
x=8
16-8=8

Use a calculator to find the square root of 8.
 
        
             
        
        
        
Answer:
Prove set equality by showing that for any element  ,
,  if and only if
 if and only if  .
.
Example:
 .
.
 .
.
 .
.
 .
.
 .
.
Step-by-step explanation:
Proof for ![[x \in (A \backslash (B \cap C))] \implies [x \in ((A \backslash B) \cup (A \backslash C))]](https://tex.z-dn.net/?f=%5Bx%20%5Cin%20%28A%20%5Cbackslash%20%28B%20%5Ccap%20C%29%29%5D%20%5Cimplies%20%5Bx%20%5Cin%20%28%28A%20%5Cbackslash%20B%29%20%5Ccup%20%28A%20%5Cbackslash%20C%29%29%5D) for any element
 for any element  :
:
Assume that  . Thus,
. Thus,  and
 and  .
. 
Since  , either
, either  or
 or  (or both.)
 (or both.)
- If  , then combined with , then combined with , , . .
- Similarly, if  , then combined with , then combined with , , . .
Thus, either  or
 or  (or both.)
 (or both.)
Therefore,  as required.
 as required.
Proof for ![[x \in ((A \backslash B) \cup (A \backslash C))] \implies [x \in (A \backslash (B \cap C))]](https://tex.z-dn.net/?f=%5Bx%20%5Cin%20%28%28A%20%5Cbackslash%20B%29%20%5Ccup%20%28A%20%5Cbackslash%20C%29%29%5D%20%5Cimplies%20%5Bx%20%5Cin%20%28A%20%5Cbackslash%20%28B%20%5Ccap%20C%29%29%5D) :
:
Assume that  . Thus, either
. Thus, either  or
 or  (or both.)
 (or both.)
- If  , then , then and and . Notice that . Notice that since the contrapositive of that statement, since the contrapositive of that statement, , is true. Therefore, , is true. Therefore, and thus and thus . .
- Otherwise, if  , then , then and and . Similarly, . Similarly, implies implies . Therefore, . Therefore, . .
Either way,  .
. 
Therefore,  implies
 implies  , as required.
, as required.
 
        
             
        
        
        
For this use the law of sines:


cross-multiply:
16×sin (J) = 11×0.97
sin(J) = 10.72/16
sin(J) = 0.67
hit the "arcsin" button on your calculator:

therefore answer B. 42 is the correct answer!!
 
        
        
        
Answer:
   27, 26
Step-by-step explanation:
   27^2 -26^2 = 729 -676 = 53
If the numbers are integers, they must differ by an odd number. For some odd number k, we will have ...
   (x +k)^2 -x^2 = 53
   2xk +k^2 = 53
   x = (53 -k^2)/(2k)
   x = 53/(2k) -k/2
The second term is an odd multiple of 1/2. The first term will be an odd multiple of 1/2 only for k=1. For k = 1, we have ...
   x = (53 -1)/2 = 26
The two numbers are 26 and 27.
 
        
             
        
        
        
Answer:
9/4 = 2 1/4
Step-by-step explanation: