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| − | ==Problem==
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| − | The number of faces (<math>F</math>), vertices (<math>V</math>), and edges (<math>E</math>) of a polyhedron are related by the equation <math>F + V - E = 2</math>. If a polyhedron has <math>6</math> faces and <math>8</math> vertices, how many edges does it have?
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| − | <math> \text{ (A) }\ 12 \qquad\text{ (B) }\ 14 \qquad\text{ (C) }\ 16 \qquad\text{ (D) }\ 18 \qquad\text{ (E) }\ 10 </math>
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| − | ==Solution 1==
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| − | We can use the equation provided in the problem, and plug in <math>6</math> for <math>F</math>, and <math>8</math> for <math>V</math>:
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| − | <math>6 + 8 - E = 2</math>
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| − | We can combine <math>6</math> and <math>8</math> to get:
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| − | <math>14 - E = 2</math>
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| − | Adding <math>E</math> to both sides, we get:
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| − | <math>E + 2 = 14</math>
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| − | Subtracting <math>2</math> from both sides of the equation, we get:
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| − | <math>E = \boxed {\textbf {(A) } 12}</math>
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| − | ~anabel.disher
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| − | ==Solution 2==
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| − | We can remember that a rectangular prism has <math>6</math> faces, <math>8</math> vertices, and <math>\boxed {\textbf {(A) } 12}</math> edges, without doing any calculation.
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| − | ~anabel.disher
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