Answer:
x = 60°
Step-by-step explanation:
let the missing angle be = x
Cos x = 8/16
x = Cos-¹ 0.5
x = 60°
 
        
             
        
        
        
Answer:
x = 4(y + 6)/5
Step-by-step explanation:
2x - y = (3/4)x + 6
2x - (3/4)x = y + 6
(8x - 3x)/4 = y + 6
5x/4 = y + 6
5x = 4(y + 6)
5x = 4y + 24
x = (4y + 24)/5
Therefore, x = 4(y + 6)/5
 
        
             
        
        
        
For this case we convert the mixed numbers to fractions:
Dwight:
Mike:
It is observed, that in fact, Mike takes more time to travel the road.
We subtract to know how much more time it takes Mike:

So, Mike takes  hours more than Dwight to walk the road.
 hours more than Dwight to walk the road.
Answer:
Mike takes hours longer than Dwight to walk the road.
hours longer than Dwight to walk the road.
 
        
             
        
        
        
Answer:
   α² +β² = 3 4/9
Step-by-step explanation:
Assuming α and β are solutions to the equation, it can be factored as ...
   (x -α)(x -β) = 0
Expanding this, we get ...
   x² -(α +β)x +αβ = 0
Dividing the original equation by 3, we find ...
   x² +(1/3)x -5/3 ≡ x² -(α+β)x +αβ   ⇒   (α+β) = -1/3, αβ = -5/3
We know that the square (α+β)² can be expanded to ...
   (α +β)² = α² +β² +2αβ
   α² +β² = (α +β)² -2αβ . . . . . . subtract 2αβ
Substituting the values for (α+β) and αβ, we find the desired expression is ...
   α² +β² = (-1/3)² -2(-5/3) = 1/9 +10/3 = 31/9
   α² +β² = 3 4/9
 
        
             
        
        
        
Answer:
100
Step-by-step explanation:
(18 + 7) x (11 - 7) 
25(11-7)
275-175
100