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3 years ago

Solve the following inequality. Then place the correct answer in the box provided. Answer in terms of a mixed number.

Mathematics

2 answers:

Mama L [17]3 years ago

5 0

2P + 2 + 3P + 6 > 2
5P + 8 > 2
Subtract 8 from both sides.
5P > -6
Divide each side by 5.
P > -6/5

drek231 [11]3 years ago

3 0

Answer: $-1\frac{1}{5}$

Step-by-step explanation:

$2(P +1) + 3(P + 2 ) > 2$

Distribute 2 and 3

$2P+2+3P+6>2$

Combine like terms;

$5P+8>2$

Subtract 8

$5P>2-8$

$5P>-6$

Divide by 5

$P>-\frac{6}{5}$

Convert to a mixed number by dividing. However, when we have the numerator greater than the denominator, we must find a way to make the numerator lower. We can achieve this by separating it into 2 fractions.

$-\frac{6}{5}=-\frac{5}{5}-\frac{1}{5}$

When we do this, we can see that 5/5 = 1

$-1-\frac{1}{5}=-1\frac{1}{5}$

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jek_recluse [69]

<h3>Answer: Choice D</h3>

$(f \circ g)(x) = x+12$

Domain = [-3, infinity)

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Work Shown:

$f(x) = x^2 + 9\\\\f(g(x)) = (g(x))^2 + 9\\\\f(g(x)) = (\sqrt{x+3})^2 + 9\\\\f(g(x)) = x+3 + 9\\\\f(g(x)) = x+12\\\\(f \circ g)(x) = x+12\\\\$

In step 2, we replaced every x with g(x)

In step 3, we plugged in g(x) = sqrt(x+3)

The domain of g(x) is [-3, infinity), so this is the domain of $(f \circ g)(x)$ as well since the composite function depends entirely on g(x). Put another way: the input of f(x) depends on the output of g(x), so that's why the domains match up.