CPhill

7.5  / 5     =     ????

(45/360)  * 2pi  *  10   =

(1/8) * 2pi * 10  =

(20/8) pi  =

( 5pi) / 2   =

(5/2) pi  =

2.5 pi     ⇒    correct  !!!!

We have 10 hours between  8PM  and 6AM  =   10 * 60  = 600 minutes

Sleep    8 -10

Awake  10 - 10:15

Sleep 10:15 - 12:15

Awake 12:15 - 12:30

Sleep 12:30 - 2:30

Awake 2:30 - 2:45

Sleep 2:45 - 4:45

Awake 4:45 - 5

Sleep  5 - 6

There are 4 periods of  2 hour sleep  and 1 period of 1 hour sleep  =  4*2(60) + 1(60)  =  480 + 60  = 540 minutes asleep

So      540/600   =  54/60   =  9/10   =   90%  of the time asleep

Second one ....top right

Note that arc QU  = arc RS  = 25°

arc TQ  =  arc TU + arc QU  =  44 + 25   =   69° 

To find arc QR, we need to do a little work

arc QS  = 180

arc RS  =  25

So   arc QR   =      arc QS - arc RS  =   180 - 25  =  155°

arc TS  =   arc QR  - arc UT  - arc  RS  =   180 -  44 - 25  =  180 - 69  = 111°

arc SQR  =    arc SQ + arc  arc QR   =  180 + 165  =   345°

arc RQT   = arc RU  + arc UT   =   180 + 44   =  224°

Not as hard as it looks.....factor the denominator.....then.....split into two fractions......the stuff in red is what you need in the blanks

      3x + 2                   3x +  2                        3x                       2

___________  =   _____________  =   ___________   +  ____________

x^2 - 3x -  10         (x - 5) ( x +2)            (x + 2) (x - 5)        (x - 5) (x + 2)

5x -20                            5 ( x-4)                        5

____________   =   ____________   =      _______     (1)    

2x^2 - 5x - 12           (x - 4) (2x + 3)             2x  + 3

Note that since (x - 4)  is a factor in the numerator, we might guess that it is also a factor in the denominator.....knowing this....the denominator should be easy to factor

The hole occurs where   x - 4  =  0   ⇒   at   x  = 4

To  find the y coordinate , sub 4  back into (1)       ⇒        5                      5

                                                                                     ________   =    _____

                                                                                      2(4) + 3               11

So......the hole occurs at   (4, 5/11)

See the graph here : https://www.desmos.com/calculator/uf623od70z

First one....you are correct  !!!

So arc DEF  =   104 + 76  =  180°

Note that arc CF  = arc DE....so.....

 arc  CFD  = 104 + 180  =  284°

And arc DFE  =  arc DCF + arc FE   =180 +   76  =    256°

A seventh degree polynomial function has zeros of −6 , 0 (multiplicity of 3), 1 (multiplicity of 2), and 4.

The graph will cross straight through at   x = -6  and x  = 4

We have  an odd multiplicity > 1   at x  = 0......therefore.....the graph will "cross through while hugging" here  [ this will always be true with an odd multiplicity > 1 ]

We have an even multiplicity at x = 1......the graph will always be tangent with an even multiplicity

Here's the graph :   https://www.desmos.com/calculator/vpimkckn3k

Since Angle MRN  and Angle QRF are vertical angles, they are equal.....therefore arc MN  = arc QP

(10x - 45)  = ( 6x - 1)     add 45 to both sides, subtract 6x from both sides

4x  = 44      divide both sides by 4

x  = 11

Therefore....arc MN  =  10x - 45  =  10(11) - 45  =  110 - 45  =   65°

To find arc NP    subtract   arcs MN and QP from 360  =  360  - 2(65)  =  360 - 130  =  230°

This is the sum of the remaining arcs NP  and MQ......but since angles MRP and MRQ are equal, then arcs NP and MQ are also equal......So  arc NP  =  230/2   =  115°

Finally, arc NQP  =  360  - arc NP  =   360 - 115  =  245°

Last one

Note that the sum of arcs   YX, XW and WV  =   360  - arc  VY  =  360  - 90    = 270°

So  we have this

(10x + 9)  + ( 21x - 12) + ( 8x)  = 270        simplify

39x - 3  =  270      add 3 to both sides

39x  = 273        divide both sides by 39

x  =  7

arc WX  =  21x - 12   =  21(7)  - 12  =  148 - 12   =   136°

arc YW  =   hard to tell which  arc is being referred to, here  arc YVW  or arc YXW ???   

arc YX  = 10x + 9  =   10(7) + 9  =  70 + 9  = 79°  

arc VXW  =  360  - arc VW  =  360  - 8x  =  360 - 8(7)  =  360 - 56   =   204°