Total capacity = sum of the individual production capacities.
Here,
Total capacity = sum of f(m) = (m + 4)^2 + 100  and g(m) = (m + 12)^2 − 50.
Then f(m) + g(m) =  (m + 4)^2 + 100 + (m + 12)^2 − 50.
We must expand the binomial squares in order to combine like terms:
  m^2 + 8 m + 16 + 100
+m^2 + 24m + 144 - 50
---------------------------------
Then f(m) + g(m) = 2m^2 + 32m + 160 + 50  
       f(m) + g(m)   = 2m^2 + 32m + 210, where m is the number of
                                 minutes during which the two machines operate.
 
        
             
        
        
        
Construct<span> a perpendicular from the </span>incenter<span> to one side of the triangle to locate the exact radius. 3. place compass point at the </span>incenter<span> and measure from the center to the point where the perpendicular crosses the side of the triangle</span>
        
             
        
        
        
Answer: 6 inches
Step-by-step explanation:
1.5 miles wide * 1 inch / 0.25 miles = 6 inches :D
 
        
                    
             
        
        
        
Answer:

Step-by-step explanation:
step 1
Find the  
we know that
Applying the trigonometric identity 

we have

substitute





Remember that
π≤θ≤3π/2
so 
Angle θ belong to the III Quadrant
That means ----> The sin(θ) is negative

step 2
Find the sec(β)
Applying the trigonometric identity 

we have

substitute




we know
0≤β≤π/2 ----> II Quadrant
so
sec(β), sin(β) and cos(β) are positive

Remember that

therefore

step 3
Find the sin(β)
we know that

we have


substitute

therefore

step 4
Find sin(θ+β)
we know that

so
In this problem

we have




substitute the given values in the formula



 
        
             
        
        
        
Answer:
3.16
Step-by-step explanation: