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Rationalize the denominator of the term:  1 / [ 2·sqrt(2) + 3·sqrt(3) ] 

by multiplying both the numerator and denominator by the conjugate of the 

denominator which is:  2·sqrt(2) - 3·sqrt(3).

1 / [ 2·sqrt(2) + 3·sqrt(3) ]    ·    [ 2·sqrt(2) - 3·sqrt(3) ] / [ 2·sqrt(2) - 3·sqrt(3) ] 

      =     [ 2·sqrt(2) - 3·sqrt(3) ] / -19     =    [ 3·sqrt(3) -  2·sqrt(2) ] / 19

Rewrite this as two separate fractions:  3·sqrt(3) / 19  -  2·sqrt(2) / 19

Now, write the other two terms with a donominator of 19:

   sqrt(2)  =  19·sqrt(2) / 19          and         sqrt(3)  =  19·sqrt(3) / 19

Then, simplify this:  19·sqrt(2) / 19  +  19·sqrt(3) / 19  +  3·sqrt(3) / 19  -  2·sqrt(2) / 19

     =    17·sqrt(2) / 19  +  22·sqrt(3) / 19

     =     [ 17·sqrt(2) / 19  +  22·sqrt(3) ] / 19

From this, you can find the answer.

Your Q is missing something.....   is that SUPPOSED to be   y = 20 x    ???

Here is a graph of y = 20

https://www.desmos.com/calculator/qgdd7pe1ab

Here is a graph of y = 20x

https://www.desmos.com/calculator/myz9mbyjc6

Boy one rec'd   5 out of  (5+3)     or    5 /8 ths of 4000          5/8 * 4000 = _________

   the other boy received  3/8 x 4000 = _________

For Part D  .....   do you know how to do derivatives ?

f(6) = 24  

find the slope at this point (6) by using the derivative

   f ' (6) =   2x -2   = 10   = m        

   now you have a slope  m = 10    and a point    (6,24)     to derive the equation of the line......

If you drew a line from O perpendicular to the line DC, it would intersect at the midpoint of CD.

Call that midpoint E.

The length of the radius is the length of OA, which is also the length of BE.

We know that CE is 9, half of CD.

We now need to find the length of BC.

There is a theorem that states that AB·BA  =  CB·BD.

If we call the length CB = x, then we have the equation:  12·12  =  x(x + 18).

Solving this quadratic for x, we have that x = 6.

This means that BE  =  BC + CE  =  6 + 9  =  15.

The product of a constant factor 12 and a 2-term factor x + 3

36 bars / day  *  10 days   = 360 bars  

If you knew the answers to A and C.....WHY did you post them???????

For part B....you do it just the same way...with slightly different numbers ...

f(6) = 24

f(6+h) =   h^2 + 12h + 36 - 12-2h = h^2 + 10h + 24

The slope between the points becomes   (y1-y2)  / (x1-x2) 

(h^2+10h+24  -24) / (6+h - 6) =   (h^2 + 10h ) / h     =   h+10              (check my math.....but that is how you do it.....)

The answer is D

V=w⋅h⋅l=10·7·9=630 cm³

it will take 8 days for 128 ice cream bars

670% = 67/10 = 67/10 as a fraction

\(\sqrt2 \approx 1.41421\)

\(20 \div 1.41421 \approx 14.1421\)

Thus, the smallest integer that works is \(\color{brown}\boxed{15}\)

The answer is C

arschloch

wie bite kanst du das auf deutsch schreiben

f(1) = -1     f(8) = 48

find the slope of the line joining  (1,-1)  and  (8,48)   <======   do you know how to do that?

When the ball hits the ground, y = 0

so use the quadratic formula to solve

  0 = -16t^2 + 28t + 180                ( toss out the negaative 't' value)

(779.95 - 59.95) / 45 = _______

Thank you

idk man idk man

The same logic leads to the right answer, but Kakashi read the problem wrong. They taught it was within 1 cm, not 2. 

\(\sqrt {25} = 5\)

\(5 \times 2 = 10\)

A works, and E also does, because \(\sqrt{100} = 10\)