The question is missing the options and the the drawing of the prism. Here is the complete question and the drawing is in the attachment.
A prism is created using 2 regular pentagons as bases. The apothem of each pentagon is 2.8 centimeters.
Which expression represents the volume of the prism, in cubic centimeters?
a) 9x² + 7x
b) 14x² + 7x
c) 16x² + 14x
d) 28x² + 14x
Answer: b) 14x² + 7x
Step-by-step explanation: The formula to calculate the volume of a prism is:
V = Ab*h
Where
Ab is area of the base
h is the height of the prism
The base is a regular pentagon, which means that all the 5 sides of it is the same. The apothem of a pentagon is a line segment from the center of the pentagon to its side. The area is:
Ap = 
where:
P is perimeter
a is apothem
Area of base:
Ab = 
Ab = 
Ab = 7x
h = 2x+1
Volume of the prism:
V = Ab.h
V = 7x.(2x+1)
V = 14x² + 7x
The expression that represents the volume of this prism is V = 14x² + 7x cubic inches.
Answer: A) (2x+1)(2x−1)
How to: <u>
Since both terms are perfect squares, factor using the difference of squares formula,</u>
Have a great day and stay safe !
Answer:
x = 60°
Step-by-step explanation:
m∠EGD = m∠BGF = x°
The following m∠EGD, m∠DGC, m∠EGA lies on a straight line.
- <u>A straight line has total 180° interior angle.</u>
solve:
- m∠EGD + m∠DGC + m∠EGA = 180°
1 3 4
1 -- + 1 -- = 2 --
5 5 5
Explanation:
1 + 1 = 2
1/5 + 3/5 = 4/5<span />
X=mother's age
y=son's age
3y=x
x+y=38+(5*2)
therefore x=36 and y=12