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The GCF is the largest common factor of . To find the powers of x and y, always use the LOWEST power of each factor.

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Conic Sections Summary --

If the coefficients of and are of the same sign, but unequal coefficients, then the graph will be an ELLIPSE.

If both coefficients are the same sign with equal coefficients, it will be a CIRCLE.

If coefficients are of opposite sign, then it will be a HYPERBOLA.

A PARABOLA results when there is an but no or a but no .

The preferred method of solving such a problem is the method of completing the square:


You must first factor out the coefficients of x^2 and y^2 like this:




This is an ellipse. The standard form for an ellipse is in a form = 1, so divide both sides of the equation by 25 to set it equal to 1.


Finally invert the coefficients of 4 and 9 in order to write this:


That would be standard form for an ellipse! The center is at (2,-1), with the "radius" extending units in the x direction, and units in the y direction.


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Therefore n= 21

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P.S. Nice problem!!

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where x=2 simply means .

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3y=0, so y = 0

4x= 0, so x = 0

(0,0)

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We don't have a book, so we have no idea what the question is! You'll have to give something to work with here . . .

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–3(10x – 3) + 10(3x – 3) = x – 7
-30x + 9 + 30x - 30 = x-7
-21= x-7

Add + 7 to each side:
-21+7= x - 7 + 7
-14 = x

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3x - 2y = 6

First you must get the x term alone, in this case, on the left side, by adding +2y to each side:
3x= 6+2y

Next, divide each side by 3:



There are other ways to solve this equation that are equally correct. You might have written it like this:

or

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Do you mean ??
If so, then square both sides of the equation:



There is no solution to this equation. Perhaps I misunderstood what you meant. Did you perchance mean: or maybe ?? Maybe you can indicate with parentheses exactly what is supposed to be inside the square root symbols.

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If the system is linear, and x=8, then there is a unique solution. There will be one and only one solution to the system!

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The variable x compared to is obviously NOT a linear relationship!!

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Assuming that you meant




The correct answer is B)

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Profit = Selling Price - Cost for each disk
Profit = 13.75 - 4.85 = $8.90

Let x = number of disks to break even
Then, 8.90x= 5874
copies.

The correct answer is A)

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As I explained in the previous exercise, I interchange the x and y, and solve for y.
y = 5x^3 + 8

Step 1: Interchange the x and y:
x = 5y^3 + 8

Step 2: Solve for y:
x-8 = 5y^3


Take the cube root of each side:



This is what I got!! I think you are correct!! Why do you think it does not work???

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There are a few different ways to do this, and I don't want to conflict with your teacher or your textbook, but I like to find the inverse function in TWO steps: 1. Interchange the x and y, and 2. Solve for y.

So, y = 3x+4

Step 1: Interchange the x and y:
x= 3y +4

Step 2: Solve for y:
x-4 = 3y

Divide both sides by 3:
.

So, or

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You got it!!!

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First graph the equation 2x+3y = 6, which has x intercept: y=0, x= 3; and y intercept: x=0, y=2. Draw a DOTTED line, since you do NOT want to include the line, and shade the area ABOVE the line, since it is a POSITIVE Y coefficient, with a ">" symbol. Here is the line:

You will have to make this a DOTTED line and SHADE ABOVE THE LINE. Unfortunately, I don't know how to do this in algebra.com notation!

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.42=0.17 + 0.44 log N

Subtract 0.17 from each side:
.42-.17 = 0.44 log N
.25= 0.44 log N

Divde both sides by .44

.568 = log N

To "undo" log, raise both sides to the 10 power, which is

N= 3.6998, which rounded to the nearest whole number is 4.

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A half-dozen dozen dollar bills would be 6 dozen dollar bills or $72.

Six dozen dozen dimes would be 6 * 144 dimes or 864 dimes. The value of this is of course $86.40.

The difference would be $14.40, or I guess you could say a dozen dozen dimes.

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On the Chip and Dale problem, the problem is not entirely clear to me, but I'll give it my best interpretation.
Let x = the original number of acorns. According to the problem, they added 32 acorns to their supply, giving them a total of x+32 acorns.

Next, Dale ate half of the acorns after Chip fell asleep. I will assume that it was still Monday when Dale first ate half of the acorns. This means that he ate half and that left of the acorns.

On Tuesday he ate half of what was left, leaving half: .

On Wednesday, he ate half and left half, leaving .

On Thursday, he ate half and left half, leaving .

On Friday, he ate half and left half, leaving .

On Saturday, he ate half and left half, leaving .

The equation for all of this, since after Saturday morning there were 35 acorns left is this:



Multiply both sides by 64:


Subtract 32 from each side:


Check:
Add 2208 +32 = 2240 acorns on Monday afternoon. If Dale ate half on Monday, this leaves 1120 acorns on Monday night.

Tuesday = 560
Wednesday = 280
Thursday = 140
Friday = 70
Saturday = 35

It checks!!

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Hey, HERE'S AN EVEN BETTER WAY TO SOLVE THE ACORN PROBLEM, and it doesn't even require ALGEBRA!!

You can start with the acorns at the end of the week, which was 35 at the end of Saturday. Realizing that half were eaten each day, this means that at the beginning of Saturday, there were 35*2 = 70 acorns. Likewise at the beginning of each day, there would have been:

Saturday 35*2 = 70
Friday 70*2 = 140
Thursday = 140*2 = 280
Wednesday = 280*2 = 560
Tuesday = 560 *2 = 1120
Monday = 1120*2 = 2240
Now, undo the 32 acorns that they added on Monday before half were eaten (by subtracting!), and you have 2208 acorns to begin with.

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For a detailed explanation, see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com, then look for Basic Algebra, then Samples from Basic Algebra: One Step at a Time, then Chapter 1, then Section 1.01 Number Systems.

Meanwhile, these are the systems of numbers leading up to the Real Number System.
1. Natural Numbers = 1, 2, 3, 4, etc. It's "natural" to count on your fingers!

2. Whole Numbers= 0, 1, 2, 3, 4, etc.

3. Integers = 0, 1, 2, 3, 4, etc, also -1, -2, -3, -4, etc.

4. Rational Nunbers = any number that can be expressed as a "ratio" of two integers. This includes whole numbers, integers, fractions, terminating and repeating decimals, etc.

5. Irrational Numbers= numbers like , , , etc.

The rational and irrational numbers have NO members in common, and together they form the real number system.

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Multiply both sides of the equation by 3 to get the x alone, and you get


or 1 1/2

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y-3/5 - 1 = y-5/4
y-8/5 = y - 5/4

If you subtract y from each side, you get
-8/5=-5/4, which is a FALSE statement. It can NEVER be true, so there is NO SOLUTION!!

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I got x=3.






Add +x to each side, then +3 to each side to get all the variables on the left side and the numbers on the right. That gives you
3x=9
x=3

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Im assuming that you mean .




Therefore,



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3x + 4y = 12
If x=8/3, then 3*8/3+4y = 12
8+4y=12
4y=4
y=1
(8/3,1)

If x=0, then 3*0+4y=12
4y=12
y=3
(0,3)

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F= 9/5C + 32
F=9/5*0+32=32

F=9/5*15+32
=9*3 +32=27+32=59

F=9/5*100+32
=9*20+32=180+32=212

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First, find the amount of increase, .

Next divide by the original amount
.

Finally, change this decimal to a percent by moving the decimal two places to the right: .67555575= 67.56% (approximately).

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Let x = speed of the boat in still water
y = speed of the current of the river

x+y = rate downstream
x-y = rate upstream

Distance = Rate * Time, so


x+y==12 Downstream
x-y==4 Upstream

Add these two equations together:
2x = 16, so x = 8 mph in still water

x+y = 12, where x = 8, y = 4 mph current.

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=
=

Hey, I've got a GREAT handout on logarithms, but it's not on my website. I can send a copy to anyone who needs one. Send me a mailing address, and I'll put one in the mail to you!!

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By the law of logarithms,



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I'm not sure you stated this problem the way you meant for it to be stated, and I may be way off base with this, but I'm going to try it anyway. I think the problem you meant to ask is. Tell me if this is what you meant to ask?

If so, then remember that and that . Put these together and you have

This last statement in reverse, using "e" to replace the x, looks like this:

Now,
.

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