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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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sveticcg [70]

If the 10 books are all different, we have:

• 10 ways of selecting the first book,

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• 9 ways of selecting the second book,

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• 8 ways of selecting the third book,

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• 7 ways of selecting the fourth book.

The total number of ways to arrange 4 of the 10 books is:

10\cdot9\cdot8\cdot7=5040.

Answer

There are 5040 ways of arranging the books.

7 0
1 year ago
The circle has a radius of 5 cm. Find the circumference. Give your answer to the nearest tenth. Use pi on your calculator. DO NO
poizon [28]

Answer:

Step-by-step explanation:

Circumference is pi × diameter

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10π is the circumference

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8 0
3 years ago
Read 2 more answers
What are the results of these tasks? =<br> 4x-3=5x-3<br><br> -2x=3x-5
frez [133]

Step-by-step explanation:

I think you are trying to find x, I dunno, but if you are here's the solution.

when trying to find x, your main goal is to shift all x terms to one side.

For the first one

4x-3 = 5x-3

Carry all x terms to one side:

(4x-3)-5x = (5x-3)-5x

4x-5x-3 = -3

Shift all constants (purely just numbers, no x) to the other side

(4x-5x-3)+3 = (-3)+3

4x-5x = 0

-x = 0

x = 0

The second one:

-2x = 3x-5

5x = -5

x = -1

Done, have fun with math!

6 0
3 years ago
A regular polygon has an exterior angle of 8. what is the sum of all the interior angles
Bogdan [553]

Answer:

7740 degrees.

Step-by-step explanation:

The sum of the exterior angles of all polygons add up to 360 degrees.

So the number of sides and the number of interior angles  in this polygon = 360 / 8 = 45.

Each internal angle = 180 - 8 = 172 degrees, so the sum of all interior angles

= 172 * 45

= 7740 degrees,

8 0
3 years ago
Pls help this is my last attempt to get it right before I fail.
TEA [102]
The answer is D. SF is .4
5 0
2 years ago
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