let's recall the remainder theorem.
we know that (x-1) is a factor, that means x -1 = 0 or x = 1.
since we know that (x-1) is a factor, then dividing the polynomial by it will give us a remainder of 0, which correlates with saying that f(1) = 0, in this case, so we can simply plug in "1" as the argument, knowing it gives 0.
![f(x)=3x^3+kx-11\\\\[-0.35em]~\dotfill\\\\\stackrel{0}{f(1)}=3(1)^3+k(1)-11\implies \stackrel{f(1)}{0}=3+k-11\implies 0=-8+k\implies 8=k](https://tex.z-dn.net/?f=f%28x%29%3D3x%5E3%2Bkx-11%5C%5C%5C%5C%5B-0.35em%5D~%5Cdotfill%5C%5C%5C%5C%5Cstackrel%7B0%7D%7Bf%281%29%7D%3D3%281%29%5E3%2Bk%281%29-11%5Cimplies%20%5Cstackrel%7Bf%281%29%7D%7B0%7D%3D3%2Bk-11%5Cimplies%200%3D-8%2Bk%5Cimplies%208%3Dk)
What do bones do?
1.) They help us keep our structure.
2.) They protect inner organs.
3.) They produce blood cells in bone marrow.
4.) They allow us to move.
5.) They store minerals and some fats.
I hope this helps!
Answer:
The equation
represents the equation of the parabola with focus (-3, 3) and directrix y = 7.
Step-by-step explanation:
To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).
Using the distance formula
, we find that the distance between (x, y) is

and the distance between (x, y) and the directrix y = 7 is
.
On the parabola, these distances are equal so, we solve for y:

Answer:
D.
Step-by-step explanation:
y = (x - 5)^2 + 16
= x^2 - 5x - 5x + 25 + 16
= x^2 - 10x + 41
That corresponds with answer choice D.
Hope this helps!
Answer:
x = 19
Step-by-step explanation:
To find the value of x, you set the equations as equal to each other:

Then you simplify:
