We want to get the difference quotient for the given function, we will get see that the difference quotient is equal to:
f'(x) = 2x + 5
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The difference quotient:</h3>
For a given function f(x), we define the difference quotient as:

In this case, we have:
f(x) = x^2 + 5x + 6
Replacing that in the difference quotient we get:

Now we can cancel the factor h to get:

So the difference quotient is equal to 2x + 5.
If you want to learn more about difference quotients, you can read:
brainly.com/question/4224465
To find the number of solutions of a system of linear equations you need to identify the slope (m) in each equation:

-If the slope is the same in both lines the system has no solution
-If the slope is different in the lines the system has one solution
-If the equation are the same (incluided the value of b) the system has infinitely many solutions
You have the next equations:

Write the equations in slope-intercept form y=mx+b (solve for y).
First equation:

Second equation:

As the equations have the same slope m = -1, the system has no solution (the line doesn't cross each other)
Answer: b = -3
Step-by-step explanation:
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