Please answer question. I need some math to explain the answer, not just the answer. Ignore my work, that was wrong. Please help
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WILL GIVE BRAINLISTSSSSS!!!!
WILL GIVE BRAINLISTSSSSS!!!!
1 answer:
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Answer:
-3, 1, 4 are the x-intercepts
Step-by-step explanation:
The remainder theorem tells you that dividing a polynomial f(x) by (x-a) will result in a remainder that is the value of f(a). That remainder will be zero when (x-a) is a factor of f(x).
In terms of finding x-intercepts, this means we can reduce the degree of the polynomial by factoring out the factor (x-a) we found when we find a value of "a" that makes f(a) = 0.
__
For the given polynomial, we notice that the sum of the coefficients is zero:
1 -2 -11 +12 = 0
This means that x=1 is a zero of the polynomial, and we have found the first x-intercept point we can plot on the given number line.
Using synthetic division to find the quotient (and remainder) from division by (x-1), we see that ...
f(x) = (x -1)(x² -x -12)
We know a couple of factors of 12 that differ by 1 are 3 and 4, so we suspect the quadratic factor above can be factored to give ...
f(x) = (x -1)(x -4)(x +3)
Synthetic division confirms that the remainder from division by (x -4) is zero, so x=4 is another x-intercept. The result of the synthetic division confirms that x=-3 is the remaining x-intercept.
The x-intercepts of f(x) are -3, 1, 4. These are the points you want to plot on your number line.
Answer:
(a). 15
(b). 78
Step-by-step explanation:
Growth of the population of a fruit fly is modeled by
N(t) =
where t = number of days from the beginning of the experiment.
(a). For t = 0 [Initial population]
N(0) =
=
=
= 15
Initial population of the fruit flies were 15.
(b).Population of the fruit fly colony on 11th day.
N(11) =
=
=
=
=
= 77.82
≈ 78
On 11th day number of fruit flies colony were 78.