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3 years ago

17.) An ostrich can run 174 feet in 3 seconds. What is the slope of the line and what does it

Mathematics

1 answer:

german3 years ago

3 0

The slope of the line is positive.

The slope of the line is 58.

The ostrich can run 58 feet per second.

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Ryan runs 100 m two times. His times were 14.19 s and 13.78 s.

OLEGan [10]

Answer is 4.04 by adding both of the time of each then subtracting then from each others time

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4 years ago

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Kevin says it will take him less than 1 hour to play soccer, and practice piano because these tasks will take a total of 8/12 ho

OverLord2011 [107]

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4 years ago

What is the answer to 4/3.8/3

kondor19780726 [428]

$\frac{4}{3}\times \frac{8}{3}
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3 years ago

A bag contains 5 yellow marbles, 7 pink marbles, and 3 purple marbles. Gordon selects a marble without looking. What is the prob

eduard

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B is the answer.

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4 years ago

Use the Factor Theorem and synthetic division to show x + 5 is a factor of f(x) = 2x3 + 7x2 − 14x + 5

olga2289 [7]

Answer:

Factor theorem: $f(-5) = 0$ .

Synthetic division: $f(x) = (x + 5)\, (2\, x^2 -3\, x + 1)$ .

Step-by-step explanation:

<h3>Factor Theorem</h3>

By the factor theorem, a monomial of the form $(x - a)$ (where $a$ is a constant) is a factor of polynomial $f(x)$ if and only if $f(a) = 0$ .

In this question, the monomial is $(x + 5)$ , which is equivalently $(x - (-5))$ . $a = -5$ .

$\begin{aligned}& f(-5) \\ &= 2 \times (-5)^{3} + 7 \times (-5)^{2}- 14\times (-5) + 5\\ &= -250 + 175 + 70 + 5 \\ &= 0\end{aligned}$ .

Hence, by the factor theorem, $(x + 5)$ , which is equivalent to $(x - (-5))$ , is a factor of $f(x)$ .

<h3>Synthetic Division</h3>

$\begin{aligned}& f(x) \\ &= 2\, x^{3} + 7\, x^{2} - 14\, x + 5 \\ &= \underbrace{(x + 5) \, (2\, x^2)}_{2\, x^{3} + 10\, x^{2}} - 3\, x^{2} - 14\, x + 5 \\ &= \underbrace{(x + 5) \, (2\, x^2)}_{2\, x^{3} + 10\, x^{2}} + \underbrace{(x + 5)\, (-3\, x)}_{-3\, x^{2} - 15\, x} + (x + 5) \\ &= (x + 5)\, (2\, x^{2} - 3\, x + 1)\end{aligned}$ .

The remainder is $0$ when dividing $f(x)$ by $(x + 5)$ . Hence, $(x + 5)\!$ is a factor of $f(x)\!$ .

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3 years ago