CPhill

It denotes the of area ABC  [ a triangle ]

We could also have the area of a quadrilateral  -  [ABCD ], for example

And so on

10x^3 + 20x^2 + 2x + 4       factor by grouping

10x^2 ( x + 2)  + 2 ( x + 2)

(x + 2) ( 10x^2 + 2)

(x + 2) * 2( 5x^2 + 1)

2 ( 5x^2 + 1) ( x + 2)

Let Donna's rate be R

And Rico's rate is R + 2

And we know that

R / [ R + 2 ]  = 2 / 3    cross-multiply

[ R + 2 ] * 2  =  3R

2R + 4  = 3R     subtract 2R  from  both sides

4  = R  = Donna's Rate  = 4 mph

And Rico's rate  =  6 mph

And 2 hrs 10min  =  2 + 1/6 hrs  =  13/6 hrs

So...Rate  * Time  = Distance

6 * (13/6)   =   

13 miles 

Thanks, ILP......!!!!

Angle OAD  is a right angle

So....Angle AOD is complementary to Angle OAD  =  90 - 28  = 62°  = Angle AOC

Note that Angle AOC is a central angle intercepting minor  arc CA

And Angle ABC  is an inscribed angle intercepting minor arc CA....so it has 1/2 the measure of AOD  =  (1/2) (62)  =  31° 

sin ( u + v)   =  sin u cos v +  sin v cos u

Note...sin v  = sqrt  [ 1 - cos^2v]  = sqrt [  1 - (-8/17)^2]   =  sqrt [ 1 - 64 / 289]   = sqrt [ [289 - 64 ] / 289]  = sqrt[ 225/289]  =  15/17...and this is positve in Q2

cos u  = sqrt [ 1 - sin ^2u ]  = sqrt [ 1 - (7/25)^2 ] = sqrt [ 1 - 49 / 625 ] = sqrt [ [625- 49]/ 625 ]=

sqrt [ 576/ 625]   =  24 / 25....but...this is Q2 angle so cos u =  -24/25

So...we have

7/25   * -8 /17   +   15 /17  *  -24 / 25  =

[-56 -  360] / [ 425   =

-416 / 425

I think it's the way you are entering data into the first box

For example

The first one should be

C (  [ 8 ,1 ] )   

So...     8,1   should be the answer in the box

Knowing this....the rest should be easy

First box ⇒  GR

Box under this  ⇒ BR

Box to the right of this ⇒ BB

The odd numbers  are 1, 3 and 5

1 comes up 11 times

3 comes up 14 times

5 comes up 13 times

So.....spinning an odd number   =    [ 11 + 14 + 13 ]  / 60   =  38 / 60   =  19 / 30

r / 5  = 4/ 7

cross-multiply

7 * r  =  4* 5 

7 * r   = 20   

divide both sides by 7

r  =  20 / 7

C. 180 degrees, because the terminal side is on the x-axis