Evan and Peter have a radio show which consists of 2 segments. They need 4 less than 11 songs in the first segment. In the second segment, they need 5 less than 3 times the number of songs in the first segment. Part A Write an expression for the total number of songs they need for their show. A. ( 11 − 4 ) + 3 × 11 − 4 − 5 B. ( 11 − 4 ) + 3 × ( 11 − 4 ) − 5 C. ( 11 − 4 ) + 3 − 4 × 11 − 5 D. ( 11 − 4 ) + 3 − 5 × ( 11 − 4 )

B. ( 11 − 4 ) + 3 × ( 11 − 4 ) − 5

Step-by-step explanation:

There are 2 segments

First segment,

They need 4 less than 11 songs

=(11-4)

Second segment

They need 5 less than 3 times the number of songs in the first segment

3 times the number of songs in first segment

=3*(11-4)

5 less than 3 times the number of songs in first segment

={3*(11-4)} - 5

Total expression=

(11-4)+ {3×(11-4)} - 5

B. ( 11 − 4 ) + 3 × ( 11 − 4 ) − 5

8

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!