CPhill

Note that

Floor   (  8  < h  < 9)  =  8

and

Ceiling  ( 8 < h < 9)   =  9

So

Floor ( 8 < h < 9)  *  Ceiling ( 8 < h < 9)  = 

8 * 9   = 

72

The interval   is     8 < h < 9

Nice, hectictar   !!!!

Note 

sin 23  =  cos(90 - 23)   =  cos (67°)....so x  = 67

The second one seems trickier than it really is

RP....note that

sin P  =  cosR       and

cos P  =  sin R

so

Sin R  - cos R   =

Cos P  - Sin P  =   .8192   - . 5736  =   0.2456

Edit to correct a previous mistake  !!!

(4/x + 2)  /   ( (1/2)x  - 8 )  =

[ (4 + 2x) / x ]  /  [ (1/2) ( x - 16) ]   =

[ 2 (2) ( 2 + x) / x ]  / (x - 16)  =

[ 4(2 + x)]  / [ x ( x - 16) ]  =

[ 8 + 4x ]  / [ x^2 - 16x) ]

Statements  1  and 2 only

These statements are the definitions of  sin (x) and cos(y), respectively

Statement 4  is a consequence of substitution

So  "C"  is correct

Correct...!!!

Due to symmetry  the x coordinate of the vertex = 5

The points  (3,0) (7,0) and (2, - 5)  are on the graph

And we have this form

y  =  ax^2 + bx + c

The x coordinate of the vertex  =  

-b / (2a)  =  5

-b  = 10a

b  =  -10a

So we have that using  (3,0)

0  =  a(3)^2 - 10a(3)  + c

0 =  9a - 30a + c

0  =  - 21a + c

-c = -21a

c = 21a

And using  (2, -5)

-5  =  a(2)^2  - 10a(2) + 21a

-5  = 4a - 20a + 21a

-5  = 5a

a  =  -1

And b =  -10(-1)  =  10

And c = 21(-1)  = -21

So our function is :

y = -1x^2 + 10x  - 21

Here;s the graph : https://www.desmos.com/calculator/u2qnb8dswx

Remember that....if V and T are complementary....the sine of one angle  = the cosine of the other

So......

cos T  =  sin V

cos T  = 0.84     and   sin V  = 0.84

First one

A tangent to a circle meets a radius at right angles

So  ABD  =  90°

Second one :

Ths is the intersecting chords theorem....specifically, we have that

9(n + 7)  = 18(n + 1)    divide both sides by 9

n + 7  =  2(n + 1)     simplify

n + 7  =  2n + 2   subtract n, 2  from both sides

n   = 5

Last one

Notice that ABC  =  180  - 47 - 48  =  85°

But ABC  would have to  = 90°   for BC to be tangent

So...the second  answer is correct

Correct !!!