1. On Saturdays, the #14 bus makes roundtrips between Susan's school and the
mall, and the #11 bus makes roundtrips between the mall and the museum.
Next Saturday, Susan wants to take the bus from her school to the museu
#14 bus leaves Susan's school every 15 minutes, beginning at 7 A. M. It takes the
bus 30 minutes to travel between the school and the mall. A #11 bus leaves the
mall every 12 minutes, beginning at 7 A. M.
a. If Susan gets on the #14 at 9:30 A. M., how long will she have to wait at the
mall for a #11 bus? Explain your reasoning.
b. If Susan gets on the #11 bus at the museum and arrives at the mall at
11:48 A. M., how long will she have to wait for the #14 bus? Explain your
reasoning.
c. At what times from 9 A. M. until noon are the #14 and #11 buses at the mall
at the same time? Explain your reasoning.

answer: 25.4 units

step-by-step explanation: radius = 12.7 units

diameter = twice the radius

diameter = 12.7 x 2

= 25.4

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!