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1 answer:
Answer: Choice B
All real numbers except 2 and 5
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Explanation:
Factor the denominator. We need to find two numbers that multiply to 10 and add to -7.
Through trial and error, those two numbers are -2 and -5
-2 times -5 = 10
-2 plus -5 = -7
This means the denominator factors to
. You can use the FOIL rule to confirm this.
Then each piece is set equal to zero to solve for x
x-2 = 0 leads to x = 2
x-5 = 0 leads to x = 5
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In short, if x = 2 or x = 5, then it causes the the denominator to turn into 0.
Dividing by 0 is not allowed; therefore, x = 2 nor x = 5 is allowed in the domain. Any other x value is valid.
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Answer:
(x +6)^2 +(y +2)^2 = 72
Step-by-step explanation:
The given points are vertices of a right triangle. The circle circumscribing that triangle (through all 3 vertices) will have its center at the midpoint of the hypotenuse:
((0, 4) +(-12, -8))/2 = (-6, -2)
The equation of a circle with center (h, k) through point (a, b) is ...
(x -h)^2 +(y -k)^2 = (a -h)^2 +(b -k)^2
For center (-6, -2) and point (0, 4), the equation is ...
(x +6)^2 +(y +2)^2 = (0+6)^2 +(4 +2)^2
(x +6)^2 +(y +2)^2 = 72
Every function associates input values with output values. The domain of a function is the set of all the inputs the function accepts.
You will basically always find your function graphed with the inputs on the horizontal axis and the outputs on the vertical axis. This means that every point on the graph has coordinates , and the domain is the set of all the x values.
The points on your red line have all coordinates , where d starts from 0 and ranges up to 12. So, the domain of the function is
Assuming the function is 
, and not 
which would be its own Maclaurin polynomial right away.
Recall the geometric power series,
where
. Replace 
and we have
and so
We want the 4th degree polynomial, so
Recall the geometric power series,
where
and so
We want the 4th degree polynomial, so