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## Topic review (newest first)

mathstudent2000
2013-08-12 02:46:51

thanks, its correct

bob bundy
2013-08-11 06:44:01

That's what I think.

B

mathstudent2000
2013-08-11 06:19:04

so is the answer 10?

bob bundy
2013-08-11 06:16:41

five more!

mathstudent2000
2013-08-11 06:07:31

is it still five

mathstudent2000
2013-08-11 06:06:07

so how many different ways are there

bob bundy
2013-08-11 05:57:59

Those answers, 5 and 6, are correct.

If you place the hole in the cardboard so there's a vertex at the top, and always read the letters clockwise then the first 5 answers are

ABCDE
BCDEA
CDEAB
DEABC
EABCD

Now flip the pentagon over.

AEDCB
etc

Bob

mathstudent2000
2013-08-11 05:52:18

i don't get about how many ways you can get when you can also reflect

mathstudent2000
2013-08-11 05:51:15

for no. 2 i got 5 and for no. 1 i got 6 but i don't know about no.3

bob bundy
2013-08-11 05:06:14

A dilation is what I call an enlargement.  O is fixed and P is stretched out away from O by an amount so that its distance increases by times 4

So OP x 4 = OQ.

Using the x and 18 you can form an equation for x and solve it.  (hopefully )

Bob

mathstudent2000
2013-08-11 04:48:32

but i don't really understand the first problem

bob bundy
2013-08-11 04:37:39

hi mathstudent2000

OPQ is a straight line so call OP = x  ....   We know that PQ = 18 so  OQ = x + 18

So make an equation using the scale factor and solve for x.

Label one side AB.  If you cannot turn the pentagon over then once you have placed side AB, all the other sides are fixed in place too.  So how many ways can you place AB?

If you can turn it over then placing BA is a new way.  So how many extra ways does that give you?

Bob

mathstudent2000
2013-08-11 04:31:03

1. Point Q is the image of point P under a dilation with center O and scale factor 4. If PQ = 18, then what is OP?

2.We cut a regular pentagon out of a piece of cardboard, and then place the pentagon back in the cardboard.
How many different ways can we place the pentagon back in the cardboard, if we are allowed to rotate but not reflect the pentagon?

3.How many different ways can we place the pentagon back in the cardboard, if we are allowed to rotate and reflect the pentagon?