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The following expression gives the irrational number known as pi.

(2+1/3)/(2/5) = 5.8333333333333333

7+7=14

g(x)  = 12(2)^{x - 1}

h(x)  = 3^x  

We are looking for this :

g(6) * h(6)     ....so we have....

12(2)^6-1  * 3⁶   =

12(2)⁵  * 729  =

12*32 * 729   =  279,936 points

What question? (Your problem did not show.)

#1. Fractions MUST have a common denominator to be added or subtracted.

#2. 2⁰=1, so yes. Two to the power of zero equals one.

1/3^3=1/27=0.037 repeating.

P  = 2(L + W)       →   L + 9   = 2W

42 = 2L + 2W

42 = 2L + [ L + 9]    simplify

42  = 3L + 9     subtract 9 from both sides

33 = 3L     divide both sides by 3

11  = L           

And  2W  = L + 9  

So    2W  =  11 + 9    

2W  = 20    divide both sides by 2    and    W  = 10 

So  L = 11  and W   = 10

And the area  = L *W  =   (11) (10)  = 110 units^2

Here's the proof in the opposite direction :

1/x  - 1/y    =

1/ [ tanA + tanB]  - 1 /[ cotA+cotB]

[(cotA + cotB) - (tanA + tanB)] / [(tanA + tanB) ( cotA + cotB)]

[(cotAcotB - 1)/(cot(A + B) - [tan(A + B)(1 - tanAtanB) ] / [(tanA + tanB) ( cotA + cotB)]

[ (cotAcotB -1) - cot(A +B)tan(A+B)( 1 - tanAtanB)]/ [ (cot(A+B)(tanA + tanB)(cotA + cotB)]

[(cotAcotB -1 ) (1 - tanAtanB)] / [(tanA + tanB)(cotAcotB -1)]

(1 - tanAtanB) / (tanA + tanB)  =

1 / [( tanA + tanB) / (1 - tanAtanB)]  =

1 / tan(A + B)   =

cot(A + B)

69/pi

yes i put in my gmail

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2/3

It can be written as 22/7 in fraction form, and 3.14159265359 in decimal form.

Amount  after six years  =  3000(1 + .06)^6  =  $ 4255.56

f(x) = log₂(x + 6), find the value of f⁻1(3)

Write the given function as     y = log₂ (x + 6)

Writing this in exponential form, we have

2^y  = x + 6        subtract 6 from both sides

2^y - 6   = x       "swap" x and y

2^x - 6  = y       and, for y, write f^-1(x)

So 

f^-1(x)   = 2^x - 6     and   f^-1(3)  =    2⁽³⁾  - 6    =   8  - 6  = 2

So  the point (3, 2)  is on the inverse graph....then the point (2, 3)  should be on the original graph.....and you can verify for yourself that this is true......

Here's an alternative method.

\(\displaystyle \cot(A+B)=\frac{1}{\tan(A+B)}=\frac{1-\tan(A)\tan(B)}{\tan(A)+\tan(B)} \\ \displaystyle =\frac{(\cot(A)+\cot(B))(1-\tan(A)\tan(B))}{(\cot(A)+\cot(B))(\tan(A)+\tan(B))} \\ \displaystyle =\frac{\cot(A)+\cot(B)-\tan(A)-\tan(B))}{(\cot(A)+\cot(B))(\tan(A)+\tan(B)} \\ \displaystyle=\frac{1}{\tan(A)+\tan(B)}-\frac{1}{\cot(A)+\cot(B)}=\frac{1}{x}-\frac{1}{y}.\)

.6666..... is 2/3.

(-2,8) and (-8,-4)

Distance  =   sqrt [  ( -8 - -2)^2 + ( -4 - 8)^2 ] =

sqrt [ (-6)^2 + (-12)^2 ] =

sqrt [ 36 + 144]  =

sqrt [ 180] =

sqrt [ 36 * 5] =

6*sqrt(5)   = about 13.4 units