Question

the length of time in hours of two airplane flights are represented by the following functions, where x is the number of miles for the flight:
flight a: $f(x) = 0.003x - 1.2$
flight b: $g(x) = 0.0015x + 0.8$
which function represents the total of the flight times, $h(x) = f(x) + g(x)$?
$\circ$ $h(x) = 0.0015x - 2$
$\circ$ $h(x) = 0.045x - 0.4$
$\circ$ $h(x) = 0.0045x - 0.4$
$\circ$ $h(x) = 0.0045x - 2$

Explanation:

Step1: Substitute the functions

We know that \( h(x)=f(x)+g(x) \), and \( f(x) = 0.003x - 1.2 \), \( g(x)=0.0015x + 0.8 \). So we substitute these into the equation for \( h(x) \):
\( h(x)=(0.003x - 1.2)+(0.0015x + 0.8) \)

Step2: Combine like terms

First, combine the \( x \)-terms: \( 0.003x+0.0015x = 0.0045x \)
Then, combine the constant terms: \( - 1.2 + 0.8=-0.4 \)
So, \( h(x)=0.0045x - 0.4 \)

Answer:

\( h(x) = 0.0045x - 0.4 \) (the third option)