Answer:
See proof below
Step-by-step explanation:
An equivalence relation R satisfies
- Reflexivity: for all x on the underlying set in which R is defined, (x,x)∈R, or xRx.
- Symmetry: For all x,y, if xRy then yRx.
- Transitivity: For all x,y,z, If xRy and yRz then xRz.
Let's check these properties: Let x,y,z be bit strings of length three or more
The first 3 bits of x are, of course, the same 3 bits of x, hence xRx.
If xRy, then then the 1st, 2nd and 3rd bits of x are the 1st, 2nd and 3rd bits of y respectively. Then y agrees with x on its first third bits (by symmetry of equality), hence yRx.
If xRy and yRz, x agrees with y on its first 3 bits and y agrees with z in its first 3 bits. Therefore x agrees with z in its first 3 bits (by transitivity of equality), hence xRz.
The profits at x = $185 is 0 and the graph is attached below:
<h3>What is graph?</h3>
Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Function is to model the profits of a new pet-monitoring system, so, if the profits are y and x then y = f(x)
The curve shows that y is negative at values of x< $95, then the profits increase when x varies between $95 and $140.
The profits reach a maximum at $140 and then the profits start to reduce as x increases again.
So, the profits at x = $185 is 0.
Learn more about this concept here:
brainly.com/question/16887458
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Answer:
The area of square in terms of x = 16x² -24x + 9
Step-by-step explanation:
It is stated in the question that the length of a square = 4x - 3
Formula to find the area of the square is
Area = length²
Area = ( 4x - 3 )²
by using ( a - b )² = a² + b² - 2ab
here a = 4x and b = -3
So,
(4x)² + (-3)² - 2(4x)(3)
16x² + 9 - 2(12x)
16x² + 9 - 24x
16x² -24x + 9
The area of square in terms of x = 16x² -24x + 9
