sold for $20.84 cents.
THE PROVE:
57 cassettes at $20.84 each = $1187.88, which can be rounded to the nearest unit to become $1188 (the profit made by the store).

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BIG TIP: Post one question at a time or else your questions will be ignored by the tutors.
First of all, question 1 is incomplete. Where is the question?
Understand?
2)The Perimeter of a rectangle is 600. The length of the rectangle is 2 more than 3 times the width.

Question 2 is also imcomplete. Where is the question?
3)3 times the first of three consecutive numbers is 4 more than 2 times the second.

The third question is also incomplete. Where is the question?
What are we solving for per question?

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BIG TIP: Post one question at a time or else no one will reply.
I will do: Given the function g(v) = 3v+4, find g(5), g(-7), and g(6.7).
Replace v with each given value simplify individually.
Let v = 5
g(5) = 3(5) + 4
g(5) = 15 + 4
g(5) = 19
===============
Let v = -7
g(-7) = 3(-7) + 4
g(-7) = -21 + 4
g(-7) = -17
===============
Let v = 6.7
g(6.7) = 3(6.7) + 4
g(6.7) = 20.1 + 4
g(6.7) = 24.1

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No such equation for your expression.
However, x ≠ y means that x and y do not represent the same value.
If we let x = 5 and y = 3, we can then say that 5 ≠ 3.

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It's easier working with improper fractions than with mixed numbers.
So, we change 15_2/3 days to 47/3 days.
Also, let t = the time is takes Rebecca to write her research paper.
Here is your equation:
47/3 = 9t/10
Can you solve for t now?

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What do you want to do with this function?

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What do you want to do with your function?
What are the directions?

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12P4 + 10P4 =
The number of permutations of n objects taken r at a time is:
nPr = n!/(n - r)!
We each separately and then add the results.
12P4 = 12!/(12 - 4)!
12P4 = 479001600/8!
12P4 = 479001600/40320
12P4 = 11,880
=============================================
10P4 = 10!/(10 - 4)!
10P4 = 3628800/6!
10P4 = 3628800/720
10P4 = 5040
=============================================
We now add both.
12P4 + 10P4 = 11,880 + 5040
12P4 + 10P4 = 16,920 ways

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What proof? Where is it?

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The y-intercept form for an equation is y = mx + b, where m is the slope and b is the y-intercept.
We need to change your equation into the form y = mx + b.
To do so, we isolate y on the left side of the equation.
3x - 2y = 5
-2y = -3x + 5
y = (-3x + 5)/-2

y = (3/2)(x) - 5/2
From this final equation, we know that m = 3/2 and b = -5/2

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In distance word problems, times is measured in miles per hour not minutes.
This means we need to convert hours to seconds.
We also need to use the formula D = rt, where D = distance, r = rate or speed and t = time in hours and then solve for t.
100 = 35t
Solving for t, we get 100/35 = t.
We now convert 100/35 hours to seconds.
100/35 in terms of seconds is about 10285.714285714

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What exactly are you trying to do here?
Are you trying to solve for a specific variable?
Consecutive integers can be more generally represented by x, x +1, x + 2,
x + 3, etc where x is any integer.
Let x = the lesser number
Let x + 1 = the greater number
2x = (x + 1) - 12
Can you solve for x now?

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22-42=4(x-1)
22 - 42 = 4x - 4
-20 = 4x - 4
-20 + 4 = 4x
-16 = 4x
-16/4 = x
-4 = x
THE PROVE:
Let x = -4
22 - 42 = 4((-4)-1)
-20 = 4(-5)
-20 = -20
The answer is x = -4

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6(5+c)=5(c-4)
30 + 6c = 5c - 20
6c - 5c = -30 - 20
c = -50

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Do you have a list of the points to choose from?

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Which of the following? Where is your list?

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2x - y ≥ 4
Here's a good math site that teaches how to graph inequalities:
http://www.purplemath.com/modules/ineqgrph.htm
Check it out. If you do not understand the site, write back.

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Which variable are you solving for?
Are you solving for x, y, p or q?
Understand?
Write back....

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What are you solving for?
This question is incomplete.
Please, send the entire question.
In other words, are you solving for x or y?

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Treat it like a regular equation.
(k/5) + 2 > 6
Multiply each term by 5.
After doing so, we get k + 10 > 30.
Subtract 10 from 30.
k > 30 - 10
k > 20
This means that for your inequality to be a true statement, the values of k must be greater than 20.
THE PROVE:
Say k = 25
(25/5) + 2 > 6
5 + 2 > 6
7 > 6....This is a true statement because 7 is bigger than 6.
What about if k = 15?
(15/5) + 2 > 6
3 + 2 > 6
5 > 6....This is not true because 5 is not bigger than 6.
Understand?
The correct answer is k > 20.

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Volume = lenth * width * height
V = LWH
105 = 6*3.5*H
105 = 21H
105/21 = H
5 = H
The height is 5 inches.

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Sara has twice as much money as Miguel. If she had $6 more, she would have 4/3 as much money as he has. How much money does each have now?
Sara:
money = 2x
Miguel:
money = x

2x + 6 = (4/3)(x)
Can you solve for x now?

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Least to greatest: .23, 2.3, 23

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There are 60 seconds in one minute.
There are 60 minutes in one hour.
So, 60 times 60 = 3600 seconds = 1 hour.
Then 3600 times 10 hours = 36,000 seconds.