. (square rt. 5) +(square rt. 25) =

2. If y=x^2 +2x +k passes through the point (1,2), then k =

3. If F(x) = 1 +3x^2, where X cannot be 0, then F(x+2)-F(2)/(x) =

1. To simplify the expression (square root of 5) + (square root of 25), you first need to find the square root of 5 and the square root of 25 separately.

The square root of 5 is an irrational number, approximately equal to 2.236.
The square root of 25 is a rational number, equal to 5.

Adding them together, you get 2.236 + 5 = 7.236 (approximately).

2. We are given the equation y = x^2 + 2x + k and the point (1, 2) that the graph of the equation passes through. To find the value of k, we substitute the coordinates of the point into the equation and solve for k.

So, plugging in x = 1 and y = 2 into the equation, we get:
2 = (1)^2 + 2(1) + k
2 = 1 + 2 + k
2 = 3 + k

To isolate k, we subtract 3 from both sides of the equation:
2 - 3 = k
-1 = k

Therefore, k is equal to -1.

3. To simplify the expression (F(x+2) - F(2))/(x) using the given function F(x) = 1 + 3x^2, we substitute the expressions inside the function and calculate step by step.

Let's start with F(x+2):
F(x+2) = 1 + 3(x+2)^2
= 1 + 3(x^2 + 4x + 4)
= 1 + 3x^2 + 12x + 12
= 3x^2 + 12x + 13

Now, let's find F(2):
F(2) = 1 + 3(2)^2
= 1 + 3(4)
= 1 + 12
= 13

Substituting these values back into the expression ((F(x+2) - F(2))/(x)), we have:
((3x^2 + 12x + 13) - 13)/(x)
= (3x^2 + 12x + 0)/(x)
= (3x(x + 4))/(x)

Finally, we can simplify further by canceling out the common factor of x in the numerator and denominator:
= 3(x + 4)

Therefore, the simplified expression is 3(x + 4).