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4 years ago

Factor 9x^4 -225y^8 10 points

Mathematics

1 answer:

natita [175]4 years ago

4 0

Answer:

9(x² + 5y⁴) (x² - 5y⁴)

Step-by-step explanation:

9x⁴ - 225y⁸

factor out a 9

9(x⁴ - 25y⁸)

factor (x⁴ - 25y⁸)

(x⁴ - 25y⁸)

x² • x² = x⁴

5y⁴ • -5y⁴ = -25y⁸

(x² + 5y⁴) (x² - 5y⁴)

↓

9(x² + 5y⁴) (x² - 5y⁴)

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If y is proportional to the sqaure root of x and y equal x when x equal 5,evaluate y when x eqaul 9.

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Answer:

$y = 3\, \sqrt{5}$ when $x = 9$ .

Step-by-step explanation:

The question states that $y$ is proportional to $\sqrt{x}$ . In other words, there is a constant $a$ ( $a \ne 0$ ) such that $y = a\, \sqrt{x}$ for all $x \ge 0$ .

The question also states that $y = x$ when $x = 5$ . Make use of this equality to find the value of $a$ .

Since $x = 5$ and $y = x$ , it must be true that $y = 5$ . Substitute $x = 5\!$ and $y = 5\!$ into the equation $y = a\, \sqrt{x}$ and solve for $a$ :

$5 = a\, \sqrt{5}$ .

$\begin{aligned}a &= \frac{5}{\sqrt{5}} \\ &= \sqrt{5}\end{aligned}$ .

Thus, $y = \sqrt{5}\, (\sqrt{x})$ for all $x \ge 0$ .

Substitute in the value $x = 9$ to find the corresponding value of $y$ :

$\begin{aligned} y &= \sqrt{5} \, (\sqrt{9}) \\ &= \sqrt{5} \times 3 \\ &= 3\, \sqrt{5}\end{aligned}$ .

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an actor gains 20pounds for a part and then losses 15 pounds during the filming of the movie to go along with the story.who do y

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