By looking at the degree of the polynomials, we conclude that the option that is not linear is option C.
<h3>Which of the following functions is not a linear function?</h3>
A polynomial is an expression of the form:

Where all the exponents are natural numbers.
We define the degree of a polynomial as the largest exponent, and we define a linear function as a polynomial of degree 1.
So a linear function is of the form:

Now, if you look at option C, you can see that the degree of that polynomial is 2. So that is not a linear function.
Then the correct option is C.
If you want to learn more about linear equations:
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we know that
1 ft is equal to 12 in
1 cubic yard is equal to 27 cubic feet
Step 1
<u>Find the area of the circular border of uniform width around the pool</u>
Let
x---------> the uniform width around the pool
we know that
The diameter of the circular pool measures 10 feet
so
the radius r=5 ft
the area of the circular border is equal to
![A=\pi *(5+x)^{2}- \pi *5^{2} \\A= \pi *[(x+5) ^{2}-5^{2} ] \\ A= \pi * [x^{2} +10x]](https://tex.z-dn.net/?f=A%3D%5Cpi%20%2A%285%2Bx%29%5E%7B2%7D-%20%5Cpi%20%2A5%5E%7B2%7D%20%5C%5CA%3D%20%5Cpi%20%2A%5B%28x%2B5%29%20%5E%7B2%7D-5%5E%7B2%7D%20%5D%20%5C%5C%20A%3D%20%5Cpi%20%2A%20%5Bx%5E%7B2%7D%20%2B10x%5D)
step 2
volume of the concrete to be used to create a circular border is equal to
V=1 yd^{3}-------> convert to ft^{3}
V=27 ft^{3} -------> equation 1
the depth is equal to 4 in-------> convert to ft
depth=4/12=(1/3) ft
volume of the concrete to be used to create a circular border is also equal to
V=Area of the circular border*Depth
-------> equation 2
equate equation 1 and equation 2
![27=\pi * [x^{2} +10x]*(1/3) \\ x^{2} +10x- \frac{81}{\pi }=0](https://tex.z-dn.net/?f=27%3D%5Cpi%20%2A%20%5Bx%5E%7B2%7D%20%2B10x%5D%2A%281%2F3%29%20%5C%5C%20x%5E%7B2%7D%20%2B10x-%20%5Cfrac%7B81%7D%7B%5Cpi%20%7D%3D0)
using a graph tool------> to resolve the second order equation
see the attached figure
the solution is the point
x=2.126 ft
therefore
<u>the answer is</u>
The uniform width around the circular pool border is 2.126 ft
Answer
23.70
Proof
3Q+5+2-8-5=65 ~ Simplify
3Q-6=65 ~Cancel out the six
+6 +6 ~Add 6 to both sides since it is a 3Q=71 negative.
/3 /3 ~Cancel out the three.
Answer ~Divide both sides by 3
Q=23.66
Rounded Up
Q=23.70
Answer: f(x) = -ln(x + 1) + 3
Step-by-step explanation:
We want it to be decreasing, then we can write it, for a start, as:
f(x) = -ln(x)
Ok, now we want it to have a positive y intercept, then we can add a real number inside the logarithm, and other outside: such that f(0) = positive number.
f(x) = -ln(x + 1) + 3
Now, when x = 0 we have:
f(0) = -ln(1) + 3 = 0 + 3 = 3
Then we have a decreasing logarithmic function, with an y-intercept larger than zero.