Explanation:
In order to prove that affirmation, we define the function g over the interval [0, 1/2] with the formula 
If we evaluate g at the endpoints we have
g(0) = f(1/2)-f(0) = f(1/2) - f(1) (because f(0) = f(1))
g(1/2) = f(1) - f(1/2) = -g(0)
Since g(1/2) = -g(0), we have one chance out of three
- g(0) > 0 and g(1/2) < 0
- g(0) < 0 and g(1/2) > 0
- g(0) = g(1/2) = 0
We will prove that g has a zero on [0,1/2]. If g(0) = 0, then it is trivial. If g(0) ≠ 0, then we are in one of the first two cases, and therefore g(0) * g(1/2) < 0. Since f is continuous, so is g. Bolzano's Theorem assures that there exists c in (0,1/2) such that g(c) = 0. This proves that g has at least one zero on [0,1/2].
Let c be a 0 of g, then we have

Hence, f(c+1/2) = f(c) as we wanted.
Answer:
80
Step-by-step explanation:
<h2>Hope this helped </h2>
Answer:
9r
Step-by-step explanation:
4r+9r-11r+7r
Combine like terms
13r -11r+7r
2r+7r
9r
X=16
Y=-6
im not good at factorization but this is what i got
Step-by-step explanation:
parallel means same slope/gradient
2y = 3x + 10
y = 1.5x + 5
let equation be y = 1.5x + b
sub (2, -5)
-5 = 1.5(2) + b
b = -8
therefore y = 1.5x - 8
Topic: Coordinate Geometry
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