Latasha and we could go on a road trip first they drive 80 miles east to visit a waterfall then they drive 50 miles north to a mexican restaurant after their meal the friends drive like 40 miles west to visit a cave finally be drive 95 miles south to see a music festival latasha and mika are now what distance from the starting point

60.21 miles

SOLUTION

The trip is as follows:

80 miles East

50 miles North

40 miles West

95 miles South

Since, they drove 80 miles East and 40 miles West

Total horizontal displacement = 80 – 40 (Since east and west are in opposite directions)

Total horizontal displacement = 40 miles (East)

Since, they drove 50 miles North and 95 miles South

Total vertical displacement = 95 – 50 (Since north and south are in opposite directions)

Total vertical displacement = 45 miles (South)

This forms a right angled triangle

40 miles horizontal displacement

45 miles vertical displacement

Current distance from the starting point, d = Hypotenuse of the triangle

d² = 40² + 45²

d² = 1600 + 2025

d² = 3625

√d² = √3625

d = 60.21 miles

Therefore, Latasha and Mike are 60.21 miles from the starting point.

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!