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you need a break

take your time bro we appreciate it

Most definitely! 

Look at the graph  : https://www.desmos.com/calculator/ynlysx9bnq

Note that the midline  is  y  = 6

1.  The graph is vertically stretched by a factor of 2 and shifted up 3 units.

2.   y  =  10sin ( pi * x / 12)  + 70    where  x  =  0   =  6AM

Here's the graph  :   https://www.desmos.com/calculator/7czvz6iknl

Thank you CPhill. Do you think that you are able to answer my other questions? It came before this one.

The period   goes from  "top of the curve"  to "top of the curve"    =    pi / 2

y  =  (5/4)x - 2

A perpendicular line to this will have a negative reciprocal slope  =  -4/5

So..we have

y  =  (-4/5)(x - 10) + 5

y  = (-4/5)x + 8 + 5

y =  (-4/5)x + 13

sine F  = DE/DF  =  sine C  =  AB/AC  =   12/13

Not the first option  because  reflecting D =  (- 1, 1)   across the x  axis produces (-1,-1)  and  reflecting this across the y axis produces  ( 1, - 1)   which isn't  D'

Not he second option  because    rotating  D =  (-1, 1)  180°   about thhhe origin produces ( 1, - 1)....shifting this 4 units too the left produces  ( -3, -1)  which isn't  D'

Third  option because  

 (2, 6)  across x  ⇒ (2, - 6) ⇒ 90° clockwise ⇒  (-6, -2)  = A'

(5, 6)  across x   ⇒ (5, -6)  ⇒ 90° clockwise ⇒ (-6, - 5) = B'

(7, 1) across x ⇒ (7, - 1)  ⇒ 90° clockwise ⇒  (-1, -7) = C'

( - 1, 1)  across x ⇒ ( -1, - 1) ⇒ 90° clockwise ⇒ (-1, 1) = D'

N =[Log(L/F) / Log(R)] + 1, where N=Number of terms, L=Last term, F=First term, R=Common Ratio.

N =[Log(512/2) / Log(2)] + 1

N = 9 - this is the number of terms. Then sum it up as Geometric Series:

First term =2

Common Ratio = 2

Number of terms =9

You should get S = 1,022

Sum it up as Geometric Series:

First term = -800

Common Ratio = 1/4

Number of terms = 8

You should get S = - 1,066.65

​PC=P′C​​

m∠ACP=90∘​​

12)

  3x          x + 7

____   -   _____

x - 7          x

3x ( x)             (x + 7) ( x - 7)

______     -    ___________

(x - 7) x             (x - 7) x

3x ( x) -  (x - 7) ( x + 7)

__________________

    (x - 7)  x

3x^2  -  [ x^2 - 49)

_______________

  (x - 7)  x

2x^2 + 49

________

x ( x - 7)

factor the numerators and denominators to get

(x+5)(x+4)    (x-4)(x+3)

-------------------------------

(x+3)          (x-1)(x+4)    

Denominator cannot = 0   so x cannot equal  -3 +1 -4      

cancel out like terms in Num and denom and you are left with:

(x+5)(x-4)

--------------

(x-1)

When we have two tangents drawn to a circle as above....it sets up the following :

measure  XYZ   =  (1/2) (arc XSZ - arc XZ )  =

(1/2)  (  220  -  140 )  =

(1/ 2) ( 80)    =

40°

Thank You!!!!!!!!!!!!!!!!!!11

LMN  is an inscribed angle in a circle

The measure of its intercepted arc  (LN)  is twice the measure of the angle  =  64°

So....the measure of arc  LMN  =  360 - 64   =  296°

t^2 + 2t - 24

__________

t^2  -  36

(  t + 6) ( t - 4)

____________

(t + 6) ( t  - 6)

(t - 4)

____          t  not equal to -6 or 6

(t - 6)