Jason wants to earn at least $250 each week working during the summer. Jason earns $6.00 an hour babysitting.
Jason earns $7.75 an hour working at a store.
He can work no more than 40 hours each week.
Let b equal hours of babysitting, and s equal hours working at the store.

Which system of inequalities models the constraints?

6.00b + 7.75s ≤ 40
b + s ≥ 250

6.00b + 7.75s ≥ 250
b + s ≤ 40

6.00b + 7.75s ≥ 40
b + s ≥ 250

6.00b + 7.75s ≤ 250
b + s ≤ 40

6.00b + 7.75s ≥ 250

b + s ≤ 40

Step-by-step explanation:

6.00b + 7.75s ≥ 250---this represents how much he will make

b + s ≤ 40---these are his hours. B+S are his hours, and they can't be greater than 40 hrs, so ≤.

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!