If the polynomial x5 − 105 can be split as the product of the polynomials

1 answer:

5 0

To answer this item, all that needs to be done is dividing the mathematical expression of x⁵ - 10⁵, our dividend, by x - 10, which is our divisor.

The mathematical expression that can be used in order to properly express the given scenario is,
x⁵ - 10⁵ = (x - 10)(a)

The value of a, as stated above, can be calculated by the equation,
a = (x⁵ -10⁵) / (x - 10)

There are two ways to solve the problem: synthetic division and the long way. Each of which will yield the same answer. Simplifying the value of a will give us a final answer of,
<em> a = x⁴ + 10x³ + 100x² + 1000x</em>

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Two college roommates have each committed to donating to charity each week for the next year. The roommates’ weekly incomes are

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Answer:

C. 5 weeks.

Step-by-step explanation:

In this question we have a random variable that is equal to the sum of two normal-distributed random variables.

If we have two random variables X and Y, both normally distributed, the sum will have this properties:

$S=X+Y\\\\\ \mu_S=\mu_X+\mu_Y=30+60=90\\\\\sigma_S=\sqrt{\sigma_X^2+\sigma_Y^2}=\sqrt{10^2+20^2}=\sqrt{100+400}=\sqrt{500}=22.36$