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anonymous
 one year ago
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
anonymous
 one year ago
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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Use\[ve+f=2\]where v is no. of vertices, e is no. of edges, f is no of faces.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Figure has 5 square faces PLUS 4 triangular faces, so 9 faces in total.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ut oh, I'm confused.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What don't you understand?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So 18 edges, I think :o

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not quite. The equation is given above, and you know that f = 9 and v = 9. Are you able to solve for e?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think so, because E is what I'm suppose to find out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's right. Go ahead. What do you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK. Let's take it step by step. The equation is\[ve+f=2\]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
 one year ago
Best ResponseYou've already chosen the best response.0so e will cancel out? v+f=2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But 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
 one year ago
Best ResponseYou've already chosen the best response.0I don't do too well with just variables :o

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's OK. Work with them just as you would work with numbers.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What do you get when you add e to BOTH sides of the equation?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No. Let's write it out. Adding e to both sides of the equation we get\[ve+f+e=2+e\]See how we did that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now, 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
 one year ago
Best ResponseYou've already chosen the best response.0Yep yep, that part makes sense

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So 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
 one year ago
Best ResponseYou've already chosen the best response.0we subtract 2 from both sides, but I'm not too sure how that will look

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's right. Let's write it out just like before.\[v+f2=2+e2\]Does that make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh okay, I understand

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Almost there. Now, simplify the right hand side. What will the equation look like?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we subtract 2 again right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yup. There's a 2 and a 2 on the right hand side. They 'cancel each other out'.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Perfect. Well done. Now just plug in the values for v and f and calculate the value of e. What do you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.09+ 9 ? Because earlier you said 4 faces and 5 faces, which is 9 :o

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But you're forgetting something. v=9 and f=9 so we have\[e=v+f2\]\[e=9+92\]\[e=?\]
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