<h2>
Answer:</h2>
The area of the top surface of the washer is: 160.14 square mm.
<h2>
Step-by-step explanation:</h2>
The top of the surface is in the shape of a annulus with a outer radius of 10 mm and a inner radius of 7 mm ( since the diameter of the hole is: 14 mm and we know that the radius is half of the diameter)
Now, we know that the area of the annulus region is given by:
where R is the outer radius and r is the inner radius.
Here we have:
Hence, we have:
Answer:
6 Chickens
Step-by-step explanation:
Let H represent the number of horses and C represent the number of chickens. Since there are 32 legs altogether this means that on equation to use would be given by:
2C + 4 H = 32 (Eq. 1)
Another equation can be made from the fact that there are 11 heads or 11 animals altogether which can be written as:
C + H = 11 (Eq. 2)
From Eq. 2, solve for the number of chickens:
C + H = 11
C = 11 - H (Eq. 3)
Substituting Eq. 3 in Eq. 1, the number of horses can be determined:
2 C + 4 H = 32
2 ( 11 − H ) + 4 H = 32
22 − 2 H + 4 H = 32
2H = 32 − 22
2 H = 10
H = 5 Eq.4
Putting Eq.4 in Eq.1
2C + 4*5 = 32
2C = 32 - 20
2C = 12
C = 12/2
C = 6
F^-1(x) is the inverse so...
f^-1(x) = (-1/5)x - 11/5
Answer:
The solution is 
.
Step-by-step explanation:
Given:
The inequality given is:
In order to simplify for 'x', we first isolate 'x' on one side.
Adding -4 on both sides, we get:
Now, 
is an absolute value function which is defined as:
Therefore, the given inequality can be rewritten as:
and 
Therefore, the solution is .
