We have the rational expression

; to simplify it, we are going to try to find a common factor in the numerator, and, if we are luckily, that common factor will get rid of the denominator

.
Notice that in the denominator all the numbers are divisible by two, so 2 is part of our common factor; also, all the terms have the variable

, and the least exponent of that variable is 1, so

will be the other part of our common factor. Lets put the two parts of our common factor together to get

.
Now that we have our common factor, we can rewrite our numerator as follows:

We are luckily, we have

in both numerator and denominator, so we can cancel those out:


We can conclude that the simplified version of our rational function is

.
Answer:
Answers are in bold type
Step-by-step explanation:
f(x) = 
The parabola opens up, so has a minimum at the vertex.
Let (h, k) be the vertex
h = -b/2a = - (-144)/2(1) = 57
k = 57^2 - 144(57) = 3249 - 6498 = -3249
Therefore, the vertex is (57, -3249)
The minimum value is -3249
The domain is the set of real numbers.
The range = {y | y ≥ -3249}
The function decreases when -∞ < x < 57 and increases when 57 > x > ∞
The x - intercepts:
= 0
x(x - 114x) = 0
x = 0 or x = 114
x-intercepts are (0, 0) and (0, 114)
When x = 0, then we get the y-intercept. So, 0^2 - 114(0) = 0
y-intercept is (0, 0)
#7
2,4,8,16
15,30,60,120
#9
1,2,3,
4,8,12
Answer:
The triangles are similar due to AAA
Step-by-step explanation:
'The triangles ABC and DBE are similar because they have a common angle < B, and also angle < E is marked as congruent to angle < A. Then the third angle <C is going to be congruent to angle D as well due to the property of addition of internal angles of a triangle must add to 180 degrees.
Then the triangles are similar due to AAA