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.
Since, the number w and 0.8 are additive inverses.
A number 'a' is said to have an additive inverse '-a' if "a+ (-a)= 0".
Since, 'w' and '0.8' are additive inverses of each other such that 
Therefore, the value of 'w' should be '-0.8' so that 
.
So, the value of 'w' is =0.8
Now, Refer to the attached image which represents the position of 0.8 , w ( that is -0.8) and the sum of 0.8 and w.
Sum of 0.8 and w = 0.8 + w
= 0.8 +(-0.8)
= 0.
Segment addition postulate
Substitution
Distribution Property of Equality
Simplification, or Adding like terms
Subtraction property
Division Property
Answer:
A: Yes, I agree. Why? Because if you look at the shape, its a triangle right, and a triangle both sides are equal, while the bottom line is not. But because both sides are equal, and half of the triangle is MPN and the other side is QPN, they both are congruent (or equal to)
B: Like I said, both MPN and QPN are both equal, and if you remove the P, it would still be the same because the shape has not changed.
I hope I helped :)
Answer:
c<-3
Step-by-step explanation:
move the constant to the right-hand side and change its sing
Then canculate the difference
Then divide both sides for the inequality of 3
