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.

i assume that by 5 you mean 5 gallons.

(20)(0.25) = 15

removing 15 gallons reduces the tank from 20 to 5.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."