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Using Euler's formula, how many edges does a polyhedron with 9 faces and 14 vertices have?

Euler's Formula: [tex] F + V = E + 2 [/tex]

[ ? ] edges

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GinnyAnsweridn
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.
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