The base area of an oblique pentagonal prism is 15 sq. in. the prism measures 3 inches in height and the edges connecting the bases measure 5 inches each. which statements about the prism are true? check all that apply.

- the volume of the prism is computed using the expression (15)(3).

- the volume cannot be determined because the dimensions of the base are unknown.

- the edge length can be used in place of the height of an oblique prism if the height is unknown.

- the unit on the volume measure of the prism is cubic inches.

-the edge length times the height is the area of the base in any prism.

we know that

The volume of an oblique pentagonal prism is equal to

where

B is the area of the base of the prism

h is the height of the prism

In this problem we have

so

The volume is equal to

Statements

case A) The volume of the prism is computed using the expression

The statement is true

See the procedure

case B) The volume cannot be determined because the dimensions of the base are unknown

The statement is false

Because, the dimensions of the base are not required, as the area of the base and the height of the prism are known

case C) The edge length can be used in place of the height of an oblique prism if the height is unknown

The statement is false

Because, the edge length and the height are different measures

case D)The unit on the volume measure of the prism is cubic inches

The statement is true

see the procedure

case E) The edge length times the height is the area of the base in any prism

The statement is false

Because, the edge length times the height is the lateral area of any prism

the answer is

The volume of the prism is computed using the expression

The unit on the volume measure of the prism is cubic inches

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12