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hint: you use the mid-point formula. 

see this link for the formula: https://www.thoughtco.com/geometry-midpoint-formula-2312239

I will give the answer later

see https://web2.0calc.com/questions/help_28639 for answers.

This is easy

If the line is perpendicular to  y  = 7   then the equation  we are looking for is

x  = (the x coordinate of the given point)   ...so......

x  =  2

Here's the way we can find the last point

[ 2  + (3 - 1) ,   2  + (5 - 4) ]  =

[ 2 + 2,    2  + 1  ]  =

( 4 , 3)

 Here's one way to do this

By symmetry....FC  =   DC   = 3

Connect  CA

Triangle FCA  is right  and CA  =   sqrt  (3^2  + 6^2)  =  sqrt ( 45)  = 3sqrt (5)

And by the Law  of Sines 

sin AFC / CA  =  sin FCA / FA

sin (90)  / [ 3sqrt (5) ]  = sin  FCA  / 6

6 / [ 3sqrt (5) ] =  sin FCA

2 /sqrt (5)  = sin FCA

arcsin (2/sqrt (5))  =  FCA

So  angle  ACP  = angle CAP =  arcsin (2/sqrt(5))

So  angle  APC  =  [180 - 2arcsin (2/sqrt(5))]

Draw PE perpendicular to   AB....so   AE   = 3

And since angles APE  and APC are supplemental sin APC  = sin  APE

So  by the Law of Sines

PA/ sin PEA   =    3 / sin APE   

PA  / sin 90   =  sin   [180 - 2arcsin (2/sqrt(5))] /  3

PA  =   3  /  [ sin180 * cos (2 arcsin (2/sqrt(5)))  -  cos 180 * sin (2arcsin (2 /sqrt(5))]  

PA  =   3 /  [  sin (2 arcsin (2/sqrt(5))) ]

PA  =   3 / (4/5)

PA  =  15/4 

PA  =  3.75

So....PE  =  sqrt  ( PA^2  - AE^2) =  sqrt  (3.75^2 - 3^2)  =  2.25

So....the area  of  APB  =  

AE   *  PE   =

3  *  2.25  =

6.75  units^2

yes it does

If you are just going to put an answer,  please state how you got it.

I assume you got some program to help you?  If so, what did you use?

Or maybe you nutted it out but the working was to long to include? In which case you could include a rough outline.

ABC must be a right triangle, so statement (3) must be true.

Angle BHC is 55 degrees.

Not as bad as it looks

Sum of values

_______________

Number of values

n  ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 )                  n (45)

________________________________   =       _______     =     5n

                            9                                                    9

Does this make sense  ???

OK.....and   144/ pi  =   ????

Let's use some math......"intuition" is often incorrect

We can calculate the coordinates for C as follows

[14  +  (1/3)(14 - 2)  ,  4 + (1/3)(4 - -2) ]  =

[ 14  + (1/3) *12 ,  4 + (1/3) * 6 ]  =

[ 14 + 4 , 4  + 2 ]

( 18, 6)

See  this  :

I THOUGHT OF IT IN MY MIND

    144

___________            

       π

Post your answers.....let's  see where you went wrong......

123  in the first through third positions,   we have  (00 - 99) in the last two positions  =  100 integers

123  in the second position through fourth positions,  we have  (1 - 9)  in the first position and  ( 0-9)  in the last position

So   9  * 10  =  90 integers

123 in the last three positions we have  (1 - 9)  in the first position and  (0 - 9)  in the second position

So  9 * 10  =  90 integers

So

100 + 90  + 90   =

280  integers

1. A

2. C

First one

arctan  (12/50)     .....make sure your calculator is in DEGREE mode....

Second one 

arcsin  ( 20 / 25)

Correct  !!!

OK.....evaluate

      1200

___________              ?????

(1/3) pi * 5^2

Correct   !!!

√3 cos θ  - sin θ  =  1/3

 √3 cos θ  =  sin θ  +1/3       square both sides

3cos^2θ  =  sin^2θ + (2/3)sin θ + 1/9

3 (1 - sin^2θ)  = sin^2 θ + (2/3)sin θ  + 1/9 

3 - 3sin^2 θ = sin^2θ + (2/3)sin θ + 1/9         rearrange as

4sin^2 θ + (2/3) sinθ - 26/9  =  0             multiply through by 9

36sin^2θ +6sin θ - 26  =   0     

18 sin^2 θ + 3sin θ - 13  = 0          let   sin θ  =  x

18x^2  + 3x  -  13  =  0

Using the quadratic formula  and taking the poisitve result  [ since the sine is positive here, we get that ]

x  = sin θ  =  - 3   + √[ 3^2 + 4* 18 * 13]

                    ______________________  ≈  .77

                              2 * 18

Using the sine inverse  we get that 

arcsin (.77)  = θ  ≈  .88 rads

So

√3 sin (.88)  + cos (.88)  ≈  1.972

IT'S C

would be it B or D