Afamily has two cars. the first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. during one week, the two cars went a combined total of 1700 miles, for a total gas consumption of 50 gallons. how many gallons were consumed by each of the two cars that week?

The number of gallons consumed by the first car were 30

The number of gallons consumed by the second car were 20

Step-by-step explanation:

Let

x -----> number of gallons consumed by the first car during one week

y -----> number of gallons consumed by the second car during one week

we know that

The efficiency multiplied by the number of gallons is equal to miles

30x+40y=1,700 -----> equation A

x+y=50 ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (30,20)

see the attached figure

therefore

The number of gallons consumed by the first car were 30

The number of gallons consumed by the second car were 20

but there’s no any figure there!

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: