hectictar

\((\sqrt3-2)^{2017}(\sqrt3+2)^{2018} \\~\\ =\,(\sqrt3-2)^{2017}(\sqrt3+2)^{2017}(\sqrt 3+2) \\~\\ =\,[\,(\sqrt3-2)(\sqrt3+2)\,]^{2017}\,(\sqrt3+2) \\~\\ =\,[\,3-4\,]^{2017}\,(\sqrt3+2) \\~\\ =\,[-1]^{2017}\,(\sqrt3+2) \\~\\ =\,(-1)(\sqrt3+2) \\~\\ =\,-\sqrt3-2\)

12x  =  5         Multiply both sides of this equation by  32/12 .

32/12 * 12x  =  5 * 32/12

32x   =   40/3

First let's just look at the right triangle on top. The side adjacent to the  48°  angle is 30 m. And we can find the length of the side opposite using tangent.

tan 48°   =   opposite / 30        Multiply both sides by  30 .

opposite   =   30 tan 48°

And....

height of taller tower   =   16 + 30 tan 48°   ≈   49.318  m

I think the five degree measures are....

61, 61, 61, 178, 179

We know that the median is  61° .

And we know that the sum of the angles must be  540° .

In the list of angles from least to greatest, if we made the two to the left of the median any smaller, then we would have to make the two to the right of the median larger so that they will sum to 540.

Well if we made the first angle be 60°, then the 178° would have to become 179° and we would have two modes. And if we made the first two angles any smaller than that, then it would put the last two angles over 180°.

I hope that made some sense!

\(2\sqrt{-32} \\~\\ =2\cdot\sqrt{16\cdot2\cdot -1} \\~\\ =2\cdot\sqrt{16}\cdot\sqrt2\cdot\sqrt{-1} \\~\\ =2\cdot4\cdot\sqrt2\cdot i \\~\\ =8i\sqrt2\)

12% of the original price   =   $6

0.12  *  the original price   =   $6

the original price   =   $6 / 0.12   =   $50

f(2)   =   2(2)²- 3   =   5

The first part of the function ends at the point  (2,5) .  So the second part of the function must go right up to that point. The line  f(x)  =  ax + 4  would pass through  (2, 5)  if  x  had no restrictions. So...

a(2) + 4  =  5

2a  =  1

a  =  1/2

I think I found your old post Melody, here.....

17  ≥  7    so    f(17)   =   17 - 13   =   4

4  <  7    so    f(4)   =   4² - 4   =   12

12  ≥  7    so    f(12)   =   12 - 13   =   -1

f(  f( f(17) )  )   =   f(  f( 4 )  )   =   f(  12  )   =   -1

Using the one with two closed dots, put one closed dot goes on  -7  and the other on  -2  .