A box in the shape of a rectangular prism has a volume of 72 cubic feet. The box has a length of x feet, a width of (x − 1) feet, and a height of (x + 9) feet. Find the dimensions of the box.

Length => x => 3 feet

Width = (x - 1) => (3 - 1) = 2 feet

Height = (x + 9) => (3 + 9) = 12 feet

Volume = 3 * 2 * 12 = 72 feet³

Step-by-step explanation:

Given;

Volume of the rectangular prism = 72 ft³

Length of the box = x ft

width of the box = (x-1) ft

height of the box = (x+9) ft

Volume of rectangular prism = Length * Width * Height

72 =  x * (x-1) * (x+9)

72 − x(x−1)(x+9) = 0

−x³ − 8x² + 9x + 72 = 0

− (x+8) (x+3) (x−3) = 0

multiply both sides by -1

(x+8) (x+3) (x−3) = 0

Compare each part to zero

x + 8 = 0   ,    x + 3 = 0    ,   x - 3 = 0

x = -8        ,      x = -3       ,      x = 3

The value of x can only be positive considering that we are looking at an actual measurement.

Therefore, x = 3

Substitute for x in the given

Length => x => 3 feet

Width = (x - 1) => (3 - 1) = 2 feet

Height = (x + 9) => (3 + 9) = 12 feet

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)