<h2>Hello!</h2>
The answer is:
The domain of the function is all the real numbers except the number 13:
Domain: (-∞,13)∪(13,∞)
<h2>Why?</h2>
This is a composite function problem. To solve it, we need to remember how to composite a function. Composing a function consists of evaluating a function into another function.
Composite function is equal to:

So, the given functions are:

Then, composing the functions, we have:

Therefore, we must remember that the domain are all those possible inputs where the function can exists, most of the functions can exists along the real numbers with no rectrictions, however, for this case, there is a restriction that must be applied to the resultant composite function.
If we evaluate "x" equal to 13, the denominator will tend to 0, and create an indetermination since there is no result in the real numbers for a real number divided by 0.
So, the domain of the function is all the real numbers except the number 13:
Domain: (-∞,13)∪(13,∞)
Have a nice day!
We find the length of AD using the similarity of right triangle property. See image attached.
AD² = BD × CD
AD² = 9 × 36
AD² = 324
AD² = 18²
AD = 18
The length of AD is 18 units
Answer:
C & D
Step-by-step explanation:
Answer:
See attachment for rectangle
Step-by-step explanation:
Given



Required
Draw the rectangle
First, we calculate the distance between A and B using distance formula;

So, we have:





The above represents the length of the triangle.
Next, calculate the width using:


Divide both sides by 2

This implies that, the width of the rectangle is 6 units.
We have:


Since A and B are at the upper left and right, then the ther two points are below.
6 units below each of the above point are:
=> 
=> 
Hence, the points of the rectangle are:




<em>See attachment for rectangle</em>
It's a lot like solving equations.
3b-7 < 32
Add 7 to each side.
3b < 39
Divide by 3 on each side.
b < 13
Hope this helps :)