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By the exteriror angle theorem, 3y = 2y + x  ⇒ 3y - 2y  = x ⇒  y  = x

And in triangle PQR, since PQ  = RQ, then angle PQR  = angle PRQ  = x

So

3y  + x  +  x =  180

And since  y = x

3x + x + x  = 180

5x  = 180

x = 36

So 3x  = 3y  =  3(36)   = 108°

Not only Happy Birthday.....but....I might add that hectictar is a real asset to our site!!!

Her answers  are always clear and concise....

Since the line  has the form  y  = -1x   + b....the slope is -1

This means OP  = OQ  and QR  = SR

If    [QRS ] / [QOP ]  = 9/25.....the scale factor is the square root of this =  3/5  

This means that    QR : QO = 3 : 5

So...there are 8 equal parts to OR  and OQ  is 5 of them

So...the x coordinate of Q = the y coordinate of P  since OP  = OQ

And this coordinate is   ( 5 / [ 3 + 5 ] ) * 4 =  5/8 * 4  =  20/8  = 5/2 = 2.5

So...b = the y intercept P  = 5/2  =  2.5

Proof : [ QRS]  = (1/2)(QR) (SR)  = (1/2) (1.5)(1.5)  = (1/2)(2.25)

[QOP] =  (1/2) (OP)(OQ)  = (1/2)(2.5)(2.5)  = (1/2)(6.25)

[ QRS] / [ QOP ] =   2.25 / 6.25  =    9 / 25

See the graph, here :  https://www.desmos.com/calculator/m1ufgopozx

Thank you!!

Thanks so much!

See...my  corrected answer under your orginal post, Lightning...

Thank you Chris 

Thank you so much once again Chris 

Thank you so much 

Thank you so much Chris

100% - 10% =90%

90% x (100 -20)= 72%      

100 -72= 28% loss from original value.

Here in Greece we wish to take 510$ per week!We take 350$ PER MONTH :( 

8.5 hr/day  x. 5 days  x. $ 12/hr = $510.   BEFORE taxes AND assuming you get no overtime bonuses.

You work 8.5(5) hours a week = 42.5 hour and take 12$/hour so 

42.5(12)=510$ so your check is 510$ per week!

Hope this helps!

Call the value  before Monday's loss, V

After Monday...the stock is worth .90V

After Tuesday, the stock is worth  .80 (.90V)  = .72V

So....it loses  1  - .72  =    28% of its value

There are  12 * 60   =  720  possible minutes displayed

From 10 - 2....  4hrs * 60 mintes per hour   = 240  minutes display  a "1"

Every hour between 2 and 10.....the following minutes display at least one "1"

10 , 11, 12, 13, 14, 15, 16 ,17 , 18, 19

01, 21, 31, 41, 51

So...that's  15 occurrences per hour  * 8 hrs  =  120 additional minutes

So...the total number of minutes displaying  at least one "1"  = 240 + 120  = 360

So

360 / 720    = 1/2    !!!

DC  is parallel to AB

And FG  = 3  and AB  = 6

Therefore.....FG splits the sides of triangle AEB  in a 1: 1 ratio

This also  means that the altitude of triangle EFG  = BC  = 3

So...the altitude of triangle AEB is twice this = 6

So...the area of triangle AEB  =  1/2 * AB *  2 BC =   1/2 * 6 * 6  =  18 units^2

1. 15/100x=45, x=45*100/15, x=300.

3. 112%=62720, 1%=560, 100%=56000.

We can use symmetry to solve this

The area  of  the 60 degree sector on the right is given by  pi *12^2 * 1/6  = 144/6 pi =

24 pi  units^2

The area  of the  triangle on the right =  (1/2)(12^2)sqrt (3)/ 2 =  36sqrt3  units^2

So...half of the shaded area =  the differences in these areas

So....the whole shaded area  = twice this  =

2 [ 24 pi - 36sqrt 3 ]  =  [48pi - 72sqrt3 units^2] ≈  26.09 units^2

Call O the center of the circle.....draw radius OC perpendicular  to AB, and connect OB  and OA

In triangle OBC...angle OBC  = 30°  and angle BOC  = 60°

So....BC  = 6√3  cm

And in triangle OAC  = 15“  and angle COA  = 75°

Using the law of sines

CA / sin 75  = OC / sin 15

CA /  sin (30 + 45)  = 6 / sin (45 -30)

CA  =  6 sin (30 + 45)  / sin (45 - 30)

CA = 6 [ sin 30cos 45 + sin 45cos30 ] / [ sin 45cos 30 - sin 30 cos 45 ]

CA = 6  [ 1/2 * √2/2  + √2/2 * √3/2 ]  / [ √2/2 * √3 / 2 * 1/2 * √2/2 ]

CA = 6 [ √2/4 + √6/4 ] / [ √6 / 4  - √2/4]

CA = 6 [ √6 + √2 ] / [√6  - √2]

CA  = 6 [ 6 + 2√12 + 2 ] / [6 - 2]

CA = 6 [8 + 4√3 ] / [ 4]

CA = (3/2) [ 8 + 4√3]  =  3 [ 4 + 2√3]  = 12 + 6√3  cm

So....AB = BC + CA  =  6√3  + 12 + 6√3  =   12 + 12√3  cm 

Full circle perimeter is 2πρ so here is 2πPO => 2π5 = 10π but we have 3/4 of full curcle so 10π(3/4)=15/2π 

15/2π is the perimeter of circular disk we want and PO + OQ so Finally perimeter of the shaded region is:

15/2π + 5 + 5 = 15/2π + 10 or if π= ~3.14 we have ~ 33.5619449019234493 

Hope this helps!