Abigail wants to ride her bicycle 30.4 miles this week. She has already ridden 7 miles. If she rides for 3 more days, write and solve an equation which can be used to
determine m, the average number of miles she would have to ride each day to meet
her goal.

3m + 7 = 30.4

m = 7.8

Step-by-step explanation:

3m, where m is the average number of miles per day, will represent how many miles she rides in the next 3 days.

She has already ridden 7 miles, so 7 has to be added to 3m in the equation.

Then, the equation has to be set equal to 30.4, because that is her goal for the week

Put this all together:

3m + 7 = 30.4

Solve for m:

3m + 7 = 30.4

3m = 23.4

m = 7.8

So, Abigail has to ride an average of 7.8 miles per day to meet her goal.

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!