Write an expression that represents the volume of a rectangular prism (box) with length 2x^2, width 2x^3, and height 5x. (for any rectangular prism length l, width w, and height h, v=lwh)
a. 10x^5
b.10x^6
c. 20x^5
d. 20x^6

The expression that represents the volume of a rectangular prism with length 2x^2, width 2x^3, and height 5x should be in accordance to the formula of volume of a rectangular prism which is V = lwh. Thus, it should be

V=2x^2(2x^3)(5x) = 20x^6 > OPTION D

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12