To determine the number of edges [tex]\( E \)[/tex] of a polyhedron with [tex]\( F = 9 \)[/tex] faces and [tex]\( V = 14 \)[/tex] vertices, we will use Euler's formula for polyhedra. Euler's formula is:
[tex]\[ F + V = E + 2 \][/tex]
Here we know:
- [tex]\( F = 9 \)[/tex] (faces)
- [tex]\( V = 14 \)[/tex] (vertices)
We need to find [tex]\( E \)[/tex] (edges). Start by substituting the given values into Euler's formula:
[tex]\[ 9 + 14 = E + 2 \][/tex]
Simplify the left-hand side of the equation:
[tex]\[ 23 = E + 2 \][/tex]
To isolate [tex]\( E \)[/tex], subtract 2 from both sides of the equation:
[tex]\[ 23 - 2 = E \][/tex]
[tex]\[ 21 = E \][/tex]
So, the number of edges [tex]\( E \)[/tex] is:
[tex]\[ \boxed{21} \][/tex]
Thus, a polyhedron with 9 faces and 14 vertices has 21 edges.
