This problem asks you to find the measurements of two angles. I will call those two measurements x and y. You are given that the measurement of one angle is five times the measurement of the other, and that the sum of the measurements of the two angles is 180 degrees. You can turn...

Actually, Joshua, this question doesn't require permutations or combinations at all. The selection of the leads are independent choices, so the answer is 6*8=48 ways.

This question hinges on the fact that you will get a whole number of advertisements and a whole number of letters from friends. Thus, your total number of letters must be divisible by 8 and 5. Your teacher probably wants the least common multiple of 8 and 5, which is 40.
However,...

For A intersect B, you need to find the probability that if you draw two cards, one will be the ace of spades and the other will also be black.
The chance that you will draw the ace of spades in two draws is 2/52 = 1/26. Given that, the chance that the other card is black is...

You can convert any number from base 10 to another base by repeatedly dividing it by the new base and keeping track of the remainders. To start with an easy example, I will convert 10 into binary (base 2).
10/2 = 5 R0
5/2 = 2 R1
2/2 = 1 R0
1/2...

A: population, in millions
e: Euler's number
k: exponential rate of increase
t: number of years after 1982
Putting the numbers into the equation, you get:
29=24e^(15k)
Divide both sides by 24 and take the natural logarithm of both sides:
ln(29/24)=15k
Then...

When working on a ratio problem like this, the only thing that is important is the relationship between the numbers. In this case, it is easy to see that five is twice as large as five halves. Thus, the answer is two to one.

One centimeter and one decimeter are both units on the metric scale. Since the metric scale uses SI prefixes, it is very easy to compare units.
1 kilometer=10 hectometers
1 hectometer=10 decameters
1 decameter=10 meters
1 meter=10 decimeters
1 decimeter=10 centimeters
1...

There are three envelopes which each have independent choices between three options. Thus, there are a total of 3*3*3=27 different ways the money can be configured.
Of those 27 ways, four of them add up to exactly $60:
1. $5+$5+$50
2. $5+$50+$5
3...

The trick to solving this problem is realizing that you need to break it up into parts. Find the number of totals with one, two, three, or four bills, then add them up. Since this is a combination problem, you can find each of the numbers with the combination formula, but the numbers...

10.5 is equal to the fraction 21/2, so you can multiply 1.79 by two and divide by 21.

As has been noted above, the problem can be solved both factoring and the quadratic formula. If you can't factor or remember the formula, you can also solve it using a process called completing the square.
First, divide the equation through by a, and subtract c from both sides...

The absolute value of x is x if x is positive and -x if x is negative. For example, |5|=5 and |-4|=4.
I'm going to assume that for your problem you meant 10=|4x-6|. What you need to do is try the problem assuming that 4x-6 is positive and that 4x-6 is negative. Then you need...

The answer is y=3x+1.
There are several ways to find the answer to this question, and a few different formats in which to put the answer. I prefer slope-intercept form, so I will explain it by that method.
y=mx+b
m=slope
b=y-intercept
The y-intercept is the value...

The formula for the length of a line segment is naturally the same as the formula for the distance between two points, or sqrt((x1-x0)^2+(y1-y0)^2). In this instance:
sqrt((0-0)^2+(12-3)^2))=sqrt(0+81)=9
As a way of understanding the solution, you may want to graph the...

A cube has 8 vertices (corners, points), 12 edges (line segments), and 6 faces (planes). One formula that works for any solid with flat sides and no holes is vertices+faces-edges=2.

Two functions are inverses if the composition of the functions equals x. In other words, f and g are inverse functions if fog(x)=gof(x)=x.
f(g(x))=(7/2)(2x+8)/7-4=x+4-4=x
g(f(x))=(2((7/2)x-4)+8)/7=(7x-8+8)/7=x
So, f and g are inverses.

The first step is always to assign letters to the variables. We can call length L and width W.
Since all units are in cm, unit conversion is unnecessary.
Next, set up some equations. L=2W-6 because of the first sentence of the problem. Length times width equals area,...