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:
y = 
x + 5
Step-by-step explanation:
The Line equation is:
y = 
The line equation is in the form of y = m x + c
Slop of this line is (m1) =
Let another line with slop (m2) , passes through point (4 , 2)
As per question the another line is parallel to the given line equation
So, slop of both the lines are equal
∴ (m2) = (m1) =
Hence equation of another line with slop and passing through points ( 4 , 2) is
y - y1 = (m2) (y - x1)
I.e y - 2 = (x - 4)
Or, 
Or , 4y - 8 = -3x + 12
Or, 4y = -3x + 12 + 8
Or , 4y = -3x + 20
∴ y = x + 5
Hence The value of y = x + 5 Answer
There is a rule:
One input(x-value) can only have one output(y-value) in order to be a function.
If one input has more than one output, it is not a function.
(This doesn't apply to outputs, one output can have more than one input and still be a function)
(2,10),(4,15),(6,20),(8,25)
This is a function because each input only has one output.
Your answer is A
The area of the square is obtained by taking the square of the length of one side. Since it is said that the area of the square is less than 100 m^2, taking the square root of that where: sqrt (100) = 10, the side of that square should be less than 10 as well. Among the choices, D. 0 <y <10 (where y = length of side of square) is the correct answer.
