A boat can travel 140 kilometers on 35 liters of gasoline. How much gasoline will
it need to go 432 kilometers?

Given parameters:

Distance  = 140km

 Volume of gasoline  = 35liters

Unknown:

Volume of gasoline needed for 432km  = ?

Solution:

Let us first find the rate of gasoline consumption per mile. Using this value, we can then determine the volume of gasoline used for the distance given.

  Rate of gasoline consumption by the boat =

                                                    =  

                                                    = 0.25liters/km

Now, the volume of gasoline needed for 432km;

   Volume of gasoline needed  = rate of gasoline consumption x distance

                                                    = 0.25 x 432

                                                    = 108liters of gasoline            

7

step-by-step explanation:

the answer would be 7

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.