Ineed to find the volume of the prism

Option d

Volume of the prism is, 2184 cubic inches

Step-by-step explanation:

Since this figure represents the rectangular prism;

from this figure; we have

Length of rectangular Prism = 13 in

Width of rectangular Prism (w)= 14 in

and height of rectangular Prism (h) = 12 in

Now, we  can determine the volume of a rectangular prism by either multiplying the area of the base times the height or by multiplying the length, width and height.

i.e, cubic unit where A is the area of the rectangular prism and is the length respectively or

⇒ cubic inches

Simplify we get,

cubic inches

Therefore, the volume of the prism is,  2184 cubic inches

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.

e) none of the above because the measure of angle cba is 101°