CPhill

Thanks, heureka!!!!

That was a tough one....!!!

Thanks, fiora   !!!

Not enough info to answer this

We need to know in what quadrants u and v lie.....

Reason??

sin u  = 12/13

But cos u  might be 5/13  or - 5/13

cos v = -4/5

But sin v might be 3/5  or - 3/5

Let the angle bisector be AD, where D intersects the circle

Join DB  and DC 

And we have two triangles - BAD  and CAD

Then

AB = AC

And angle BAD  = angle CAD

And AD is common

So...by SAS, triangle BAD is congruent to triangle CAD

But  angle DBA  = angle DCA...so....they intersect equal arcs

So....arc DBA  = arc DCA

But the sum of these arcs = 360°

So.....each angle intercepts an arc = 180°

But......the measures of these angles = 1/2 of their intercepted arcs = 90°

But...in a circle....an inscribed angle of 90° has its enpoints on a diameter

So...DA  must be a diameter

And a diameter always passes through the center of a circle

But DA is the angle bisector

So....DA passes through the center of the circle

Look at the graph here, Leaded : 

https://www.desmos.com/calculator/gapq6o4w2i

The dark area in the middle is the feasible region....

On your graph, it appears that the points in this area are :

(2, 4)

(-3, 5)

You have played 20 games

Each additional week you will play 4 games

Let W  be the number of additional weeks it takes to win at least 65% of your games

So......we want to solve this

Total Wins  / Total Games  ≥ .65

[ 3 + 3W]

_________ ≥  .65            multiply both sides by 20 + 4W

[ 20 + 4W ]

3 + 3W ≥  .65 [ 20 + 4W]

3 + 3W ≥ 13 + 2.6W    subtract 3, 2.6W from each side

.4W ≥  10       divide both sides by .4

W ≥ 25  ⇒  you must play at least 25 + 5  =    30 weeks to win 65% of your games for the first time

Correct!!!!....I forgot  about the interval notation.......!!!!

This graph may help you, Leaded : 

https://www.desmos.com/calculator/o5nyleiqox

3x-7  ≤   5x+9   subtract  5x from both sides

-2x  - 7  ≤  9      add 7 to both sides

-2x  ≤  16       

Divide both sides by -2  and reverse the inequality sign [ since we are dividing an inequality by a negative  ] 

x ≥  -8

35000 x 2000   =

3.5 x 10^4  x  2 x 10^3   =

3.5 x 2 x 10^4 x 10^3   =

7.0 x  10^7  lbs