anonymous
  • anonymous
A solid has faces that consist of 5 congruent squares and 4 congruent equilateral triangles. The solid has 9 vertices. How many edges does the solid have? (no image) A. 16 edges B. 18 edges C. 20 edges D. 22 edges
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Use\[v-e+f=2\]where v is no. of vertices, e is no. of edges, f is no of faces.
anonymous
  • anonymous
so 9- ? + 5 = 2 ?
anonymous
  • anonymous
Figure has 5 square faces PLUS 4 triangular faces, so 9 faces in total.

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anonymous
  • anonymous
ut oh, I'm confused.
anonymous
  • anonymous
What don't you understand?
anonymous
  • anonymous
oh wait, 9+9 is 18
anonymous
  • anonymous
So 18 edges, I think :o
anonymous
  • anonymous
Not quite. The equation is given above, and you know that f = 9 and v = 9. Are you able to solve for e?
anonymous
  • anonymous
I think so, because E is what I'm suppose to find out
anonymous
  • anonymous
That's right. Go ahead. What do you get?
anonymous
  • anonymous
20 edges?
anonymous
  • anonymous
OK. Let's take it step by step. The equation is\[v-e+f=2\]and you need to solve for e. I don't like the -e on the left hand side, so my first step would be to get of it by adding e to both sides. Can you do that?
anonymous
  • anonymous
so e will cancel out? v+f=2
anonymous
  • anonymous
But to maintain equality you have to add e to BOTH sides of the equation. So you have to fix up the right hand side.
anonymous
  • anonymous
I don't do too well with just variables :o
anonymous
  • anonymous
It's OK. Work with them just as you would work with numbers.
anonymous
  • anonymous
What do you get when you add e to BOTH sides of the equation?
anonymous
  • anonymous
v+ f(e)= 2 ?
anonymous
  • anonymous
No. Let's write it out. Adding e to both sides of the equation we get\[v-e+f+e=2+e\]See how we did that?
anonymous
  • anonymous
ooh yes okay
anonymous
  • anonymous
Now, we can simplify the left hand side by combining the -e and the +e. They combine to give zero, and we don't have to write +0. Some people say that they cancel each other out. Understand?
anonymous
  • anonymous
Yep yep, that part makes sense
anonymous
  • anonymous
So now we have\[v+f=2+e\]To solve for e we have to get rid of the 2 on the right hand side. How will we do that?
anonymous
  • anonymous
we subtract 2 from both sides, but I'm not too sure how that will look
anonymous
  • anonymous
That's right. Let's write it out just like before.\[v+f-2=2+e-2\]Does that make sense?
anonymous
  • anonymous
ohh okay, I understand
anonymous
  • anonymous
Almost there. Now, simplify the right hand side. What will the equation look like?
anonymous
  • anonymous
we subtract 2 again right?
anonymous
  • anonymous
Yup. There's a 2 and a -2 on the right hand side. They 'cancel each other out'.
anonymous
  • anonymous
so v + f - 2 = e ?
anonymous
  • anonymous
Perfect. Well done. Now just plug in the values for v and f and calculate the value of e. What do you get?
anonymous
  • anonymous
9+ 9 ? Because earlier you said 4 faces and 5 faces, which is 9 :o
anonymous
  • anonymous
But you're forgetting something. v=9 and f=9 so we have\[e=v+f-2\]\[e=9+9-2\]\[e=?\]
anonymous
  • anonymous
18-2 = 16
anonymous
  • anonymous
Yayyyy!

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