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AELN  suggests  a good  method

If  you  draw it out......we will  have a side  =   8 opposite the 30°  angle

The altitude will  be  opposite  the 60°  angle  = 8√3

So......the  area = 

(1/2) base (height)  =

(1/2) (16) ( 8√3) =

64√3

750 pencils in 3 hours

100 pencils in x hours

(750 / 7.5) = 100

(3 / 7.5) = x

Find x

1st Dial

10 possible numbers

2nd Dial

9 possible numbers (because all four digits have to be different)

3rd dial

8 possible numbers

4th dial 

7 possible numbers

10 * 9 * 8 * 7 = 5040

Welp never mind CPhill did the problem

I don't know.....yours  is pretty good, too, AELN   !!!!

I gave  you a point  !!!!

Thank you for correcting me guest!

Anyways, can you now divide the equilateral triangle into halves with each half as a 30-60-90 triangle? I recommend you draw it out!

A regular polygon has all sides  the same......so.....this is an equilateral triangle

The  area  =

(1/2) (16) (16)√3 /2 

(√3/4) * 16^2  =

(√3) ( 64)  ≈

110.9 ft^2

I recommend you just list them out.

By the way this would make a fun, short, coding challenge!

Organize the list by the tength's place:

Now list each number in increasing order in the given table.

regular polygon means all sides are equal AND all angles are equal

An equalteral triangle.  

regular polygon means all of its sides are equal.

What shape do you think of when a triangle has all of its sides equal?

Is it a 90 60 30 degree triangle?

Another method, and more efficient!

Hint

It says regular polygon.

Do you know what shape that is?

We have the  set ...... ( R, R , R ,R, D, D, D , D , D , D)

We can choose  any  4 of 10  positions in the set to place  the R  or  6  of 10 postions in the set  to place  the D

We  can  either  use    C(10, 4)   or C(10,6)   =  210 paths

The 42nd row of Pascal's Triangle has 43 terms, the 2nd of which is: 42

I'm friends with CalculatorUser. . But he doesn't go on anymore for some reason .

Was 11 minutes quick enough?

Alison is twice as old as mike.

[1] A = 2M

4 years ago, Alison was three times as old as Mike.

[2] (A - 4) = 3(M-3)

Substitute [1] and [2]

1. (2M - 4) = 3(M-3)

2. 2M - 4 = 3M - 9

3. M = 5

Now how old is Alison? (Hint: Substitute M back in [1])

I am an eigth grade, and I am soon to go into high school. I have a few friends who also use this forum :)