Each lap around pavia park is 1 7/8 miles. ellen rode her bike for 3 1/2 laps before leaving the park. how many total miles did ellen ride her bike in pavia park?

Step-by-step explanation:

The distance of each lap around pavia park is 1 7/8 miles. Converting

1 7/8 miles to improper fraction, it becomes 15/8 miles.

Ellen rode her bike for 3 1/2 laps before leaving the park. Converting

3 1/2 laps to improper fraction, it becomes 7/2 laps.

The total number of miles that Ellen rode her bike in pavia park would be the product of the distance of each lap and the number of laps that he covered. It becomes

15/8 × 7/2 = 105/16 = 6.5626 miles

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!