Anew compact car can travel 288 miles on nine gallons of gas. the distance driven in miles y varies directly with the number of gallons of gas x. this situation can be represented by the equation y = 32x.

Explanation of why is correct.

Step-by-step explanation:

The number of miles that the car can drive can be written as a function of the number of miles that each gallon is capable of by this following function:

In which a is the number of miles each gallon runs.

A new compact car can travel 288 miles on nine gallons of gas. How many miles can it travel on one gallon? This can be solved by a rule of three.

288 miles - 9 gallons

a miles - 1 gallon

So

y = 32x is a correct representation for this problem, since with each gallon of gas the car can run 32 miles.

2x + 2y = 10

(d) is the correct option.

Step-by-step explanation:

The  given set of equations are 3x + y = 19 and x + 3y = 1

Now, Let us try and find the values of x and y from these equation.

3x + y = 19 (1)

x + 3y = 1  (2)

Multiple equation (2) by 3 and subtract from (1), we get

3x + y  - 3(x+ 3y) = 19 - 3(1)

or,  3x + y - 3x - 9y = 19 -3

or, -8y = 16

or, y = 16/-2  = -2

So, y = -2

Put this value in (1), we get

3x  - 2 = 19

or, 3x = 19 +2 = 21  ⇒  x  = 21/3 = 7

So, x = 7 and y = -2 is the solution of the given set of equations.

So, 2x + 2y = 2(7) + 2(-2) = 14 - 4 = 10

⇒  2x + 2y = 10

(d) is the correct option.