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3 years ago

If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to f(g(x))?

Mathematics

1 answer:

Tomtit [17]3 years ago

7 0

Answer:

3(x^2+1)+2

Step-by-step explanation:

since g(x) is equal to x^2+1 you can substitute x^2+1 for g(x) which will be f(x^2+1). then you can substitute f(x) for 3x+2 and in the end you will get 3(x^2+1)+2

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Dale works at a mattress store, and makes a salary plus commission. He has a $500 weekly salary and makes a 5% commission for sa

Anni [7]

Answer:

1. $\( f\circ g(x)=0.05x-150$

2. $\( g\circ f(x)=0.05x-3000$

3. The first one represents Dale's commission

Explanation:

1. The composition of the function

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

means that you first apply the function g(x) and then f(x) on the output of g(x).

That is:

f(x) = 0.05x
g(x) = x - 3000

$f(g(x)=0.05(x - 3000)$

$f(g(x))=0.05x-150$

2. The composition of the function

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

means that you first apply the function f(x) and then g(x) on the output of f(x).

That is:

$g(f(x))=((0.05x)-3000)=0.05x-3000$

3. Which one represents Dale's commission

To calculate Dales's commision you must subtract $3,000 from the sales, to find the sales over $3000. That is: x - 3,000, which is the function g(x).

Therefore, you first use g(x).

Then, you must multiply the output of g(x) by 0.05 to find the 5% of the sales over $3,000. That is: 0.05(g((x)) = 0.05(x - 3000) = 0.05x - 150.

Therefore, the composition that represents Dale's commission is the first one:

$f(g(x)=0.05(x - 3000)$

$f(g(x))=0.05x-150$

4 0

3 years ago

Find the length of the third side. If necessary, round to the nearest tenth. 4 7

Natalija [7]

Can you show a picture of the question

8 0

3 years ago

Read 2 more answers

A collection of nickels and quarters is worth 2.85 . There are 3 more nickels than quarters how many nickels and quarters are th

Zolol [24]

A nickel is equal to 5 cents or 0.05 dollars.

A quarter is equal to 25 cents or 0.25 dollars.

Let number of nickels be = n

Let number of quarters be = q

$0.05n+0.25q=2.85$ ...........(1)

As it is given, there are 3 more nickels than quarters so equation becomes,

$n=q+3$ ................(2)

Plug in the value of 'n' from (2) in (1)

$0.05(q+3)+0.25q=2.85$

= $0.05q+0.15+0.25q=2.85$

$0.30q=2.70$

$q=9$

As $n=q+3$ we get, $n=9+3=12$

Hence, there are 12 nickels and 9 quarters.

3 0

3 years ago

Dont even know where to start

zalisa [80]

Answer:

$\displaystyle M = ( 3,1 )$

Step-by-step explanation:

we are given the endpoint i.e P and Q of a line segment

we want to figure out the Midpoint of the Line segment

in order to do so we can use Midpoint formula given by

$\displaystyle M = \bigg( \frac{ x_{1} + x_{2} }{2} , \frac{ y_{1} + y_{2}}{2} \bigg)$

so let

$x_1=-2\\x_2=8\\y_1=-2\\y_2=4$

substitute

$\displaystyle M = \bigg( \frac{ - 2 + 8}{2} , \frac{ - 2 + 4}{2} \bigg)$

simplify addition:

$\displaystyle M = \bigg( \frac{ 6}{2} , \frac{ 2}{2} \bigg)$

simplify division:

$\displaystyle M = ( 3,1 )$

hence,

the Midpoint of the line segment is (3,1)

5 0

3 years ago

The temperature in Hokkaido in Japan was -8 degrees at 24:00 one night. By 09:00 the temperature had risen 12 degrees. What was

likoan [24]

Answer:

Step-by-step explanation:

On a number line you will got to -8 and go up 12 and you would get 4

5 0

3 years ago