1. (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 evaluate the expression (square root of 5) + (square root of 25), we can simplify each square root separately and then add them together.
The square root of 5 is an irrational number and cannot be simplified further, so we leave it as is.
The square root of 25 is a whole number, which is 5.
Now, we add the two results together: (square root of 5) + 5 = √5 + 5
This form (√5 + 5) is the final answer, since the square root of 5 cannot be simplified any further.
2. To find the value of k in the equation y = x^2 + 2x + k when it passes through the point (1, 2), we substitute the values of x and y into the equation and solve for k.
Given that the point (1, 2) lies on the graph of the equation, we have:
2 = 1^2 + 2(1) + k
Simplifying, we get:
2 = 1 + 2 + k
Further simplifying, we have:
2 = 3 + k
To isolate k, we subtract 3 from both sides of the equation:
2 - 3 = k
Therefore, we find that k = -1.
3. To evaluate the expression F(x+2) - F(2) / x for the function F(x) = 1 + 3x^2, we substitute the given values into the function and perform the necessary calculations step by step.
First, we need to find the value of F(x+2). To do this, we substitute (x+2) into the function:
F(x+2) = 1 + 3(x+2)^2
Next, we need to find the value of F(2). By substituting 2 into the function, we get:
F(2) = 1 + 3(2)^2
Now, we can substitute both values into the expression:
F(x+2) - F(2) / x = (1 + 3(x+2)^2 - (1 + 3(2)^2)) / x
Simplifying further, we get:
(1 + 3(x^2 + 4x + 4) - (1 + 3(4))) / x
Continuing to simplify, we have:
(1 + 3x^2 + 12x + 12 - 1 - 12) / x
Combining like terms, we get:
(3x^2 + 12x) / x
Finally, we can cancel out an x from the numerator and denominator:
3x + 12.
Therefore, the simplified expression is 3x + 12.