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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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Verify sine law by taking triangle in 4 quadrant<br>Explain with figure.<br>​
Ksivusya [100]

Proof of the Law of Sines

The Law of Sines states that for any triangle ABC, with sides a,b,c (see below)

a

 sin  A

=

b

 sin  B

=

c

 sin  C

For more see Law of Sines.

Acute triangles

Draw the altitude h from the vertex A of the triangle

From the definition of the sine function

 sin  B =

h

c

    a n d        sin  C =

h

b

or

h = c  sin  B     a n d       h = b  sin  C

Since they are both equal to h

c  sin  B = b  sin  C

Dividing through by sinB and then sinC

c

 sin  C

=

b

 sin  B

Repeat the above, this time with the altitude drawn from point B

Using a similar method it can be shown that in this case

c

 sin  C

=

a

 sin  A

Combining (4) and (5) :

a

 sin  A

=

b

 sin  B

=

c

 sin  C

- Q.E.D

Obtuse Triangles

The proof above requires that we draw two altitudes of the triangle. In the case of obtuse triangles, two of the altitudes are outside the triangle, so we need a slightly different proof. It uses one interior altitude as above, but also one exterior altitude.

First the interior altitude. This is the same as the proof for acute triangles above.

Draw the altitude h from the vertex A of the triangle

 sin  B =

h

c

      a n d          sin  C =

h

b

or

h = c  sin  B       a n d         h = b  sin  C

Since they are both equal to h

c  sin  B = b  sin  C

Dividing through by sinB and then sinC

c

 sin  C

=

b

 sin  B

Draw the second altitude h from B. This requires extending the side b:

The angles BAC and BAK are supplementary, so the sine of both are the same.

(see Supplementary angles trig identities)

Angle A is BAC, so

 sin  A =

h

c

or

h = c  sin  A

In the larger triangle CBK

 sin  C =

h

a

or

h = a  sin  C

From (6) and (7) since they are both equal to h

c  sin  A = a  sin  C

Dividing through by sinA then sinC:

a

 sin  A

=

c

 sin  C

Combining (4) and (9):

a

 sin  A

=

b

 sin  B

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7 0
3 years ago
I just need help with first 2! Show work please it’s due soon and round answers to the nearest tenth !!!
natima [27]

Answer:

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V = pi(4)^2(6)

V = 301.59

Rounded* = 301.6

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4/3pi(18)^3

D =  24429.02

Rounded* = 24429.0

I cant read the last one completely, hope this helps.

5 0
2 years ago
What is the probability of getting 6 as a product explanation and calculation
Mrrafil [7]

For an individual die roll, the probability of rolling 6 is \dfrac{1}{6}

6

1

.

Effectively, this problem is asking for P(\text{1st roll is 6}\cap\text{2nd roll is 6})P(1st roll is 6∩2nd roll is 6).

Using the rule of product, this is:

\dfrac{1}{6}\times\dfrac{1}{6}=\dfrac{1}{36}

6

1

×

6

1

=

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8 0
2 years ago
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jeka57 [31]

Answer: how much did the calculators cost seperetely dummy

Step-by-step explanation:

7 0
3 years ago
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stira [4]
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R=6%
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8 0
3 years ago
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