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Unless you give us the perimeter of the rectangle, we can't give you the dimensions. We just aren't quite THAT good!!

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If a cube has a volume of 1728 cubic inches, you don't need to know the surface area in order to find the dimensions of the cube. Let x = side of the cube.



inches .

As a check each side has area = 12*12 = 144. There are 6 sides, so total surface area is 864 square inches. It must NOT be a cube. Are you sure this is stated correctly? I don't see how it can be a CUBE. Someone correct me if I'm wrong!!

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Let x = base of triangle
x-3 = height of triangle

Area =


Multiply both sides by 2 to clear the fraction:



Quadratic equation, so set equal to zero:


x=8 base
x-3= 5 height
Reject x=-5, since the base of a triangle cannot be negative.

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I would let x = the complement, since that is at the end of the first sentence.
2x + 25 = the supplement

The equation is based upon the fact that if you subtract the supplement minus the complement, you get 90 degrees.
2x + 25 - x = 90
x + 25 = 90
x= 65 complement
90-x = 25 = the angle

There may be easier ways to do this if we think about it, but at least this works to solve the problem.

OH! I see it!! THE WAY YOU DID IT IS CORRECT!! YOU JUST FORGOT THE 25.
Your equation: 180-x= 2(90-x)

Should have been: 180-x= 2(90-x)+ 25
This works!! x= 25.

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The angle bisector of angle BAC is perpendicular to side BC, so it forms a right triangle with angle at point A of 18 degrees, and hypotenuse AB=1. Therefore,

sin 18 = , where x = half of the side BC.

Be sure your calculator is in degree mode and calculate sin 18 = .3090.

Double this value to obtain BC = .618 approximately.

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Start with a rectangle for an example, and draw a diagonal. Notice that you have a 4 sided figure, and there are 2 triangles, each with a sum of 180 degrees for a total of 2*180 = 360 degrees.

Next, draw a pentagon, and from any given vertex, draw the two diagonals from that vertex to the other vertices. Notice that you have a 5 sided figure, with two diagonals. There are 3 triangles, each with sum of 180 degrees for a total of 3*180 = 540 degrees.


Next, draw a hexagon, and from any given vertex, draw the three diagonals from that vertex to the other vertices. Notice that you have a 6 sided figure, with three diagonals. There are 4 triangles, each with sum of 180 degrees for a total of 4*180 = 720 degrees.

Now, notice the pattern. If there are n sides, there will be two less triangles than sides, which is n-2 triangles, and the sum of the angles will be (n-2)* 180 degrees.

The formula for the sum of the angles of a polygon with n sides is 180(n-2).

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By the fundamental counting principle, just multiply 3 times 3 times 2 = 18 different outfits.

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Change both mixed fractions to improper fractions:
56 1/2:7 2/3
(2*56 +1)/2 : (3*7 +2)/3
113/2 : 23/3

The ratio of two numbers can be written as a division problem:
113/2 divided by 23/3
113/2 * 3/23

Nothing divides out or reduces, so multiply numerators and denominators:
339/46

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Turn on the air conditioner!

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The sum of the three angles of the triangle must be 180 degrees. If two of the angles are 30 and 70 (which adds up to 100 degrees), what would you have to add to 100 degrees to get 180 degrees? You can probably figure this out in your head, right? Did you get 80 degrees? Does it check? Does it all add up to 180 degrees?

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And what would you like to do with these complex numbers???

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x = amount of antifreeze at 100%
5 = amount of water at 0%
x+5 = total mixture at 60% or 80%

x = .6(x+5)
x = .6x + 3.0
x - .6x = 3.0
1.0x - .6x = 3.0
.4x = 3.0
x = 3.0/.4 = 30/4 = 7.5 liters for the minimum of 60%

x = .8(x+5)
x = .8x + 4.0
x - .8x = 4.0
1.0x - .8x = 4.0
.2x = 4.0
x = 4.0/.2 = 40/2 = 20 liters for the maximum of 80%

In other words, you should use between 7.5 and 20 liters (inclusive!) of antifreeze.

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Let x = smaller angle
5x = larger angle
x + 5x = 120
6x = 120
x= 20 degrees -- smaller angle
5x = 100 degrees -- larger angle

Now consider the choices.
1. They are NOT supplementary since they do not add up to 180 degrees.
2. They are NOT complementary since they do not add up to 90 degrees.
3. They are NOT both acute since the larger angle is larger than 90 degrees.
4. One angle is acute and the other is obtuse. This is true.

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First find the slope of the given line:




The slope of a line perpendicular to this line is tne negative reciprocal of the slope of this line. So, the slope of a line perpendicular to this line has a slope of .

The equation of a line that is perpendicular to the line between these two points will be in the form where b is the y-intercept of the line. Notice that there are many, many (in fact, infinitely many) lines that are perpendicular to this line segment, and to determine which particular line you are looking for, more information must be given in the problem.

Final answer, .

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It would appear that the plumber charges $50 for the additional two hours from 3 hours to 5 hours, which is $25 per additional hour. At this rate, for an additional 3 hours, he/she would be charging an additional $75, added to the $160, for a total of $235.

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If two angles are congruent, then that means the measure of the angles is the same. If they are supplementary, then they add up to 180 degrees.

So, x+ x = 180
2x = 180
x= 90 degrees.

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Since angle a is given in terms of angle b and angle c is given in terms of angle b, everything is in terms of angle b, so let x = angle b.

Let x = angle b
4x = angle a
x-20 = angle c

The sum of the angles is 180 degrees.
x + 4x + x - 20 = 180
6x - 20 = 180
6x = 200 {Note: Answer doesn't come out even, but then that's life sometimes!)
x= 200/6 = 100/3 = 33 1/3 degrees -- angle b
4x = 400/3 = 133 1/3 degrees -- angle a
x-20 = 33 1/3 - 20 = 13 1/3 degress -- angle c
Check: 33 1/3 + 133 1/3 + 13 1/3 = 180 degrees
It checks!

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Check:

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Where did you get this one??
Do you by any chance mean f(f(f(x))) = 8x + 21? This would be a very interesting problem. If it is, please re-post it, or send me an Email.
I'm not sure what you mean by b(b(b(x))).

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This looks like an absolute value problem (although it does look strangely like the previous problem that I posted a solution for!). This is the product of -4 times the result of taking the absolute value of 5-12. First take the 5-12 which is -7. Next take the absolute value of -7, which would be 7. Last step, take -4 times 7, and you have a final answer -28.

The moral here is to be REALLY careful in writing your math problems, because sometimes a minor difference or sloppiness in writing the problem can end up with a completely different result!!

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This looks like a -4 multiplied by the difference (15-121). Am I reading this right? So take 15-121 which is -106, and multiply this times -4. Remember that a negative times a negative is a positive. The final answer is 424.

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Let x = cost of each doughnut
3x + 1.95 = 3.60
3x + 1.95-1.95 = 3.60-1.95
3x =1.65

Divide by 3
x = $.55

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Let x = smaller angle
2x = larger angle

Sum of the angles = 90 degrees
x+ 2x = 90
3x = 90
x= 30 degrees -- smaller angle
2x = 60 degrees -- larger angle

Sum of the angles 30 + 60 = 90
It checks!

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This figure is a right triangle with the balloon at a height of x miles above Sara's house. The base of the triangle represents the distance from Sara's house to where Sara is at her friend's house. The angle from Sara's friend's house to the balloon is 15 degrees, so trigonometry is required.

tan 15 = x/2

Multiply both sides by 2:
2 tan 15 = x

Are calculators allowed here? Be sure you are in degree mode!
x = 2 tan 15 = .535898 . . .

In case you want that in feet, multiply by 5280 (don't round it off until AFTER you do the calculation!!)
about 2830 feet.

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Let's count them:

First the units digit equal to 3:
13, 23, (NOT 33 since it has two digits equal to 3), 43, 53, 63, 73, 83, 93

Next, the ten's digit equal to 3:
30, 31, 32, 34, 35, 36, 37, 38, 39

Total equals 8 + 9 = 17

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Complementary angles means that the sum of the angles equals 90 degrees.

x+5 + 4x -15 = 90
5x -10 = 90
5x - 10 + 10 = 90 + 10
5x = 100
x= 20 degrees-- Final answer!

However, as a check, let's find the two angles and see if they add up to 90 degrees.
x+5 = 25 degrees
4x-15= 80-15 = 65 degrees
25 + 65 = 90
It checks!

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First, notice that Bob's money is given in terms of Anthony, and Anthony's money is given in terms of Lisa. So, let x = the quantity at the end of all of this, which is Lisa.

Let x = amount of money of Lisa
x+ 7 = amount of money of Anthony
2(x+7) = amount of money of Bob

The equation is that the sum of all these amounts = 73
x + x+7 + 2(x+7) = 73
x + x + 7 + 2x + 14 = 73
4x + 21 = 73
4x + 21 - 21 = 73 -21
4x = 52
x= $13 Lisa
x+ 7 = $20 Anthony
2(x+7) = $40 Bob

Check: 13+20 + 40 = 73
It checks!

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Express the fraction 2/5 as a decimal by dividing 5 into 2.00 (you get .40), and then convert the decimal to a percent, by moving the decimal two places to the right. This means that .40 = 40%.

Another way to do this particular problem is to start with the fraction 2/5 and multiply the numerator and denominator by 2. This gives the very special fraction 4/10, which as a decimal would be .4 or .40. Then convert to a percent as above .40 = 40%.

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You need more information for this problem. What is f(x)? There must be a formula that you forgot to give us.

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If two angles are complmentary, then the sum of those angles is 90 degrees. Since the sum of all three angles must be 180 degrees, the third angle must be 180-90 = 90 degrees.

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Let x = width of the rectangle
x+3 = length of the rectangle
Area = L*W
x(x+3)= 70


x=-10
Reject, since width of a rectangle can't be negative

x= 7 cm Width
x+ 3 = 10 cm Length

Check:
Area= 7*10= 70 sq.cm.

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The rule that I use is not the way most people teaching math use, but I like it. Whenever you have an equation with a
POSITIVE coefficient of y > or >= , you must shade ABOVE the line.
POSITIVE coefficient of y < or <= , you must shade BELOW the line.

That's as simple as it gets! Examples:
2x+3y < 6 Shade Below
2x+3y > 6 Shade Above
2x+3y >= 6 Shade Above
2x+3y <= 6 Shade Below

So, what if you have a NEGATIVE COEFFICIENT of Y? Well, if you multiply both sides of an inequality by a negative, this reverses the inequality, and therefore it REVERSES the RULE!!
2x - 3y < 6 same as -2x+3y> -6 Shade Above!!

See if that helps. If you need more, I might be able to send you a section from my book in a word file.

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