Varxaax

(2V-3)².

Let's do this!

Apply perfect square formula!

(a-b)²=a²-2ab+b²

Simplify it!

4V²-12V+9

BABABABOWWWWW!

Yay!

Edit: 

How is this off topic?

Most AoPS questions are already on the internet, and I'm pretty sure some people have all the answers downloaded somewhere.

Drawing it out would help, but I'm new to the "write code to make funny pictures on web2.0.calc" thing so this is the best I can do.

The side of the triangle is ABC = 3a
The side of the hexagon = a
Area of triangle = (root3 /4 )*(3a)^2 = 9a^2 *(root3/4)
Area of hexagon with side a = 6*(root3 /4 )*(a)^2
Ratio of areas of hexagon to that of triangle = { 6*(root3 /4 )*(a)^2 } / { 9a^2 *(root3/4)} = 6/9 = 2/3
and we get = 2 : 3

Yay!

One man can finish in X days.
2 machines finish in 13 days, so 1 machine finishes in 26
3 men and 8 machines finish in 1/2 the time it takes 3 machines and 8 men.
Because of that 3/M + 8/26 = 2(8/M + 3/26)
3/M + 4/13 = 16/M + 3/26
16/M – 3/M = 4/13 – 3/13
13/M = 1/13
M = 169
Number of men to finish the job is: 13 days = 169/13 = 13

Yay!

I can do this. Although it has been a couple years since I studied mesopotamia.

Zoroaster started Zoroastrinism and was an iranian prophet.

Hammurabi wrote hammurabi's code, based off of eye for an eye. His punishments were harsh, but not as harsh as some of the others. It is said that his code actually influenced the US's law system. (But thats what I heard, it might be wrong.)

Nebuchadnezzar (who's name is too long and I'm going to call Chad) was a Babylonian king, who reined for wayyyy too long. He didn't do too much lol.

Sargon was the first Akkadian ruler and conquered the sumerians with his chariots. He was the first ruler of an Empire.

Cyrus the Great created the Archaemenid Empire, later becoming Persia.

Thanks for the recap of Mesopotamia

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The square root of H lies inbetween (10/3)² and (24/5)²

We first fine 10/3 squared and 24/5 squared. 

10/3 squared is 11.111111111111...

and 24/5 squared is 23.04

Find the amount of integers inbetween. 

12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23

 Count them up and there you have it.

Yay!

Let x = kg of silver to be added
11.8 kg of silver in 10% alloy

We can make an equation. 11.8+x=0.25(118+x)

Simplify it to be 11.8+x=29.5+0.25x

Subtract. 0.75x=29.5-11.8

Subtract 2:Electric Boogaloo 0.75x=17.7

Simplify it to be x=23.6

Yay!

No. In one day she read 1/3

1/3+1/3=2/3

2/3 is less than 3/4.

Hope it helps!

Yay!