Answer:
A. 
Step-by-step explanation:
So to get the area of a square, we need to find the length of one side.
We know the length of the larger square is a, so the area of the larger cube is 
We can find the length of a side of the smaller square by using pythagoreans theorem to find the hypotenuse of the triangle formed in the bottom left corner. The length of one side along the x axis is a - b, and the length of the other side, along the y-axis, is b.
We can plug it into pythagoreans theorem to get
(C represents the length of one side of the smaller square, and the hypotenuse of the triangle)
The area of the smaller triangle is C squared to the area of the smaller triangle is
To get the ratio of the smaller square in comparison to the larger square we divide the area of the smaller square by the area of the larger square.
So the ratio should be
Step-by-step explanation:
In the expression a^n, for integer values of n greater than 1, there are n factors. For example, a^2 = a * 2 (2 factors), a^3 = a * a * a (3 factors), etc.
For a non-negative value of a, a^n is non-negative for all values of n.
If a is negative, and n is even, then a^n is non-negative.
If a is negative, and n is odd, then a^n is negative.
|a| is non-negative for all values of a.
sqrt_n(a^n) is negative for negative a and odd n, but |a| is always non-negative, so sqrtn(a^n) cannot equal |a| for odd n.
This one is prime. The sum of two squares doesn't factor.
The more interesting case is q^2-1, which factors into (q-1)(q+1).
7) 29/9; repeating
8) 301/20; terminating
9) -101/20; terminating
