Answer:
a = 
b = 12
 c = 
Step-by-step explanation:
Since the triangles are right triangles with 60 and 45 degree angles, their side lengths follow special triangles.
A 45-45-90 right triangle has side lengths  .
.
A 30-60-90 right triangle has side lengths  .
.
Starting with the top triangle which has a 60 degree angle, its side length 6 corresponds to a side length of 1 in the special triangle. It is 6 times bigger so its remaining sides will be 6 times bigger too.
Side a corresponds to side length  . Therefore,
. Therefore,  .
.
Side b corresponds to side length 2, b = 2*6 = 12.
The bottom triangle has a 45 degree angle, its side length b= 12 corresponds to  . This means
. This means  was multiplied by
 was multiplied by  . This means that side c is
. This means that side c is  .
.
 
        
                    
             
        
        
        
Answer:
csc
A
, as desired!
Step-by-step explanation:
cos
2
A
sin
A
+
sin
2
A
cos
A
 ,
=
cos
2
A
cos
A
+
sin
2
A
sin
A
sin
A
cos
A
,
=
cos
(
2
A
−
A
)
sin
A
cos
A
,
=
cos
A
sin
A
cos
A
,
=
1
sin
A
,
=
csc
A
, as desired!
 
        
             
        
        
        
Answer:
The equation of the parabola is  , whose real vertex is
, whose real vertex is  , not
, not  .
.
Step-by-step explanation:
A parabola is a second order polynomial. By Fundamental Theorem of Algebra we know that a second order polynomial can be formed when three distinct points are known. From statement we have the following information:
 ,
,  ,
, 
From definition of second order polynomial and the three points described above, we have the following system of linear equations:
 (1)
 (1)
 (2)
 (2)
 (3)
 (3)
The solution of this system is:  ,
,  ,
,  . Hence, the equation of the parabola is
. Hence, the equation of the parabola is  . Lastly, we must check if
. Lastly, we must check if  belongs to the function. If we know that
 belongs to the function. If we know that  , then the value of
, then the value of  is:
 is:


 does not belong to the function, the real point is
 does not belong to the function, the real point is  .
.
 
        
             
        
        
        
Answer:
-1/3(x+36)
Step-by-step explanation: