<h3>
Answer: n = -11</h3>
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Explanation:
Since x-2 is a factor of f(x), this means f(2) = 0.
More generally, if x-k is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.
So if we plugged x = 2 into f(x), we'd get
f(x) = x^3+x^2+nx+10
f(2) = 2^3+2^2+n(2)+10
f(2) = 8+4+2n+10
f(2) = 2n+22
Set this equal to 0 and solve for n
2n+22 = 0
2n = -22
n = -22/2
n = -11 is the answer
Therefore, x-2 is a factor of f(x) = x^3+x^2-11x+10
Plug x = 2 into that updated f(x) function to find....
f(x) = x^3+x^2-11x+10
f(2) = 2^3+2^2-11(2)+10
f(2) = 8+4-22+10
f(2) = 0
Which confirms our answer.
Answer:
see explanation
Step-by-step explanation:
The 2 equations are
x + 2y = 8 → (1)
2x + 4y = 20 → (2)
Answer:
5 cubes
Step-by-step explanation:
The volume of a square pyramid is given in terms of its side length (s) and height (h) as ...
V = (1/3)s^2·h
For the given measurements, the volume is ...
V = (1/3)(9 cm)^2 ·(10 cm) = 270 cm^3
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The volume of each cube of wax is the product of its length, width, and height, so is ...
V = (4 cm)^3 = 64 cm^3
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Then the number of wax cubes required to fill the pyramid is ...
(270 cm^3)/(64 cm^3/cube) = 4 7/32 cubes
Four cubes are not quite enough to make the candle.
Devin will need 5 cubes to make the candle.
