Answer:
z =23
Step-by-step explanation:
The three angles in a triangle add to 180 degrees.
62+95+z = 180
Combine like terms
157 +z = 180
Subtract 157 from each side
157-157 +z = 180-157
z =23
In this question, it is given that the diagonal of the board is 18 inches long and one side of the board is 12 inches long.
Let the other side is of length b inches .
Now we use pythagorean identity, which is

Here, a = 12 and c=18
Substituting these values, we will get

And the formula of perimeter is

Substituting the values of the two legs, we will get

Half the perimeter is equal to the length plus the width.
326 /2 = 163
Length + width = 163
87 + width = 163
Width = 163 - 87
Width = 76 meters
Answer:
A. H(x) is an inverse of F(x)
Step-by-step explanation:
The given functions are:



We compose F(x) and G(x) to get:






Hence G(x) is not an inverse of F(x).
We now compose H(x) and G(x).



We simplify to get:


Since
, H(x) is an inverse of F(x)
First find the critical points of <em>f</em> :



so the point (1, 0) is the only critical point, at which we have

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

Find the critical points of <em>g</em> :



where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at




So <em>f</em> has a minimum of -7 and a maximum of 299.