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viva [34]
3 years ago
11

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

Mathematics
1 answer:
qwelly [4]3 years ago
3 0
<h3>By Euler's Formula </h3>

F + V = E + 2

<h2><u>Solution</u></h2>

  • F = 9

  • V = 14

  • E = ?

<h3>Substuting the values</h3>

⇨ 9 + 14 = E + 2

⇨ 23 = E + 2

⇨ 23 - 2 = E

⇨ 21 = E

Hence , the number of edges in polyhedron is 21.

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Step-by-step explanation:

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1. What is the solution to the system of equations?
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\large\boxed{x=-8\ and\ y=9\to(-8,\ 9)}

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b)\ \text{Substitution method:}\\\\\left\{\begin{array}{ccc}3x+4y=12\\x+2y=10&\text{subtract 2y from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}3x+4y=12&(1)\\x=10-2y&(2)\end{array}\right\qquad\text{subtract (2) to (1)}\\\\3(10-2y)+4y=12\qquad\text{use distributive property}\\(3)(10)+(3)(-2y)+4y=12\\30-6y+4y=12\qquad\text{subtract 30 from both sides}\\-2y=-18\qquad\text{divide both sides by (-2)}\\\boxed{y=9}\\\\\text{Put the value of y to (2):}\\x=10-2(9)\\x=10-18\\\boxed{x=-8}

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3 years ago
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