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Just ignore these people....remember....their words can't hurt you on here !!!

And..I'll check...

Graph : This is symmetric with the y axis....this is characteristic of an even function

Graph here : https://www.desmos.com/calculator/w76y3q8fup

Table

x  y

1  4

-1 4         this is also characteristic of an even function...  if (-x, y) is on the graph....then so is (x , y)

Algebraically

If f(x) = f(-x)....then even

f(x) = x^2 + 3

f(-x) = (-x)^2 + 3  =  x^2 + 3   =  f(x)...so.....even

OK man...!!!!

Not expert on this....but....

First one....we are only interested in the number of paths to "N"   [ from here, there is only one way to get to O ]

Note that  the movements that get us to  N from A  are ( right, up, up, up, up, up)

And in this set  we can choose any 1 of the 6 positions for "right" = C(6, 1)....or...alternatively, any 5 of the 6 positions for "up".....so....the number of paths to N  are  C(6,1) = C(6,5)  =  6  paths

Second one....again, we are only interested in getting to P   

We have the following moves from A to P  =  

(R, R, R, R, R, U, U, U, U )  

We can choose any 5 of 9 positions for R  or, alternatively, any 4 of the 9 positions for U

So....the total paths are C(9, 5) = C(9,4)  = 126 paths

Thank you so much!

Here is the graph : https://www.desmos.com/calculator/oxg0lwauzy

The point (0,4)  makes both inequalities true

I believe that C + D   are correct

The other two only have one dimension of motion

The number of cubes =  Volume of box / Volume of cubes

Volume of box  =  (9/2) (2) (3/2)  =  54/4 in^3  = 27/2  in ^3

Volume of cube = (side)^3 =  (1/2)^3  =  1/8 in^3 

So

(27/2) / (1/8)  =

(27/2) * (8/1)  =

(27) (8/2)  =

27 * 4  =

108 cubes

The object allowed to fall from rest ...or thrown vetically have only vertical components of motion.

The ones thrown at an angle or horizontally and allowed to fall have x and y  (2 dimensional) components of motion...

Noice

6x-6y+11=17    ⇒  6x - 6y  =  6    ⇒  x - y  =  1    ⇒   x = 1 + y      (1)

9y=3x+15      (2)

Put (1) into (2)  for x

9y =  3(1 + y)  + 15       simplify

9y  = 3 + 3y + 15

6y =  18

y =  3

And using (1)

x = 1 + 3  =  4

(x, y) = (4 , 3)

I think "arrow"  is correct

Correct...!!!

like so?

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thank you 

B. False

[ a^(1/6) ] ^(5)  =    a^(5/6)

So... (5/6) is what we need

3/4 doesnt have anything to do with the problem, it was just show how the problem should be written

3/4 doesnt have anything to do with the problem, it was just show how the problem should be written

False.... a scalar quantity has only one dimension associated with it....like tempaerature .