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We aren't quite THAT good!! You really need to give us a PROBLEM!! You give us the expression first, THEN we can simplify it!!

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A ratio of two numbers is like a fraction .
A proportion is a ratio of two numbers equal to a ratio of two other numbers:
. So, I would say that the ratio is . I suppose if had been written in the form , then that too would have been an example of a proportion.

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First you need to find the sum of all the angles within a regular octagon. To do this, draw an octagon (8 sides, like a stop sign!), select a vertex (any vertex will do!), and draw diagonals from that vertex to each other vertex in the octagon. These diagonal will divide the octagon into 6 triangles (it's always 2 less than the number of sides in the figure being "diagonalized"). Each triangle has 180 degrees, which multiplied times 6 gives you 1080 degrees. This 1080 degrees represents the sum of the 8 vertex angles of the octagon. To find the size of each angle, divide 1080 by 8, or 135 degrees.

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Earnings = or
Earnings =

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Factors into


The quadratic factor can be solved by either the quadratic formula, the pluggable solver, or by completing the square. Completing the square is fairly easy:




, and of course, x=2!!

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Again, Jon's answer should be simplified further, giving YOUR answer:




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In Jon's solution, he didn't simplify the answer completely. If you simplify HIS answer , you will get YOUR answer, which is

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OOps, Jon is going too fast! The answer of 2/4 reduces to 1/2.

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A prime number is a number larger than 1 that cannot be broken down into a product of smaller numbers. A number larger than 1 that CAN be broken down into the product of two or more numbers is said to be a composite number. The number 1 is neither prime nor composite. For examples, 2, 3, 5, 7, 11, etc. are prime numbers since they cannot be broken down. The numbers 4, 6, 8, 9, 10, 12, etc. are composite numbers.

Real numbers consist of all numbers whose distance can be measured on the numberline, including whole numbers like 1, 2, 3, 4, etc. 0 and the negative integers like -1, -2, -3, etc. all fractions, and decimals, and even numbers that don't come out even, like etc. See the page on my own website which is not yet a lesson plan for algebra.com (maybe coming soon to algebra.com, who knows!) from Basic Algebra by clicking on my tutor name "rapaljer" anywhere in this website, go to Basic Algebra, look for "Samples of Basic Algebra: One Step at a Time", "Chapter 1," then "Section 1.01 Number Systems." This section may be helpful.

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It looks right so far.
Substitute the first formula for NM into the second equation:
GA = 4(NM) - 52000
GA = 4(2/5MD -3000) - 52000
GA = 8/5 MD - 12000 - 52000
GA = 8/5 MD - 64000

Now, substitute THIS GA and the NM into the third equation:
MD = 10613000 - (NM + GA)
MD = 10613000 - ( 2/5MD -3000 + 8/5 MD -64000)
MD = 10613000 - (10/5 MD - 67000)
MD = 10613000 - 2MD + 67000
MD = 10680000 - 2MD

Add +2MD to each side of the equation:
3MD = 10680000 Divide by 3
MD = 3560000
It's late! I have no idea if this is right or not! It's the UGLIEST problem I've seen in a long time! At least it came out even, right?? Ask me in the morning!! Oops! It IS morning!!

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X-intercept is where y = 0. So, just plug in y=0,
2x - 5y = 6
2x - 5(0) = 6
2x = 6
x=3

If you want the coordinates of the point, that would be (3,0).

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After I solved the following exercise, it occurred to me that you MAY have meant this to be an absolute value problem!! Did you intentionally use brackets [ ] in the problem? Brackets in a math problem do NOT mean absolute value. Before continuing, let's make sure you MEANT to give me a bracket function. If you meant absolute value, then IGNORE all of this HARD work that I did trying to solve a BRACKET FUNCTION!!

Bracket function, the greatest integer function!! What this means is that whatever you get when you substitute a value of x, you round it down to the greatest integer.

y= [x+3] -4 means that
if x= 0, then y= [0+3] - 4 = 3 - 4 = -1
if x=.5, then y= [.5+3] - 4 = 3 - 4 = -1
if x=1, then y = [1+3] - 4 = 4 - 4 = 0 which is an x-intercept
if x=1.5, then y = [1.5+3] - 4 = 4 - 4 = 0 which is also an x-intercept
if x=1.9, then y = [1.9+3] - 4 = 4 - 4 = 0 which is also an x-intercept
if x=2, then y = [2+3] - 4 = 5 - 4 = 1

In other words, everything between 1 and 2 including the 1 but NOT including the 2 will be x-intercepts. This is called the "unit step function. However, this may NOT have been what you were asking!

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Before continuing with the solution, you must realize that both of the lines that you have given must be DOTTED lines, since they involve the symbol "<" or ">". Secondly, you must shade the area BELOW the lines, since you are looking for the areas in which "y < ". Use the graphs given below, but graph BOTH lines on the same xy axes. You are probably looking for the INTERSECTION, which would be the overlapping of the two areas shaded below the two lines. In other words, shade the area below BOTH lines.
The following graphs are thanks to a special solver written by Igor Chudov, the owner of this website. Send HIM the thank the note!!

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -3/1 = -3. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -3/-1 = 3. Slope is -1/-1 = 1. Equation in slope-intercept form: y=1*x+3.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 4/2 = 2. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 4/1 = 4. Slope is -2/1 = -2. Equation in slope-intercept form: y=-2*x+4.

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Your first step in ANY factoring problem is to take out the common factors! In this expression, each term is divisible by 7 and y^2, so take out a common factor of





The trinomial factors if you can find two numbers whose product is -72 and whose difference is 21. Try 24 and -3




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This is SO INTIMIDATING!! It probably is really easy if you dare to look at it.

First, simplify the numerator at the very top: 3*8 is 24, and add 11, which is 35.

Second, in the middle, go ahead and multiply the (2t)*(3*8) which is 2t*24 or 48t. Then simplify the fraction that follows, which is and simplifies to 4t. This combines with the 48t, so 48t - 4t = 44t.

Third, the denominator at the bottom likewise simplifies, with the 3 and -3 subtracting out, to .

The net result is this: divided by

Invert and multiply:


As you can see the t's all divide out, the 2 divides out, and you are left with .

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P.S. Congratulations on writing that equation in an algebra.com formatted equation!! You must be a math teacher???

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Can you be a bit more specific? I probably have a lesson plan for you either on algebra.com or on my own website. Check out my own website by clicking on my tutor name "rapaljer" anywhere in this website, go to "Basic Algebra" then look for "Samples of Basic Algebra: One Step at a Time", and look in Chapter 1. This probably has everything from simplifying algebraic expressions Section 1.06 or translating words into algebraic expressions, Section 1.09."

Let me know if you don't find what you need. Happy hunting!

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In this case, r = 5 1/3 ft, which as an improper fraction is 16/3 feet.

Square the numerator, which is 256, and the denominator, which is 9.

which can be written as feet.

However, some books want you to substitute 3.14 for pi, and calculate the decimal approximation. Do what you need to do! I like leaving it in terms of .

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Let x = width of the rectangle.

Notice that there are two widths to this rectanglar fence, and only one length, since the other side doesn't need any fence. To find the length, you'll need to start with the total amount of fence, which is 1150, and subtract the TWO widths, which would be 2x, which leaves you the
length = 1150 - 2x.
b)AREA = WIDTH * LENGTH
A = x(1150 - 2x)

C)

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(In this problem, you really have to watch your p's and q's!!)
Since there are an odd number of negative signs in a product or quotient, the answer will be negative. Then multiply 4 times p times q, which would be 4pq, so the final answer is -4pq.

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(5)(-x)
Since there is no sign between the 5 and the -x, it means to multiply. Since you are multiplying a postivie times a negative (opposite signs!), the answer is negative, and the product of 5 times x is 5x.

Final answer, -5x

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The equation is based upon the fact that "Her weight is equal to 60 lbs. plus half her weight."

Srart by letting x = thw weight of the woman (if she is like most women I know, in this case, x is REALLY the unknown!)

"Her weight is equal to 60 lbs. plus half her weight."


You probably don't like that fraction, so just multiply both sides of the equation by 2 and get rid of it.



Subtract x from each side, and you get:



Check it out: Her weight is 120, which equals 60 plus half of her weight, which is another 60.

You might figure out a way to do this intuitively (like in your head), but I like equations. They are reliable!

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Jennifer's solution is NOT correct! When you add the base and to the height you do NOT get the hypotenuse, as she suggested!!

Area of a triangle:






Since this seems unreasonable to solve, perhaps you stated the problem wrong!! Recheck the problem. I was thinking that maybe the area is just , without the "squared."





Solve by quadratic formula, and it just comes out ugly?? Recheck your copying of the problem to make sure that is correct.

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Eliminate the fractions by multiplying both sides by 3:



Now, to solve for h, you need to get rid of the which are being multiplied times the h.
So divide both sides of the equation by .




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We already did the first question, so here is the second part:

Let x= width of the rectangle
x+3 = length of the rectangle
P = 2(W) + 2(L)
P = 2(x) + 2(x+3)
P = 2x + 2x + 6
P = 4x + 6

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It looks right to me!!

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Normally this is a word problem that must be worked out with an equation (see my Lesson Plan on Word Problems--Coin and Mixture Problems--Part I). However, there is an intuitive solution to this one if you think about it. You are mixing some 60% and some 40% solutions, trying to obtain a 50% solution, which is exactly halfway between the 60% and the 40%. You will obviously need to mix them half and half. The solution is 50 L of each.

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Take out the common factor, which is x:
x(x+3)

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Do you mean

Assuming that this is the case, the LCD for the entire problem is 2x, so multiply both sides of the equation by 2x:


This eliminates all the denominators:
4 + 1 = 14x
5= 14x

Divide both sides by 14:
x=

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The slope intercept form of the equation of a line is y = mx+b, where m is the slope and b is the y-intercept. In this case, you are given the slope and the y intercept, so just substitute these numbers into y=mx+b, and you have
y=0x + 2
or
y=2.

Also, a line with slope 0 is always a horizontal line, which is always in the form of y = a number. In this case, the y-intercept is 2, so y = 2.

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The way I did it, always start off by identifying the variables:

Let x = length of smaller piece
18-x = length of longer piece

The equation is tricky, but just follow the wording of the sentence that is given:
5(smaller) - 2 = 3(longer) - 8
5(x) - 2 = 3(18-x) - 8
5x - 2 = 54 - 3x - 8
5x - 2 = 46 - 3x

Add 3x to each side:
5x + 3x - 2 = 46 - 3x + 3x
8x - 2 = 46

Add +2 to each side:
8x = 48
x=6 smaller piece
18-x = 12 longer piece

Check:
5(6) -2 = 3(12) - 8
30-2= 36-8
28 = 28
It checks!

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Because one of the equations is in the form of y=___ (or also x=____), I think the substitution method is the easiest way.

Rewrite the first equation
5x + 6y = 14, and leave a blank space in place of the y.
5x + 6(_____) = 14.

In that blank space, substitute the value y from the second equation, that is, 4x-17.

5x + 6(_____) = 14
5x + 6(4x-17) = 14 Now just solve for x.
5x + 24x - 102 = 14
29x - 102 = 14
29x - 102 + 102 = 14 + 102
29x = 116 Divide both sides by 29
x= 4.

Now, the easiest place to find y is in the y=___ equation.
y=4x- 17
y=4(4) - 17
y = -1
Check in the OTHER equation:
5x+ 6y = 14
5(4) + 6(-1) = 14
20 - 6 = 14
It checks!!

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