The right pengtagonal prism has a height of of 14 units.
the volume of the prism is 840 cubic units. what is the
perimeter of the base?
o
o
o
12 units
15 units
21 units
30 units
o
14

30

Step-by-step explanation:

Perimiter is the length of each side added up.  We don't know the side lengths, but we can find it.

It tells us the volume and height, and we use the side lengths to find volume, so lets use that.  I'm not sure how you have learned how to find the area of a pentagon, but I am going to use the formula google shows.  I am going to use x for the side length

A = sqrt(25+10sqrt(5))x^2/4

Now, for any right prism you take the volume of you get the area of the base and multiply it by the height So we can work that out to find the sides.

A*h = V

(sqrt(25+10sqrt(5))x^2/4)*14 = 840

(sqrt(25+10sqrt(5))x^2/4) = 60 (Divide  both sides by 14)

sqrt(25+10sqrt(5))x^2 = 240 (Multiply both sides by 4)

x^2 = 34.874 (Divide both sides by sqrt(25+10sqrt(5))

x = 5.905 (square root of both sides)

Now we have the length of one side.  Since there are five sides we multiply that by 5.

5 * 5.905 = 29.525 So it rounds up to 30.

Let me know if there is something you did not understand.

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.