Step-by-step explanation: what is the question
X^2+ (y+8)^2 = 81.....this is C.
X^2 + y^2 + 16y +64=81 so x^2 + y^2 + 16y = 17.....this is D.
So I’d say C and D are correct
Answers:
Horizontal Line: y = 5
Vertical Line: x = 8
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Explanation:
All horizontal lines are of the form y = k, for some constant k. We want the horizontal line to pass through (8,5), meaning every point on this horizontal line must have y coordinate 5. Therefore, y = 5 is the equation of the horizontal line. Two such points on this line are (1, 5) and (8, 5). All that matters is the y coordinate is 5. The x coordinate can be anything you want. The slope of any horizontal line is 0.
Flipping things around, all vertical lines will have the x coordinate of each point be the same value. Draw a vertical line through (8,5) and note how each point has x coordinate of 8. Two such points are (8,1) and (8,5). Therefore, the equation of the vertical line is x = 8. The y coordinate can be any value you want. The slope of any vertical line is undefined. Unlike the horizontal line, we cannot write this equation in slope intercept form (namely because the slope isn't defined).
A. turn all fractions into decimals or all decimals into fractions; I've decided to turn all fractions into decimals
525
------- = 0.525
1000
3
-- = 0.75 = 0.750 ~ (add a zero at the end to make the decimal places 4 equal with 0.525)
0.55 = 0.55 = 0.550 ~<span>(add a zero at the end to make the decimal places equal with 0.525 and 0.750)
</span>
<span> Answer to Problem 'a':</span>
Smallest = 0.525 = 525
-------
1000
Middle = 0.550 = 0.55
Largest = 0.750 = 3
--
4
b. <span>turn all fractions/mixed fractions into decimals or all decimals into fractions; I've decided to turn all fractions/mixed fractions into decimals
</span>
3.805 = 3.805
3.85 = 3.850 ~ ( <span>add a zero at the end to make the decimal places equal with 3.805)
</span>
3 4/5 = 80
----- = 0.80 =0.800 ~ (add a zero at the end to make the decimal
100 places equal with 3.805 and 3.850)
Answers to Problem 'b':
Smallest = 0.800 = 0.80 = 3 4/5
Middle = 3.805 = 3.805
Largest = 3.850 = 3.85
Using Descartes' Rule of Signs:
The signs are: - + - + - +
There are 5 signs changes in this sequence, so there could be either 5, 3, or 1 positive roots.
If we negate the terms with odd numbers (x^5, x^3), we end up with the signs: - - - - - +
Since there is 1 sign change, there can be only 1 negative root.
This means the positive and negative roots can either be 6, 4, or 2.
Since the total number of roots cannot exceed 6, there are either 0, 2, or 4 complex roots.
