9514 1404 393
Answer:
- common denominator: (x² -4)
- simplified complex fraction: (2x +1)/(9 -2x)
Step-by-step explanation:
It is helpful to remember the factoring of the difference of squares:
a² -b² = (a -b)(a +b)
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Your denominator of (x² -4) factors as (x -2)(x +2). You will note that one of these factors is the same as the denominator in the other fraction.
It looks like you want to simplify ...
Using derivatives, it is found that regarding the tangent line to the function, we have that:
- The equation of the line is y = 962x - 5119.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The slope of the line tangent to a function f(x) at x = x' is given by f'(x'). In this problem, the function is given by:
f(x) = 5x³ + 2x + 1.
The derivative is given by:
f'(x) = 15x² + 2.
Hence the slope at x = 8 is:
m = f'(8) = 15(8)² + 2 = 962.
The line goes through the point (8,f(8)), hence:
f(8) = 5(8)³ + 2(8) + 1 = 2577.
Hence:
y = 962x + b
2577 = 962(8) + b
b = -5119.
Hence the equation is:
y = 962x - 5119.
More can be learned about tangent lines at brainly.com/question/8174665
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For the answer to the question above asking <span>What additional information would you need to prove that ΔABC ≅ ΔDEF by SSS?
The answer to your question is </span><span>AB = DE & BC = EF, so the only sides missing are AC = DF, </span>
<span>so Side AC is congruent to side DF is the answer.
I hope my answer helped you. Have a nice day!
</span>
Answer:
3
Step-by-step explanation:
9-6=3
