CPhill

b)  We have an irregular pentagon.... the sum of the interior angles  = 540°

So  x  = 540 - 158  - 122 -  2(90)   =  80°

Middle one at top

We have a triangular prism

The  top/bottom are congruent triangles  with base = 15 in  and height of 7.7 in

So the total area of top/bottom  is    15  * 7.7  = 115.5 in^2

The sides are rectangles with height  of  8 in and widths of  ( 15,15 and 8  in)

So the side area  is     8 [ 15 + 15 + 8 ]  = 8 [ 38  ] =  304 in^2

So..the total surface area is   115.5  + 304  =  419.5 in^2

Third one  (on top right)

We have a  triangular  pyramid

The sides are 3 congruent triangles  with bases of 9 cm  and heights of 19.2 cm

So...their  total area  is  (3)(1/2) (9) (19.2)   = 259.2 cm^2

The base is a triangle with a base  of  9cm  and a height of 7.8 cm

Its  area is  (1/2) (9)(7.8)  = 35.1 cm^2

So.....the total surface area  is   259.2  + 35.1   =  294.3 cm^2

If I didn't mis-count :

5 lattice points on the boundary

8 interior points on the y axis

And  using symmetry, we  have  2(8)  = 16 more interior points

So...the total  is  5 + 8  + 16  =    29 lattice points

See the graph here: https://www.desmos.com/calculator/fsvb23vcgb

Nice job,  tertre.....!!!

You are correct,  tertre !!

f^{-1}(f^{-1}(3))

f^-1 (3)  = 4

So

f^-1 ( f^-1(3) )  =

f^-1 ( 4)  =   7

4√12 * 5√10  =

4 √ [4 * 3]  * 5 √ [ 5*2 ]= 

8√3  * 5√10

So...the answer is...No !!

2x+y−z =−3

5x−2y+2z = 24

3x−z = 5    (1)

Using the last equation    z = 3x  - 5

Using (1) and the first equation we get :

2x + y - (3x - 5)  =  -3

2x + y - 3x + 5  = -3

-x + y + 5  = -3

y  = x - 8   (2)

Sub  (1)  and (2) into  the second equation and we have

5x - 2(x - 8 ) + 2(3x - 5)  = 24

5x  - 2x + 16 + 6x - 10  = 24

9x + 6  = 24  subtract 6 from each side

9x  =18  divide both sids by 9

x  = 2

And using (2)... y  = 2 - 8   =  -6

And z = 3(2) - 5  = 6  - 5   = 1

So   (x, y, z)  = ( 2, -6, 1)

Last One  [ you owe me  BIG TIME...LOL!!! ]

Rational

These might be anything but here is the graph of   y  = (x + 1)  /( x - 1)  :  https://www.desmos.com/calculator/watidrudhk

[ This is actually the graph of a "rotated" hyperbola ]

End Behavior : Far left end : UP   ...as we approach x = 1 from  the  left :  DOWN....as we approach x = 1 from the right : UP.....as we approach infinity : DOWN

Avg Rate of Change...Calculus, again...there is no "average rate of change"...the slope at any point on the graph is :

-2/ (x -1)^2

Positive/ Negative : The graph is  above the x axis  on  (-inf, -1) U ( 1, inf)..it is below the x axis on ( -1, 1)

x, y intercepts  :  intercepts x axis at  (-1,0)  and the y axis  at (0, -1)

Real World :  If you find any, let me know  !!!  LOL!!!