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Karo-lina-s [1.5K]
4 years ago
9

For the following inequality, indicate whether the boundary line should be dashed or solid. x ≤ 5

Mathematics
1 answer:
lukranit [14]4 years ago
6 0
Answer: The boundary lien should be solid because the inequality indicates that the value “5” is included. Remember: “greater than or equal to; less than or equal to,” as solid lines. While “<;>” are dashed lines.
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Determine the degree of the polynomial -57
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Answer:

linear polynomial

Step-by-step explanation:

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Which statements are correct about the average rate of change for the function f(x) = x2 + 9x + 18 ?
pshichka [43]

Answer:

Presumably this is a multiple choice question, and without seeing the potential answers, we can't tell you which ones are correct.

A few things can however be said about this function:

1) It describes a parabola that extends upward infinitely.  We can see this because it's in the classic format ax² + bx + c, and all terms are positive.

2) We can find the x-intercepts by solving for zero.  In this case we can do that by factoring it:

x² + 9x + 18 = 0

x² + 3x + 6x + 18 = 0

x(x + 3) + 6(x + 3) = 0

(x + 6)(x + 3) = 0

So the x intercepts occur at (-6, 0) and (-3, 0)

3) we can find its vertex by taking its derivative and solving for zero:

f'(x) = 2x + 9

0 = 2x + 9

x = -4.5

We can then plug that coordinate into the original function to find the y coordinate:

f(x) = x² + 9x + 18

f(-4.5) = 20.25 - 40.5 + 18

= -2.25

So the vertex is at (-4.5, -2.25)

4) As mentioned, the derivative of f(x) is f'(x) = 2x + 9.  The integral is:

x³ / 3 + 9x² / 2 + 18x + C

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Step-by-step explanation:

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