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since the ray EF is an angle bisector, DEF and FEG are equal.

this means that 5x-3 = 2x+15.

solving this equation, we get 3x = 18, and x = 6.

so DEF would be 5(6) - 3 = 27.

hope this helped!

Here is the image location:

https://us-static.z-dn.net/files/d10/1361ec469841e03bc44d9371f9b743cd.png

sorry Guest, the image just shows black pixels for me. could you please repost it so i can give the problem a shot?

remember sin 30 = 1/2       cos 30 = sqrt 3 /2

sin30 = opp / hypot

   1/2 =   21sqrt3  / x            x = 42 sqrt 3

cos 30 = sqrt3/2 = adj / hypot

               sqrt 3 /2 = y / 42 sqrt 3

                 y = 63

for the first shape, the side EB is 15 - 9 = 6. using the Pythagorean theorem, we can solve for side CB.

EB^2 + CE^2 = CB^2

6^2+15^2 = CB^2

36+225 = CB^2

261 = CB^2

CB = sqrt261.

now, we can solve the perimeter. 

9+15+15+sqrt(261) = 39 + sqrt261.

for the second shape, we can simply add all the sides.

4+12+14+12+4+9+6+9 = 70.

hope this helped! please correct me if i am wrong, or if you are confused about something:)

Each 20 minutes there is 1/2 as much    one hour is 3 half lives :

start 30      then    15     then    7.5     then   3.75  gm

30(1/2)³ = 3.75 gm

well, division is just multiplying something by the reciprocal of the other number.

so, 3/4 divided by 2 would also equal 3/4 times 1/2.

fraction multiplication is simply just multiplying the numerators together and the denominators together.

3/4 times 1/2 would be 3/8.

hope this helped! please correct me if i am wrong :)

Thank you! I wasn't sure how to switch the numbers around or if I should at all.

The distance between the circumcenter and incenter is 3*sqrt(5)/8.

I've done this before, it's from aops alcumus isn't it?

This is quite easy, let us factor out a -1 from the $(-x^2+1)$, which is $-1(x^2-1)$, we then make this into difference of squares $12*-(x+1)(x-1)$, which results in 

$\boxed{-12(x+1)(x-1)}$

https://web2.0calc.com/questions/exponents_35

y = 3x + 4      is in y = mx + b form  where m = slope = 3    parallel slope is also 3

2y = kx + 9    divide by 2

y = k/2  x   + 4.5                      k/2 has to equal 3      so k = 6

The arc intercepted is twice the measure of the inscribed angle

5x = 1/2 ( 9x+21)

10x = 9x + 21

x = 21              BAC = 5x = 105^o

Thank you so much

AK goes from   -10 to +10    a distance of 20

CG goes from -6 to 2       a distance of  8

8 out of 20 chance    8/20 =    2/5 chance       or  40% chance

sin 41 = opposite / hypotenuse

sin 41 =  79 / x

x = 79/ sin41^o         solve using calculator ....make sure calculator is in DEGREE MODE  and NOT in RADIAN MODE !  

Find slope   = (y1-y2)/(x1-x2)   =   -2/-1 = 2

y = 2x + b    sub in one of the points to calculate b

6 = 2(1) + b

b = 4

y = 2x+ 4

These are all similar ...here is the first one...you try the other two

Surface area:

Three rectangular sides   12x8    + 12x12  +  11x12     in²

    plus two triangular   sides     area = 1/2 base * height         2   *     1/2 * 12x7.1    in²

Volume

triangular area    1/2 * 12x7.1 = 42.6

     volume = triangular area * 'depth' =   42.6 * 12   in³

The interior angles   sum to 360

79 + 126 + 90   + SPQ =  360       I'll let you finish ......

Looks good , fuhsaha ! 

Opposite angles are equal

14x+ 7 = 63

x = 4      

then   63   + z formas a straight line = 180 ^o

    63 + z = 180         solve for 'z'

Exterior angles of polygons sum to 360

360 / 9 = 40 sides