I'm confused on how to do this question

CE = 35

Step-by-step explanation:

Based on the Triangle Proportionality Theorem, BD divides AC and CE proportionally. This implies that:

BC:AB = DC:DE

Plug in the values

(x - 5)/6 = 14/(2x + 3)

(x - 5)(2x + 3) = 14*6

x(2x + 3) -5(2x + 3) = 84

2x² + 3x - 10x - 15 = 84

2x² - 7x - 15 - 84 = 0

2x² - 7x - 99 = 0

Factorize

2x² - 18x + 11x - 99 = 0

2x(x - 9) +11(x - 9) = 0

(2x + 11)(x - 9) = 0

2x = -11

x = -11/2

Or

x = 9

Let's take the positive value of x

Thus:

CE = 14 + 2x + 3

Plug in the value of x

CE = 14 + 2(9) + 3

CE = 14 + 18 + 3

CE = 35

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you

answer: -8.2562234e+13