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Draw altitude CM

Then CM  must  = 8    because  sin A  = CM / AC  =   8/10   = 4/5

Using the Pythagorean Theorem   BM  =  sqrt  (BC^2 - CM^2)  = sqrt ( 17^2 - 8^2)  = sqrt ( 289 - 64) =

sqrt ( 225)  =  15

And cos B  =   BM / BC    =   15/ 17

The endpoints of  s₂  are  3  to the right and  2  down from the endpoints of  s₁

s₁  has endpoints at  (1, 2)  and  (7, 10)

s₂  has endpoints at  (1 + 3, 2 - 2)  and  (7 + 3, 10 - 2)

s₂  has endpoints at  (4, 0)  and  (10, 8)

If we have the point  (x, y)

Then reflecting this across the x axis results in the point  ( x, -y)

So    

(3, 4) ⇒   (3, - 4)

point M  =  midpoint of segment PR  =  \(\Big( \frac{1+7}{2},\frac{3+15}{2}\Big)\ =\ \Big( \frac{8}{2},\frac{18}{2}\Big)\)  =  (4, 9)

To reflect segment PR over the x-axis, we make the y-coordinate of each of its points negative. So...

image of point M  =  (4, -9)

sum of the coordinates of the image of point M  =  4 + -9  =  -5

No big deal, HL.....we all make mistakes on here

Oh boy I misinterpeted it again sorry guys : /

Thank You Hectictar!

circumference of base of cone  =  length of major arc AB

length of major arc AB  =  \(\frac{270}{360}\cdot\) circumference of circle

length of major arc AB  =  \(\frac{270}{360}\cdot2\pi\cdot4"\)

length of major arc AB  =  \(\frac{3}{4}\cdot2\pi\cdot4"\)

length of major arc AB  =  \(6\pi"\)_

Here's my best attempt....I'm not good at these, so...I can't guarantee that I'm correct....

He will not need change if

(1) He selects the 1.75 toy first   ....or....

(2) He selects the .25 toy first and the 1.75 toy second

The probability of the first  =  1/8

And the probability of the second is  (1/8) (1/7)  =  1/56

So...the probability that he will need change  is  1  - P(that he won't need change )  =

1 -  ( 1/8 + 1/56)  =

1 - ( 8/56)  =

56/56 - 8/56  =

48/56  =

6/7

m angle 1  =  (1/2) ( m arc AB  + m arc CD)

tan( angle )  =  opposite / adjacent

tan( 30° )  =  9√3 / PQ

PQ tan( 30° )  =  9√3

PQ  =  9√3 / tan( 30° )

PQ  =  27

....Or.....you can notice that this is a 30-60-90 triangle. And remember in every 30-60-90 triangle,

side opposite the 60° angle  =  √3 * ( side opposite the 30° angle )

PQ  =  √3 * 9√3

PQ  =  3 * 9

PQ  =  27

\(2^{-4}\)= reciprocal of \(2^4\)

=reciprocal of 16

=\(\frac{1}{16}\)

We have  5 possibilites for the every space in the top row  except the middle space which only has 4 possibilities

So

5^4 * 4  =   2500 possibilities

Yep....that's better   !!!

Let the teams be   (A, B)  (C, D)  (E, F)

So....the number of handshakes are

(A,C) (A,D) (A,E) (A, F)

(B, C) (B,D) (B,E) (B, F)

(C, E) ( C, F)

(D, E) (D, F)   =        12

We have

6 [ 1 - 5^(5-1) ] / [ 1 - .5]  + 6  =  17.25 ft

The literal interpretation of this:    -790 +- √790^2 - 4 (-60)(-1000) / 2(-60)

is this:     \(-790\pm\sqrt{790}^2-\frac{4(-60)(-1000)}{2}(-60)\)

However, I think what you probably mean to say is this:    [  -790 ± √[ 790^2 - 4 (-60)(-1000) ]  ] / [ 2(-60) ]

which is:     \(\frac{-790\pm\sqrt{790^2-4(-60)(-1000)}}{2(-60)}\)

The only way that a calculator would know that  -790  is part of the numerator is if you put parenthesees around the entire numerator. The same goes for the denominator.

Now because of the  ±  , to enter this expression into a normal calculator we have to enter both expressions separately.

The first expression is:  (-790+sqrt(790^2-4(-60)(-1000)))/(2(-60))

The second expression is:     (-790-sqrt(790^2-4(-60)(-1000)))/(2(-60))

I took out the spaces, changed the brackets to parenthesees, and wrote  sqrt  instead of  √  so that you can select each expression and copy and paste it directly into the calculator on this website.

For the first one you should get approximately  1.419

For the second one you should get approximately  11.748

Here is a slightly smaller number:

3  x  5  x  7 = 17 + 41 + 47 =105

I think it would be 6*4 because they wouldn't be shaking hands with there partner.

So there are 2 women on each team so that is 6 well all we do is 

6x4 whay multiply 6 by 4 because the women on a team dont hand shake with there partner so there are only 4 other people so 

6x4=24

so 24 handshakes 

Answer is = 24 Handshakes 

~Nickolas

Yep! but be careful because notice that these aren't "regular" coordinates, they're polar coordinates. 

Pertend I never posted! 

Smart

~Nickolas

So we can solve this by just keep dividing by 2 so we start with 6 and then divide by 2  5 times down... 

\(\frac{6}{2} = 3\) 

\(\frac{3}{2} = 1.5\) 

\(\frac{1.5}{2} = 0.75\) 

\(\frac{0.75}{2} = 0.375\) 

\(\frac{0.375}{2} = 0.1875\)

and thats our answer 0.1875