ZA and ZB are vertical angles. If mZA = (5x – 28) and mZB = (3x + 4), find the measure of each angle.

52

Step-by-step explanation:

Vertical angles are equal

<a = <B

5x -28 = 3x+4

Subtract 3x from each side

5x-3x-28 = 3x+4-3x

2x-28 = 4

Add 28 to each side

2x-28+28 = 4+28

2x= 32

Divide by 2

2x/2 = 32/2

x = 16

<A = <B = 3x+4 = 3(16)+4 = 48+4 = 52

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!