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:
x = -4
y = -12
Step-by-step explanation:
Since y is 3x,
3x = 2x - 4
On solving we get x as -4
Substitute x and we get y as -12
Answer:
-2.5x-.5
draw the dotted line (3/7)x-3 and shade below it
Step-by-step explanation:
First, we need the slope
Use the slope formula:
so we have
y= -2.5x+b
Solve for b by plugging in coordiantes
-8= -2.5(3)+b
-8= -7.5+b
b= -.5
Put it together and get -2.5x-.5
2.)
A line is parallel to another line if they have the same slope (and different y intercepts)
So in the formula y=mx+b we knowe that m= 2/3
Now it's just a matter of solving for B
plug in the required coordinate to do this
-1=(2/3)*0+b
-1= b
Put it all together to get
3.)
put this into slope intercept form
3x-7y>21
3x-21 > 7y
(3/7)x-3 >y
To graph this just draw a dotted line with the equation (3/7)x-3 and shade everything below it (use de_smos if you're stuck)
