Donnie and tania are math tutors. the amount donnie charges for a session h hours long is represented by the function d(h) = 40h + 10. tania charges a flat fee of $30 plus $15 an hour. write a function, t(h), that represents the amount in dollars that tania charges for h hours of tutoring. graph both functions on the same coordinate grid, and label each line. compare the slopes and y-intercepts of the graphs.

The graph is shown below.

Step-by-step explanation:

The amount Donnie charges for a session h hours long is represented by the function

Tania charges a flat fee of $30 plus $15 an hour. The amount in dollars that Tania charges for h hours of tutoring is represented by the function

Slope intercept form of a line is y=mx+b, where m is slope and b is y-intercept.

For Donnie:

Slope = 40 and y-intercept = 10

For Tania:

Slope = 15 and y-intercept = 30

It means slope of Donnie is greater than Tania and y-intercept of Tania is greater than Donnie.

Table of values for Donnie:

x      y

0     10

1     50

2     90

Table of values for Tania:

x      y

0     30

1     45

2     60

Plot these ordered pair on same coordinate plane and connect them to draw both functions.

The graph is shown below.

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!

sine

step-by-step explanation: