TheXSquaredFactor

\(1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*\sqrt{beer}\)

is a root beer float, no?

This might be the most common question on this forum. I can't figure out why. Anyway, here you go:

\(2+2=4\)

First, convert 62.5% to a fraction or decimal. I personally like fractions, so that is what I'll use:

Isn't that nice? \(62.5\%\) simplifies to, in a fraction, \(\frac{5}{8}\). By doing this, we have simplified the problem from \(62.5\%*50\) to \(\frac{5}{8}*\frac{50}{1}\). Now, let's simplify further to get our final answer:
 

Okay, the answer is clearly \(31.25\). However, there is a trick any percentage of 50. Do this:

1. Remove the percent sign
2. Divide result by 2

This is probably best demonstrated by example. I'll use the problem above, which is \(62.5\%*50\).

Step 1 says to remove the percent sign, so \(62.5\%\) becomes \(62.5\). 

Step 2 says divide the result by 2. \(62.5/2= 31.25\). Does this answer seem familiar? It should. It is the same answer as we got above but using different steps. 

First, let me show you a wrong approach. I almost fell for it myself:
\(\frac{1}{\frac{6}{2}}=\frac{1}{6}*\frac{1}{2}=\frac{1}{12}\)

This math above is simple, but this would imply that the probability of rolling a 6 is 1/12. Well, you'll see...

If you combine the probabilities of all events occurring, then the probability should be 1. Let's try that with our current answer. Let's test it:

11/12 is not equal to one 1. Therefore, the probability cannot of rolling a 6 cannot be 1/12. However, there's a trick that we can use. How can we make 11/12=1? That's right, multiply by its reciprocal, 12/11. Therefore, multiply all of your fractions by it:
 

\(\frac{12}{11}(\frac{1}{12}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6})\)

But wait! WE only need the probability of rolling a 6, so we only need to multiply 12/11 by 1/12!

\(\frac{12}{11}*\frac{1}{12}=\frac{12}{132}=\frac{1}{11}\)

As you'll see below, there are other methods to do this problem. Of course, the method above is what I chose. Isn't it beautiful how multiple approaches still leads to the same final answer?

This seems to be a common question on this forum, but I'll tell you anyway:

\(1+1=2\)

\(x=6\hspace{1cm}x=26\)

Here is the original equation:

\(x\pm10=16\)

What is this telling us? This equation is really 2 separate equations. I've laid them out for you:

1. \(x+10=16\)
2. \(x-10=16\)

Now do you understand what \(\pm\) means? It means that you both add and subtract. Solve each equation separately, and you get both values for x. I'll start with the first:

Of course, you aren't done yet! You must solve the other equation, too:

Therefore, you have 2 solutions:

\(x=6\) and \(x=26\)

...Or

Divide by 3 on both sides

Then, subtract 1 on both sides 

:)

\(\sqrt{2l^2}=l\sqrt2\)

\(\sqrt{2l^2}\)

This can be simplified further:

Im going to use a radical rule that says \(\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}\hspace{1cm}\), assuming \(a\geq0,b\geq0\). You might notice that there is a condition for using this. This rule only works when both a and b are nonnegative. In the context of geometry, \(l\) should be positive because otherwise a square couldn't exist if a side length is -8, for example. I will apply this rule:

\(\sqrt{2l^2}=\sqrt{2}\sqrt{l^2}\)

Here, too, I will apply a rule that only works with nonnegative numbers: \(\sqrt[n]{a^n}=a\), assuming \(a\geq0\). Let's apply it now:

\(\sqrt{2}\sqrt{l^2}=\sqrt{2}*l=l\sqrt{2}\).

I just wanted you to be aware of this. You can't simplify \(\sqrt{2l^2}\)   further otherwise.

\(c+2c+3c=6c\)

I'm assuming you want to simplify \(c+2c+3c\).

c, 2c, and 3c are called like terms. Like terms have variables that are the same and exponents that are the same. Is that the case here? It certainly is. c, 2c, and 3c all have the same variable of c. Also, these terms all have the same exponent: 1. It may not be visibly obvious, but anything raised to the power of 1 is itself. To simplify, add the coefficients:

\(c+2c+3c=3c+3c=6c\)

You're done!

Subtracting a negative is always the same as adding a positive:

\(7350783-(-296)=7350783+296=7351079\)