BuilderBoi

Simplify the expression: \(3y^2-22y-16\)

In order to fractor this quadratic, we need to break up the -22 to 2 numbers which multiply to -48, and add to -22. 

Looking through the list of factor pairs of -48, we find that -24 and 2 satisfy both conditions. 

Rewrite as: \(3y^2-24y+2y-16\)

Factor: \(3y(y-8) + 2(y-8)\)

Rewrite again: \((3y+2)(y-8)\)

From here, you know what \(a\) and \(b\) are, and you can solve for \(a-b\) 

Blue: \(2 \over 8\)

Pink: \(1 \over 8\)

White: \(5 \over 8\)

You can reorder them from here...

You could also write it as an equation:

\(n\) = number of sides in the polygon

\(162n=180(n-2)\)

\(162n=180n-360\)

\(0=18n-360\)

\(18n=360\)

\(n = 20\)

So, the polygon has \(\color{brown}\boxed{20}\) sides like Pavlov said.

(His method is the better method tho...)

Ok, now it is solvable. The first clue narrows the options down to 14 options: 1089, 1369, 1849, 2209, 2809, 3249, 3969, 4489, 5329, 5959, 6889, 7569, 8649, 9409. 

After looking through all the possible options, we can narrow down our list furthur (the number must have 2 of the same digits) : 2209, 3969, 4489, 5959, 6889, 9409.

Looking through the list again, we see that only \(\color{brown}\boxed {3969}\) satisfies all 4 conditions. 

The quarter is for giants, not us. 

Your question isn't fully complete. 

The 4th clue alone narrows down the number to 68 possibilities, but we can not go any farther, because the question is incomplete.

Draw this on a graph, and you will see that triangle ADE takes up half of \(1 \over 3\) of the rectangle, meaning that the ratio is \(\color{brown}\boxed{1 \over6}\)

Here is the image. The zone in black is triangle ADE, and the blue lines represent the rectangle. 

Thank You!!!

Gahh... 4 x 3 x 2 = \(\color{brown}\boxed{24}\) possible ways. 

Thanks Melody and Pavlov!!!

Multiply each term by the 3 terms in the other trinomial, and you get: \(\color{brown}\boxed{4x^4+6x^3+9x^2−4x+3}\)