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y=7

i can't explain your first question other than people think they're funny and want attention...

but as for using the Pythagorean Theorem, you should be given 2 of the unknown variables: a, b, or c ***

a² + b² = c²

so if you have a and b, b and c, or a and c, you can plug the numbers in, square and subtract, and get the third term.

*** if you don't have 2 given variables, look at the diagram or question and try to find them

There isn't one

sin2x / sin x     =  [ 2sinxcosx ] /  sinx  =    2cos x

But

sin3x / sin2x  =  [ -4sin³ x  + 3sin x ]  / [ 2sinx cosx ]  =  -2sin²x/ cosx + [ (3/2)/cosx]  =

[cos2x - 1 + (3/2)] secx  =   [cos2x + 1/2] secx

So.......there is no constant ratio between successive terms as required in a GP

12/25 =  48/100  = 48%

So......the percent remaining = 100 - 48   = 52%

P (even or multiple of 3)  = P(even) + P(multiple of 3)  -  P (even and multiple of 3)  =

                                             3/6       +     2/6               -      1/6    =

                                                       5/6                        -      1/6    =    

                                                                        4/6   = 2/3       ......just as BlueFire found !!! 

We have this, BlueFire   ......

4500   = 1000( 1 + .025/12) ^(12* t)        where t is in years

Divide both sides by 1000

4.5  = ( 1 + .025/12)^(12*t)        take the log of both sides

log (4.5)  =    log ( 1 + .025.12)^(12 * t)      and, by a log property, we can write

log (4.5)  = (12 * t) * log(1 + .025/12)     divde  both sides by 12 * log(1 + .025/12)

log (4.5)  /  [ 12 * log(1 + .025/12)]  = t   = about 60.23 years

In order to average numbers you must add them up and divide them but the amount of numbers there are.

82+88+80+100+65+88+93 = 596

596/7 = 85.1428571428571429

sqrt(456) = 21.3541565040626224

p(sum that is EVEN or a MULTIPLE of 3)

a di has 6 sides each holding a number 1,2,3,4,5,or 6

first you must find all the EVEN values:

2,4,6

now the  multiples of 3:

3 and 6

\(\frac{the possibility of an even number or a multiple of 3}{the possibility of rolling any number}=\frac{4}{6}=\frac{2}{3}\)

2)

n     [  a                 b                 c                                   d                  ]

                           an         an^2 + bn                 an^3 + bn^2 + cn

       ------------------------------------------------------------------------------

         a            b+an       an^2  + bn   + c         an^3  + bn^2  + cn  + d

But if n is a factor, then  an^3  + bn^2  + cn  + d  = 0

So

3) So .....ax^3 + bx^2 + cx + d  =  (x - n) * [ ax^2 + (b +an)x + (an^2 + bn + c) ]

4) As before,  since n is a factor,  an^3  + bn^2  + cn  + d   = 0

5)  So f(n)  = 0

2+1234567890987654321 = 1234567890987654323

next time dont put the text in white I had to highlight it to read the text

hint: 

there's a tab at the top of the screen that says Home

click it and enter your smartbutt question there

You can also just do 1/cos , 1/tan , and 1/sin if you can't find those buttons

you press the 2nd button and then press the trig function you need

the buttons are displayed as arc:

asin

acos

atan

asec

acsc

acot

2=x-y

x=2+y

y=-2+x

1)  a^6   - b^6   =        factor as a difference of squares

(a^3  - b^3) (a^3 + b^3)   =     factor each as a difference of cubes

(a -b) (a^2 + ab + b^2) (a + b) (a^2 - ab + b^2)