Answer:
Average rate of change = -6
Step-by-step explanation:
The average rate of change over the interval (a,b) is given by;
[ f(b) - f(a)] / (b-a)........................where interval is (a,b)
(a,b) interval =(-3,1)
Where;
f(x)= -12 (x+2)² +5

 
        
             
        
        
        
Answer:
   6600 yd²
Step-by-step explanation:
The area of the scale drawing is ...
   (5.5 in)(3 in) = 16.5 in²
Each square inch represents an area of the field that is ...
   (20 yd)×(20 yd) = 400 yd² . . . . per square inch of drawing
Then the scale drawing represents a field with an area of ...
   (16.5 in²)×(400 yd²/in²) = 6600 yd²
 
        
             
        
        
        
Answer:
   AKPOS/ACGF = 28√3 -48 ≈ 0.497423
Step-by-step explanation:
Let's assume the square is a unit square. Then the height of the triangle is ...
   1 +(√3)/2 = h
and half the base of the triangle is ...
   h/√3 = (√3)/3 +1/2 = b/2
The area of the triangle is the product of these:
   A = (1/2)bh
   = (2 +√3)/2 × (3 +2√3)/6
   = (6 +3√3 +4√3 +6)/12 = (12 +7√3)/12
So, the ratio of the area of the square to that of the triangle is the inverse of this, or ...
   (square area)/(triangle area) = 12/(12+7√3)
   (square area)/(triangle area) = 28√3 -48
 
        
             
        
        
        
C; the first and last letters in each group is connected, after U and V being first and last it should be W and X being first and last.
        
                    
             
        
        
        
Answer:
Therefore the required polynomial is 
M(x)=0.83(x³+4x²+16x+64)
Step-by-step explanation:
Given that M is a polynomial of degree 3.
So, it has three zeros.
Let the polynomial be
M(x) =a(x-p)(x-q)(x-r)
The two zeros of the polynomial are -4 and 4i.
Since 4i is a complex number. Then the conjugate of 4i is also a zero of the polynomial i.e -4i.
Then,
M(x)= a{x-(-4)}(x-4i){x-(-4i)}
       =a(x+4)(x-4i)(x+4i)
       =a(x+4){x²-(4i)²}      [ applying the formula (a+b)(a-b)=a²-b²]
       =a(x+4)(x²-16i²)
       =a(x+4)(x²+16)      [∵i² = -1]
       =a(x³+4x²+16x+64)
Again given that M(0)= 53.12 . Putting x=0 in the polynomial
53.12 =a(0+4.0+16.0+64)

       =0.83
Therefore the required polynomial is 
M(x)=0.83(x³+4x²+16x+64)