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B.,...................

Agree again, NSS...

For each side of the 12-gon, there are 12-4=8 non-adjacent vertices which you can use to form a triangle, so there are 12*8=96 such triangles. There are also those triangles which share two sides with the 12-gon, of which there are 12 (one for each vertex of the 12-gon--choose the two sides adjacent to the vertex). So there are 108 total excluded triangles, and thus the answer is (123)−108=220−108=112(123)−108=220−108=112.

Yes this is the same and this is faster and i think the fastest way to answer! 

[1 + 0.0262/12]^12 =

[1 +  0.00218333]^12 =

[1.00218333]^12 =

1.0265 - 1 x 100 =2.65% APY.

"A" seems correct, NSS

The answers is 

y= 9-(0)       y= 9       (0,9) 

y= 9-(2)       y= 7       (2,7)

y= 9-(6)       y= 3       (6,3) 

You have in the order of the data the values of x (-4,0,2,6),the function y= 9 - x , the values of y, (x,y)

Hope it helps!

Because its a straight so its f(x) = ax + b 

and because x,y increase at the same rate its 1 so f(x) = x + b and b = 1 to verify the equation ! 

 nevermind.... but thanks 

what the ^ sign is that multiply? 

First one

 y  = 3x

Second one

y = x^2

I'm guessing the items in red are what they want you to solve for.

There appear to be 10

\(\{1,64,729,4096,15625,46656,117649,262144,531441,1000000\}\)

We'll save  (a) for last

(b)  3 / x  =  4x + 4      this will have two real solutions  

(c)  Multiply both sides by x

3 = 4x^2 + 4x       rearrange as

4x^2 + 4x - 3   = 0      factor

(2x - 1) (2x + 3)  = 0

Set both factors to 0 and solve for x and we get   x = 1/2   or  x = -3/2

When x  = 1/2 ...... y = 3 / (1/2)  = 6

When x = -3/2.......y = 3 / (-3/2)  = -2

So..intersection pts  are  (1/2, 6)  and ( -3/2, -2)

Here's the graph : https://www.desmos.com/calculator/omkotiywia

:D helpful, thank you

Angles DAB  and CAB  are supplementary  [sum to 180]

By the Exterior Angle Theorem,  angle DAB =   angle ABC + angle ACB

Substituting...we have that

angle ABC + angle ACB  + angle CAB  = 180

And these are the 3  interior angles in the triangle

here is the question

I do not understand Dimitris answer BUT

I also think that the answer is 3

as x tends to 1  g(x) tends to 2

and f(2)=3

Second one.....

Using the first answer...we know that

CA / BD  = 48/27

CA /36 = 48/27

CA/36 = 16/9

CA =  16 * 36 / 9

CA = 16 * 4

CA  = 64

Here's the first one.....

angle EDB  = angle CBA

Therefore.....

ΔCAB  similar to ΔBED  similar to ΔABD

BE = BD

CA = CB   

AB = AD  = 48

CA / AB  = BE / ED                    CA / AB  = AB / BD

CA /AB =  BE / 27                      CA / AD =  AD / BD

CA /48 = BE / 27                        CA * BD  = AD^2                  

CA / BE   = 48 / 27                     CA * BD  = 48^2

CA / BD = 48/27                         CA =  48^2 / BD

Therefore

CA / BD  =  48/27

(48^2 / BD) / BD  = 48/27

48^2/ BD^2  = 48/27

48 / BD^2 = 1/27

48 * 27  = BD^2

1296 = BD^2

36  = BD

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where did you get from f(x) = x+1

thank you !

Thank you!!

When do you use the difference of squares?

When you hae a square expression like   16y^2  and another square expression like   9x^2

You are finding the difference between them    16y^2  -  9x^2

And you want to factorize the expression. That means one expression   multiplied by another expression.

\(\sqrt{16y^2}=4y\\ \sqrt{9x^2}=3x\\ 16y^2-9x^2=(4y+3x)(4y-3x)\)

Thank you so much Chris, no worries, here is what I got

Thank you so much Chris