Afish tank is a cube. its side length is 4 1/2 feet. the volume of water needed to completely fill the fish tank is cubic feet.

Volume of the cube = 91.125 cubic feet.

Step-by-step explanation:

Given  : A fish tank is a cube. its side length is 4 1/2 feet.

To find :  Volume of water needed to completely fill the fish tank is cubic feet.

Solution : We have given

Side length of cube  = =   feet .

Volume of the cube = .

Plug the value side length =   .

Volume of the cube = .

Volume of the cube =   .

Volume of the cube = 91.125 cubic feet.

Therefore, Volume of the cube = 91.125 cubic feet.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15