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: Sally has 4 apples.
Step-by-step explanation: If she started off with eigth apples and her brother has stolen four apples, then she has four apples left.
8-4=4
Hope this helps you out! ☺
-Karleif-
Work out 3/8 of 48.
First of all divide 48 by the denominator:
48 ÷ 8 = 6 (this gives 1/8 of 48)
Now multiply this answer by the numerator:
6 × 3 = 18 (this gives 3/8 of 48)
Answer:
Step-by-step explanation:
1-3n=-9+n+2 ---> -3n-n=-1+-9+2 --> -4n=-8 ---> n=2
n, n + 2 - two consecutive even integers
3n = 2(n + 2) + 16 |use distributive property
3n = (2)(n) + (2)(2) + 16
3n = 2n + 4 + 16
3n = 2n + 20 |subtract 2n from both sides
n = 20
n + 2 = 20 + 2 = 22
Answer: 20, 22.