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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

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  1. anonymous
    • one year ago
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    Use\[v-e+f=2\]where v is no. of vertices, e is no. of edges, f is no of faces.

  2. anonymous
    • one year ago
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    so 9- ? + 5 = 2 ?

  3. anonymous
    • one year ago
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    Figure has 5 square faces PLUS 4 triangular faces, so 9 faces in total.

  4. anonymous
    • one year ago
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    ut oh, I'm confused.

  5. anonymous
    • one year ago
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    What don't you understand?

  6. anonymous
    • one year ago
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    oh wait, 9+9 is 18

  7. anonymous
    • one year ago
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    So 18 edges, I think :o

  8. anonymous
    • one year ago
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    Not quite. The equation is given above, and you know that f = 9 and v = 9. Are you able to solve for e?

  9. anonymous
    • one year ago
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    I think so, because E is what I'm suppose to find out

  10. anonymous
    • one year ago
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    That's right. Go ahead. What do you get?

  11. anonymous
    • one year ago
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    20 edges?

  12. anonymous
    • one year ago
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    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?

  13. anonymous
    • one year ago
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    so e will cancel out? v+f=2

  14. anonymous
    • one year ago
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    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.

  15. anonymous
    • one year ago
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    I don't do too well with just variables :o

  16. anonymous
    • one year ago
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    It's OK. Work with them just as you would work with numbers.

  17. anonymous
    • one year ago
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    What do you get when you add e to BOTH sides of the equation?

  18. anonymous
    • one year ago
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    v+ f(e)= 2 ?

  19. anonymous
    • one year ago
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    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?

  20. anonymous
    • one year ago
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    ooh yes okay

  21. anonymous
    • one year ago
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    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?

  22. anonymous
    • one year ago
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    Yep yep, that part makes sense

  23. anonymous
    • one year ago
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    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?

  24. anonymous
    • one year ago
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    we subtract 2 from both sides, but I'm not too sure how that will look

  25. anonymous
    • one year ago
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    That's right. Let's write it out just like before.\[v+f-2=2+e-2\]Does that make sense?

  26. anonymous
    • one year ago
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    ohh okay, I understand

  27. anonymous
    • one year ago
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    Almost there. Now, simplify the right hand side. What will the equation look like?

  28. anonymous
    • one year ago
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    we subtract 2 again right?

  29. anonymous
    • one year ago
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    Yup. There's a 2 and a -2 on the right hand side. They 'cancel each other out'.

  30. anonymous
    • one year ago
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    so v + f - 2 = e ?

  31. anonymous
    • one year ago
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    Perfect. Well done. Now just plug in the values for v and f and calculate the value of e. What do you get?

  32. anonymous
    • one year ago
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    9+ 9 ? Because earlier you said 4 faces and 5 faces, which is 9 :o

  33. anonymous
    • one year ago
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    But you're forgetting something. v=9 and f=9 so we have\[e=v+f-2\]\[e=9+9-2\]\[e=?\]

  34. anonymous
    • one year ago
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    18-2 = 16

  35. anonymous
    • one year ago
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    Yayyyy!

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