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Ivahew [28]
2 years ago
5

Express your answer as a polynomial in standard form

Mathematics
1 answer:
Bingel [31]2 years ago
8 0

Answer:

f(g(x)) = 4x² + 16x + 13

Step-by-step explanation:

Given the composition of functions f(g(x)), for which f(x) = 4x + 5, and g(x) = x² + 4x + 2.

<h3><u>Definitions:</u></h3>
  • The <u>polynomial in standard form</u> has terms that are arranged by <em>descending</em> order of degree.
  • In the <u>composition of function</u><em> f  </em>with function <em>g</em><em>, </em>which is alternatively expressed as <em>f  </em>° <em>g,</em> is defined as (<em>f </em> ° <em>g</em>)(x) = f(g(x)).

In evaluating composition of functions, the first step is to evaluate the inner function, g(x). Then, we must use the derived value from g(x) as an input into f(x).

<h3><u>Solution:</u></h3>

Since we are not provided with any input values to evaluate the given composition of functions, we can express the given functions as follows:

f(x) = 4x + 5

g(x) = x² + 4x + 2

f(g(x)) = 4(x² + 4x + 2)  + 5

Next, distribute 4 into the parenthesis:

f(g(x)) = 4x² + 16x + 8  + 5

Combine constants:

f(g(x)) = 4x² + 16x + 13

Therefore, f(g(x)) as a polynomial in <em>x</em> that is written in standard form is: 4x² + 16x + 13.

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The correct answer is B.12.2

Step-by-step explanation:

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A right triangle has side lengths 7, 24, and 25 as shown below.
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Answer:

  • tan(A) = 7/24
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Step-by-step explanation:

The mnemonic SOH CAH TOA can help you remember the trig ratios:

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

With respect to angle A, the sides are Adjacent = 24; Opposite = 7, Hypotenuse = 25. Then the desired trig ratios are ...

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A line segment has endpoints at (–1, 4) and (4, 1). Which reflection will produce an image with endpoints at (–4, 1) and (–1, –4
katrin2010 [14]

Answer:- A reflection of the line segment across the line y = –x .


Explanation:-

A reflection over the line y = -x, the x-coordinate and y-coordinate interchange their places and they are negated (the signs are changed).

Given :- A line segment has endpoints at (–1, 4) and (4, 1) such that it reflects produce an image with endpoints at (–4, 1) and (–1, –4).

(-1, 4)→(-4, 1) and

(4, 1)→(-1, -4)

Thus this shows a reflection of the line segment across the line y = –x.

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Answer:

-2

Step-by-step explanation:

3-2n=7

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divide both sides by -2

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diameter = <span> <span> <span> 12.9934095689 </span> </span> </span>
Basically, the rug is roughly 1 foot wider than the room.


7 0
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