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)
Answer:
Choice A. P = I² · R where
- P is the power in the DC circuit,
- I is the current through the circuit, and
- R is the total resistance of the circuit.
Step-by-step explanation:
Electrical power is the rate at which the electrical force does work. So what is electrical work? That's the work
that the electrical force do when it moves charges
across a potential difference
:
W =
.
The power is the rate at which the electrical force do the work:
.
On the other hand, current
is the charge through a cross-section of the circuit in unit time. By the definition of current:
.
.
Consider Ohm's Law:
.
Therefore
.
Answer:
$175
Step-by-step explanation:
let the original price be x
if 1/5 is off the price then the sells is at 4/5
4/5 of x = 140
thus,
4/5* x=140
4x = 140*5
x=700/4
x=$175
Answer:


And we got finally:

And the amount for Zaid would be 1.2*360 ft= 432ft
So then Zaid construc 432 ft and Matias 360 ft
Step-by-step explanation:
For this case we know that Zaid and Matias, two farmers, constructed a 792 foot fence around their very large garden so then the total is represented by 792 ft
We also know that Zaid agreed to construct 20% more of the fence than Matias did. Let's assume that the amount that construct by Matias was x then the amount constructed by Zaid would be 1.2 x representing 20% more than Matias and we can set up the following equation:


And we got finally:

And the amount for Zaid would be 1.2*360 ft= 432ft
So then Zaid construc 432 ft and Matias 360 ft
X^3 = 216
by taking cubic root for both sides
![\sqrt[3]{x^3} = \sqrt[3]{216}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bx%5E3%7D%20%3D%20%20%5Csqrt%5B3%5D%7B216%7D%20)
x = 6