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midpoint of (-1, 4) and (5, 4) \(=(\frac{-1+5}{2},\frac{4+4}{2}) \\~\\ =(\frac{4}{2},\frac{8}{2}) \\~\\ =(2,4)\)

You can see it pretty clearly on a graph:

(sin a)² + (cos a)²= 1

(-4/5 )² + (cos a)² = 1

\({\cos a = \sqrt{1-(-\frac{4}{5})^2}=\sqrt{1-\frac{16}{25}}=\sqrt{\frac9{25}}=\frac35}\)
 

(sin b)² + (cos b)²= 1

(5/13)² + (cos b)² = 1

\({\cos b =\sqrt{1-(\frac{5}{13})^2} = \sqrt{1-\frac{25}{169}}=\sqrt{\frac{144}{169}}=\frac{12}{13} }\)

cos(a - b) = (cos a)(cos b) + (sin a)(sin b)

cos(a - b) = (3/5)(12/13)    + (-4/5)(5/13)

cos(a - b) = 36/65 - 4/13

cos(a - b) = 16/65

Brass has a density of 8.4 g/c³  or  0.0083 g/mm³

So:  318 mm³ x 0.0083 g/mm³  =  2.64 g

Equation:  y  =  34x² - 6x + 15

Remove the constant term (15) from the right side by subtracting 15 from both sides:

             y - 15  =  34x² - 6x

Factor out 34 from the right side:

            y - 15  =  34( x² - 6/34x  )

Simplify:

           y - 15  =  34( x² - 3/17x  )

Complete the square on the right side:

   --  First, divide the coefficient of the x-term by 2:   (-3/17) / 2  =  -3/34

   --  Second, square this result:  (-3/34)²  =  9/1156

Introduce this term into the right side:

          y - 15  =  34( x² - 3/17x + 9/1156 )

But, you now have to make a corresponding change to the left side; you have added the term 34(9/1156) = 9/34 on the right side so you must now add it to the left side:

          y - 15 + 9/34  =  34( x² - 3/17x + 9/1156 )

Simplify the left side and factor the right side:

         y - 501/34  =  34( x - 3/34 )²

The vertex will be the point ( 3/34, 501/34 )

lets see.

340+285+290+320+280+270+350+350+300+330+320+275+350+300+370+350+345+380+310+375+300+330+335+350+260+315+330+350+340+285+360+350+380+345+350+185+370+315+340+360+325+360+330+335+370+220+350+350+320

+$345

340+285+290+320+280+270+350+350+300+330+320+275+350+300+370+350+345+380+310+375+300+330+335+350+260+315+330+350+340+285+360+350+380+345+350+185+370+315+340+360+325+360+330+335+370+220+350+350+320 = 16000

=16000+$345

Yep I get the same as darkfox  :)   Sorry MJ (I'll give you a point for all your hard work though :)

S \(= \text{the midpoint of PQ} \\~\\ = \text{the midpoint of (-7, 3) and (1, 3)} \\~\\ = ( \frac{-7+1}2,\frac{3+3}{2}) \\~\\ = (-3, 3) \\~\\\)

T \(= \text{the midpoint of QR} \\~\\ = \text{the midpoint of (1, 3) and (1, -3)} \\~\\ = ( \frac{1+1}{2},\frac{3+-3}{2}) \\~\\ = (1, 0) \\~\\\)

length of ST \(=\sqrt{(-3-1)^2+(3-0)^2} \\~\\ =\sqrt{(-4)^2+(3)^2} \\~\\ =\sqrt{16+9} \\~\\ =\sqrt{25} \\~\\ =5\)

You got it right!! 

There are two solutions. Can you find them?

New Salary:     86000(1 + 0.05)⁵       --->      109 760.21

Use the Pythagorean Theorem for each tree with the distance from the house to the tree being one side of a right triangle (side a) and the height of the tree being the other side (side be). You need to calculate the hypotenuse (side c)

For the first tree:        a = 10     b = 12     c²  =  a² + b²     --->     c²  =  10² + 12²​     --->     c  =  15.6 feet

For the second tree:  a = 14     b = 8       c²  =  a² + b²     --->     c²  =  14² + 8²​       --->     c  =  16.1 feet

Its A=b1+b2 devided by 2 x h (base one-b1 base two=b2 h=height)

#SOCUTE!!!!!!!!!!!!!!!!!!!!!!!!!!

Don't say "t*ts"

 12x-4=24x+4

-12x   -12x

-4=12x+4

-4        -4

-8/12=12x/12

-8/12 = x

Simplified: -1/3 = x

I also like all of these~!

Enjoy~!

MagikalRedNiteTiger~ 

5.318

Aww, this kitty looks so adorable!

Woa You all posted some awesome pictures!!!! I cant wait to see the pics that more people post!! i love Photo contests lol

I LOVE PUSHEEN <3 <3 <3

Awesome.