Question

quadratic functions
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) )?
options:
( h(x) = 0.0045x - 2 )
( h(x) = 0.045x - 0.4 )
( h(x) = 0.0045x - 0.4 )
( h(x) = 0.0015x - 2 )

Explanation:

Step1: Substitute the functions

We know that \( h(x) = f(x) + g(x) \), \( f(x) = 0.003x - 1.2 \) and \( g(x) = 0.0015x + 0.8 \). 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 among the given \( h(x) \) expressions)