CentsLord

Try plotting the two equations on a graphing calculator, like Desmos.com. The x-value of the intersection will be your answer!

Probability of rolling a 2 or 4 on the first roll: 1/3

Probability of rolling a 5 on the second roll: 1/6

Total probability = 1/3 * 1/6 = 1/18 :D

The angles of a triangle always sum to 180 degrees.

So, we now that x + x + 10 + 3x - 5 = 180

Which means: 5x +  5 = 180

Which makes 5x = 175

And x = 175/5 = 35 :D

o _ O xD

:D AoPS?

The area of a regular octagon is given by the formula \(A = 2s^2(1 + \sqrt{2})\), where \(s\) is the side length of the octagon.

We know that \(s = 5.5\text{ in}\), so we just plug in that value into the equation to get:

\(A = 2(5.5^2)(1 + \sqrt{2})\)

\(A = 60.5(1 + \sqrt{2})\)

\(A = 60.5 + 60.5(1.414)\)

\(A = 60.5 + 85.547 = \fbox{$146.047 \text{ in}^2$}\) :D

Well explained! :D

Correct! :D

Thank you!

So we have a number \(x\) that has this property that makes the following equation true:

\(x^2 = 84 + 5x\)

Changing this to standard quadratic form, we get:

\(x^2 - 5x - 84 = 0\)

This, factored into two binomials, is:

\((x + 7)(x - 12) = 0\) 

From this, \(x\) must be either \(\fbox{$-7 \text{ or 12}$}\). I guess those are your numbers :D