(: morgan and leigh spend a certain amount of money from their money box each month to buy plants. the table shows the relationship between the amount of money (y) remaining in morgan's money box and the number of months (x): function 1 number of months (x) amount remaining (in $) (y) 1(x) 50(y) 2(x) 40(y) 3(x) 30(y) 4(x) 20(y) the equation shows the relationship between the amount of money (y) remaining in leigh’s money box and the number of months (x): function 2: y = −9x + 60 which statement explains which function shows a greater rate of change? function 1 shows a greater rate of change, because morgan spends $10 each month and leigh spends $9 each month. function 1 shows a greater rate of change, because morgan spends $10 each month and leigh spends $60 each month. function 2 shows a greater rate of change, because morgan spends $10 each month and leigh spends $60 each month. function 2 shows a greater rate of change, because morgan spends $50 each month and leigh spends −$9 each month. correct answer with shown work will get brainliest (:

Option A.

Step-by-step explanation:

If a line passes through two points and , then the rate of change is

From the given table it is clear that the Function 1 passes through the points (1,50) and (2,40). So, the rate of change of Function 1 is

Negative sign represents the money spent by Morgan.

The rate of change of Function 1 is -10. It means, Morgan spends $10 each month.

Slope intercept form of a function is

       .... (1)

where, m is slope and b is y-intercept.

The Function 2 is

       .... (2)

On comparing (1) and (2) we get

The rate of change of Function 2 is -9. It means, Leigh spends $9 each month.

Function 1 is decreasing at the rate of 10 and Function 2 is decreasing at the rate of 9. So, the Function 1 shows a greater rate of change.

Therefore, the correct option is A.

h

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!