Daisy works at an ice-cream parlor. she is paid $10 per hour for the first 8 hours she works in a day. for every extra hour she works, she is paid 1.5 times her hourly wage. if daisy works for x hours in a day, and x is greater than 8, the expression giving her net earnings for the day is x(80 + 1.5)(x - 8)1.5 80 + 15(x - 8)(8)(15)(x - 8). if daisy works 13 hours, she will be paid $1,506$600$475$155.

Equation =

Net earnings is $155.

Step-by-step explanation:

Let the number of hours Daisy works = x

It is given that, she is paid $10 for the first 8 hours. That is, she is paid 10×8 = $80 in total.

Also, for the next hours she works, she is paid 1.5 times her hourly wage.

That is she is paid 1.5×10 = $15 for every next hour she works.

As, she works for 'x' hours, where x is greater than 8.

The equation representing the net earnings of Daisy = in dollars.

So, when she works for 13 hours i.e. x= 13, her net earnings is,

Net earning = 80+15× (13-8) = 80 + 15 × 5 = 80 + 75 = $155

Thus, her net earnings after 13 hours is $155.

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!