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777dan777 [17]
3 years ago
8

The hare challenged the tortoise to a race from the water fountain to the park bench. In order to ensure a fair race, the tortoi

se will start 100 feet in front of the hare. The tortoise is walking at a rate of 2 feet per minute. The hare is walking at a rate of 6 feet per minute.
A. How long will it take for the hare to catch up to the tortoise?
B. How long did the hare wait before walking (in order for the tortoise to walk 100 feet)?
C. The distance from the water fountain to the park bench is 130 feet. Who won the race?
Mathematics
1 answer:
BabaBlast [244]3 years ago
5 0
A. I believe the hare never catches up to the tortoise
B. The hare waited 50 minutes before walking
C. The tortoise won the race
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The ascending or descending order of a polynomial is determined by the increasing or decreasing power of variable “x” respectively.

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Step-by-step explanation:

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3 years ago
Let p(x) = x^2 + 8x + 12 and q(x) = x^3 + 5x^2 - 6x. Define r(x) = p(x) \cdot q(x).
Anna [14]

The roots of the entire <em>polynomic</em> expression, that is, the product of p(x) = x^2 + 8x + 12 and q(x) = x^3 + 5x^2 - 6x, are <em>x₁ =</em> 0, <em>x₂ =</em> -2, <em>x₃ =</em> -3 and <em>x₄ =</em> -6.

<h3>How to solve a product of two polynomials </h3>

A value of <em>x</em> is said to be a root of the polynomial if and only if <em>r(x) =</em> 0. Let be <em>r(x) = p(x) · q(x)</em>, then we need to find the roots both for <em>p(x)</em> and <em>q(x)</em> by factoring each polynomial, the factoring is based on algebraic properties:

<em>r(x) =</em> (x + 6) · (x + 2) · x · (x² + 5 · x - 6)

<em>r(x) =</em> (x + 6) · (x + 2) · x · (x + 3) · (x + 2)

r(x) = x · (x + 2)² · (x + 3) · (x + 6)

By direct inspection, we conclude that the roots of the entire <em>polynomic</em> expression are <em>x₁ =</em> 0, <em>x₂ =</em> -2, <em>x₃ =</em> -3 and <em>x₄ =</em> -6. \blacksquare

To learn more on polynomials, we kindly invite to check this verified question: brainly.com/question/11536910

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