Answered

IDNStudy.com, ang iyong mapagkakatiwalaang mapagkukunan para sa eksaktong at maaasahang mga sagot. Magtanong at makatanggap ng maaasahang sagot mula sa aming dedikadong komunidad ng mga eksperto.

The dimensions of a cage are: height = (3x – 4) feet, length = (x + 3) feet, and

width = (x + 1) feet. If the volume of the cage is 120 cubic feet, what is the

value of x?

A. 3 B. 2 C. 1 D. 4​

Sagot :

KuyaEngridn

In the given problem, apply your knowledge in algebraic expression specially in mathematical operation and solving unknown variables.

Formula or finding volume of rectangular prism is L×W×H.

Assume that the cage is a rectangular prism, since there are three given dimensions (lenght, width and height).

Solution:

height = (3x – 4) feet,

length = (x + 3) feet,

width = (x + 1) feet.

Volume = 120 cubic feet

Volume = L×W×H

120 = (x+3)(x+1)(3x-4)

120 = (3x-4)(x²+4x+3)

120 = (3x³+12x²+9x-4x²-16x-12)

120 = 3x³ + 8x - 7x - 12

3x³ + 8x - 7x - 132 = 0

Solve for x using synthetic division.

3x³ + 8x - 7x - 132 = 0

x = 3 | 3x³ + 8x - 7x - 132 = 0

3 | 3 | 8 | -7 | -132

| | 9 | 51 | 132

| 3 | 17 | 44 | 0

Therefore, x = 3

Check:

height = (3x – 4) feet, → 3(3) - 4 = 5 feet

length = (x + 3) feet, → 3+3 = 6 feet

width = (x + 1) feet. → 3+1 = 4 feet

Volume = lwh

120 = (5)(6)(4)

120 = 120 ✓

Answer: A. 3

Learn more about the formula for volume of different figures here at https://brainly.ph/question/274699

#CarryOnLearning

#BRAINLYFAST

Natutuwa kami na ikaw ay bahagi ng aming komunidad. Patuloy na magtanong at magbahagi ng iyong mga ideya. Sama-sama tayong magpapaunlad ng kaalaman para sa lahat. Bawat tanong ay may sagot sa IDNStudy.com. Salamat at sa muling pagkikita para sa mas maraming solusyon.