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3 years ago

Please solve this and show how you did it. Thanks!!!

Mathematics

1 answer:

djyliett [7]3 years ago

4 0

Simplify both sides of the inequality
-2/5x - 9< 9/10
Add 9 to both sides
-2/5x<99/10
Multiply each side by 5/-2
Answer: x> -99/4

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3 years ago

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Bingel [31]

Answer:

See below.

Step-by-step explanation:

First, notice that this is a composition of functions. For instance, let's let $f(x)=\sqrt{x}$ and $g(x)=7x^2+4x+1$ . Then, the given equation is essentially $f(g(x))=\sqrt{7x^2+4x+1}$ . Thus, we can use the chain rule.

Recall the chain rule: $\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)$ . So, let's find the derivative of each function:

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We can use the Power Rule here:

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$g(x)=7x^2+4x+1$

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$g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4$

Now, we can put them together:

$y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)$

$y'=\frac{14x+4}{2\sqrt{7x^2+4x+1} } =\frac{7x+2}{\sqrt{7x^2+4x+1} }$

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Step-by-step explanation:

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