ANSWER
(2,2)
EXPLANATION
Since f(x) and its inverse function are symmetric about the line y=x, if (a,b) lies on the graph of f, then (b,a) must lie on f inverse.
The point (2,2) lies on f and the same time on f inverse.
The solution is a point that satisfies both equations.
Hence the correct choice is:
(2,2)
Answer:
L = the length of the field
W = the width of the field
The First Question:
The system is: L - 12 = w
2L + 2W = 76
Plug in L - 12 for W and you will get
2L + 2L - 24 = 76
4L -24 = 76
4L = 100
L = 25
To find W do L - 12 = w
25 - 12 = w
w = 13
2x² - 4x - 30
2(x²) - 2(4x) - 2(15)
2(x² - 4x - 15)
Step-by-step explanation:
We will prove by contradiction. Assume that 
is an odd prime but n is not a power of 2. Then, there exists an odd prime number p such that 
. Then, for some integer 
,
Therefore
Here we will use the formula for the sum of odd powers, which states that, for 
and an odd positive number 
,
Applying this formula in 1) we obtain that
.
Then, as 
we have that 
is not a prime number, which is a contradiction.
In conclusion, if is an odd prime, then n must be a power of 2.
Answer:
f(x) + k
Explanation:
Vertical shift is represented by adding/subtracting a constant from the original given equation.
If the constant added is +ve, this means that the curve is vertically shifted upwards
If the constant added is -ve, this means that the curve is vertically shifted downwards.
Now, for the given, we have the original function f(x) and the constant k, therefore, to shift the graph vertically, the new function would be f(x)+k
We have:
f(x) = x² and k = -3
This means that the new function would be:
x² - 3
Since the constant is -ve, we can conclude that the curve is shifted vertically downwards by 3 units
Hope this helps :)
