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A convex polyhedron has (a + 3) faces, (2a) vertices, and (4a – 1) edges. What is the value of a? a =
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A convex polyhedron has (a + 3) faces, (2a) vertices, and (4a – 1) edges. What is the value of a? a =

User Sbottingota
by
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2 Answers

7 votes

Answer:

a = 2

Explanation:

BECAUSE I'M CORRECT!

A convex polyhedron has (a + 3) faces, (2a) vertices, and (4a – 1) edges. What is-example-1
User Dmitry Gladkov
by
7.5k points
5 votes
Number of faces: F=a+3
Number of vertices: V=2a
Number of edges: E=4a-1

V+F-E=2
Replacing V=2a; F=a+3; and E=4a-1 in the formula above:
(2a)+(a+3)-(4a-1)=2
Eliminating parentheses:
2a+a+3-4a+1=2
Adding similar terms:
(2+1-4)a+(3+1)=2
(-1)a+4=2
Solving for a. Subtracting 4 both sides of the equation:
(-1)a+4-4=2-4
(-1)a=-2
Dividing both sides by (-1)
(-1)a/(-1)=-2/(-1)
a=2

Answer: The value of a is: a=2

User Tenwest
by
8.7k points
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