What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12?

(–∞, –3]
[–3, ∞)
(–∞, 15]
[15, ∞)

To find the possible values of x, first we mus simplify the inequality -18 + 6x ≥ 4x + 12 6x - 4x ≥ 12 + 18 2x ≥ 30 x ≥ 15 From this, it can be seen that as long as x is equal or more than 15, then it will satify the equation. In mathematicl expression, that means [15, ∞). Thus, the answer is D: [15, ∞).

The area of the base would be found using the area of a triangle formula which is 1/2 x base x height.

The base and height are the two sides perpendicular to each other, which are both 5 inches.

The area of the base = 1/2 x 5 x 5 = 12.5 square inches.

The volume of the triangular prism is the area of the base times the height, which is 4 inches.

Volume of the triangular prism is 12.5 x 4 = 50 cubic inches.

Volume of the triangular prism is 1/3 x area of base x height, which is 7:

Volume of the triangular prism = 1/3 x 12.5 x 7 = 29.17 cubic inches.

Total volume = 29.17 + 50 = 79.17 cubic inches.