6. This one is fairly nice.

Label the numbers: x-2, x-1, x, x+1, x+2, x+3.

So, we have 6x+3=153, 6x=150, x=25

Thus, their product is \(23*24*25*26*27*28=\boxed{271252800}.\)

s=side length of the triangle.

Yep, very nice, CPhill! Infinite series!

The formula to find the area of an equilateral triangle is \(\frac{\sqrt{3}}{4}s^2\)\(\) , so the answer is \(\sqrt{3}*16=16\sqrt{3}.\)

Irrational means it repeats infinitely, but not in repeating blocks, so I believe choice (B) is the answer.

The wording is a bit puzzling, but here's the take.

It has to be in form 15x+21y and a,b are integers, (not necessarily positive).

3 divides both the numbers, so 15x+21y needs to be a multiple of 3.

15a+21y=3

3?

Thank you, CPhill!

We can use the Shoelace Formula to check for the answer.

Therefore, we have \(\frac{1}{2}\left|\left(0\cdot 3+1\cdot 2+5\cdot 0+4\cdot 1\right)-\left(1\cdot 1+3\cdot 5+2\cdot 4+0\cdot 0\right)\right|=\frac{1}{2}\left|6-24\right|=\frac{1}{2}\cdot 18=\boxed{9}.\)

Thus, I advise you to read about the shoelace formula here: https://artofproblemsolving.com/wiki/index.php/Shoelace_Theorem

EP is right.

1. Angle C measures 60+90=150 degrees. Since it forms a triangle, the answer is just 180-150=30/2=15 degrees.

Minimum possible product: Take the largest two positive numbers and the smallest negative number and multiply them together.

So, -8 * 5 * 7=-280?