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The initial point is (0,0).           [There should be arrows above each of the vector names below.]

Plot the point (3,-1). a is the vector that begins at (0,0) and ends at (3,-1).

Plot the point (2,2). b is the vector that begins at (0,0) and ends at (2,2).

If you add these two vectors together:  a + b  =  (3-1) + (2,2)  =  (5,1).

In either order:                                       b + a  =  (2,2) + (3,-1)  =  (5,1).

You get the same terminal point either way.

The terminal point of  a + b  is  (5,1).

If you draw the vector from (0,0) to (5,-1), you have draw the resultant vector. 

The outside surface of a large cubical block is painted and then broken into unit cubes. If exactly 294 of the unit cubes were painted on just one side, what are the dimensions of the large cube? 

A cube has six sides so each side will be responsible for 294 / 6 = 49 of the painted cubes. 

You can't count the edges because they're painted on two sides except the corners which are painted on three sides. 

The 49 cubes on a side are in a square 7 x 7.  You didn't count the edges but they're still there, so each side is 9 x 9. 

The dimensions of the cube are 9 x 9 x 9 units. 

_.

A cupcake divided evenly into 6 equal pieces!

1) Angle CEB and Angle DEA must be congruent because they are vertical angles. 

2) Angle ADB and Angle ACB must be congruent because they are inscribed angles that intercept the same arc

3) Angle DAC and Angle DBC must be congruent because they are inscribed angles that intercept the same arc

c*****t.

Since there are 32 perfect squares between 1 and 1032, therefore: 1032 -32 =1,000. So, the 1000th term without the perfect squares will be 1032.

Did you look it up in your History Textbook?. Hint: Look in the "Index" under "The War of 1812" and I guarantee you that you will see it somewhere in your Textbook!

The 9 letters can be arranged in: 9! =362,880 ways.

Each of the 9 letters can follow another letter in: 1/9 x 9! =40,320  ways.

Conversely, each letter will be separated from the other 8 letters in:8/9 x 9! = 322,560 ways - or this is the number of ways where B cannot immediately follow A.

Can you provide a link to that post?

never mind, i got it. (it was 9.)

There are 10*9 = 90 line segments that are drawn.

So its 4/76?

Srry i have it now