Answer:
see explanation
Step-by-step explanation:
If f(x) and g(x) are the inverses of each other, then
f(g(x)) = g(f(x)) = x
f(g(x)) = f(x -  ) = x -
) = x -  +
 +  = x
 = x
g(f(x)) = g(x +  ) = x +
) = x +  -
 -  = x
 = x
Hence f(x) and g(x) are the inverse of each other
 
        
             
        
        
        
Area= 1/2(height)×(base↓1+base↓2)
Area=1/2(3)×(8+11)
Area=1/2(3)×(19)
Area=1/2(57)
Area=57/2 OR 28.5
Thus, the area of the trapezium is 28.5inches^2
        
             
        
        
        
Answer:
2n+7
Step-by-step explanation:
 
        
             
        
        
        
Answer:

Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of triangle plus the area of semicircle
so

we have

Find the height of the right triangle applying the Pythagorean Theorem


The radius of the semicircle is half the height of triangle

substitute in the formula


 
        
                    
             
        
        
        
Answer:
See explanation
Step-by-step explanation:
Let x be the number of simple arrangements and y be the number of grand arrangements.
1. The florist makes at least twice as many of the simple arrangements as the grand arrangements, so

2. A florist can make a grand arrangement in 18 minutes  hour, then he can make y arrangements in
 hour, then he can make y arrangements in  hours.
 hours.
A florist can make  a simple arrangement in 10 minutes  hour, so he can make x arrangements in
 hour, so he can make x arrangements in  hours.
 hours.
The florist can work only 40 hours per week, then

3. The profit on the simple arrangement is $10, then the profit on x simple arrangements is $10x.
The profit on the grand arrangement is $25, then the profit on y grand arrangements is $25y.
Total profit: $(10x+25y)
Plot first two inequalities and find the point where the profit is maximum. This point is point of intersection of lines  and
 and 
But this point has not integer coordinates. The nearest point with two integer coordinates is (126,63), then the maximum profit is
