Which of the following is a root of P(x)=-2x^3+x^2+4x+4? -1 0 1 2
1 answer:
Answer:
2
Step-by-step explanation:
You know 0, 1, and -1 are not roots, because the constant is not 0 and the coefficients don't add to 0, even when negating the ones of odd-degree terms.
When evaluating polynomials by hand, it often works well to write them in "Horner form."
P(x) = ((-2x +1)x +4)x +4
P(2) = ((-2·2 +1)2 +4)2 +4 = (-3·2 +4)2 +4 = -2·2 +4
P(2) = 0
2 is a root of P(x).
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I like a graphing calculator for questions like this. It can give an answer instantly. (The equation was pasted directly from the question into the calculator, so the solution took 2 clicks and 2 keystrokes.)
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We want to find a linear equation that models the given situation.
The solution is p = $0.0001*q - $23
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p = m*q + c
Where m is the slope and c is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:
Here we have the two points:
price = $9, boxes = 320,000
price = $8.50, boxes = 270,000
We can rewrite these as:
(320,000 , $9)
(270,000 , $8.50)
Then the slope of the line will be:
Then the line is something like:
p = $0.0001*q + c
To find the value of c we can use one of the two given points, I will use the first one, (320,000 , $9).
Replacing that in our equation we get:
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Then the linear equation is:
p = $0.0001*q - $23
If you want to learn more you can read:
Answer:
Step-by-step explanation:
Let x be the percentage then...
Start by dividing both sides by 4:
Simplify the fraction:
Then, multiply the fraction by 50/50, so we can get a number over 100 (that number would be the percentage). Note we can only multiply it by 50/50 since it is essentially multiplying the fraction by 1.