To answer your question, it is shown in the image below
Let n be the larger integer and n-2 be the smaller integer.
n² - (n - 2)²
= n² - (n - 2)(n - 2)
= n² - (n² - 4n - 4)
= n² - n² + 4n + 4
= 4n + 4
= 4(n + 1)
No matter what value n is, it will always be a multiple of 4.
The value of x from the given circle is 12
<h3>Circle theorem</h3>
Angle at the vertex of the circle is half the angle at its intercepted arc.
From the given circle;
The measure of <DEF = 80/2 = 4x -8
Equate both angles
4x - 8 = 80/2
Add 8 to both sides
4x - 8 + 8 = 40 + 8
4x = 48
x =12
Hence the value of x from the given circle is 12
Learn more on circle theorem here: brainly.com/question/26594685
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Based on the information, there were initially 1200 ferns; the monthly percent rate of change is 68% and this situation is modeled by an exponential growth function
<h3>How to complete the information?</h3>
The given parameters from the question are:
P(n) = 1200(1.68)^n
Where
n represent the number of months
An exponential growth function is represented as:
P(n) = a * (1 + r)^n
Where
a represents the initial value
r represents the rate
By comparison, we have
a = 1200
1 + r = 1.68
This gives
r = 0.68 = 68%
Hence, there were initially 1200 ferns; the monthly percent rate of change is 68% and this situation is modeled by an exponential growth function
Read more about exponential growth function at:
brainly.com/question/2456547
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Slope = (y2 - y1) / (x2 - x1)
Slope = (0 - 0) / (2 --4)
Slope = (0) / (6)
Slope = 0
