CPhill

x^2  - 5x  -  24

We  need two integers that multiply to  - 24   and sum to  - 5

- 8  and +3   will work

So....we can factor this as

(x - 8) ( x + 3)

Let A  be tthe amount that one brother has

Let  A + 15  be the amount the other brother has

And the combined amount  =   55    .....so.....

A  + ( A + 15)   =   55         simplify

2A  +  15   =    55       subtract 15 from both sides

2A  =  40       divide both sides by 2

A  = 20  

And  A + 15  =  20 +  15  =  35

So...one has saved $20  and the other has saved $35

THX, Nirvana  !!!!

500 - 104.95 - 165.25 - 242  = $(  -12.20 )

It is FALSE....you don't have enough money

Last one°

arc YU  = arc XV - arc XY - arc UV  =   180  - 55 - 108  =  180 - 163  =  17°

arc XW  =  arc YW  - arc YX  =  180 - 55   =  125°

arc XVW  = arc YW + arc XY =  180 + 55  =  235°

arc VW  =  arc XY  =  55°

arc YWU  = 360 - arc YU  =  360 - 17  =  343°

Third one ......bottom left

Note that arc KN  = 180°

And arc NM  = 90°

And arc LM  = 67°

So....

arc KL  =   180  - 90 - 67  =  90 - 67  =  23°  = arc ON

arc LON   =  arc LO + arc ON  =  180 + 23   =  203°

arc OM  =  arc ON + arc NM  =   23 + 90  =  113° 

arc KNL   = 360 - arc KL  =  360  - 23   =  337°

arc NL  =  arc NM + arc LM  =  90 + 67  =  157° 

Note that as  x →  -6  from both sides   (6 + x)^2  takes on a very small value  [ ≈ 0 ]

So   

lim                      -12                   -12

x → - 6           ________   =      ____  =      -∞      [ i.e., the limit does not exist ]

                       (6 + x)^2              ≈ 0

First.....convert the mixed numbers to improper fractions

1 + 1/4   =   5/4      (1)

4 + 1/2  =   9/2       (2)

The number of panels =  (2) / (1)   =   (9/2) / (5/4)  =  (9/2) * ( 4/5)  =  36/10  = 3.6 panels

However.....the whole number of panels  = 3

Let's see

Area  of the sector  =  pi * r^2  (45/360)  =   pi *  10^2 * (1/8)    =   100/8 * pi  =  12.5 pi   in^2 

Correct   !!!