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16 Sep 2014, 01:08
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What is the measure of the smaller angle formed by the intersection of the lines \(y = kx + b\) and \(y = bx + k\)?
(1) \(b + k = 1\).
(2) \(bk = 0\).
(1) \(b + k = 1\).
(2) \(bk = 0\).
16 Sep 2014, 01:08
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Official Solution:
What is the measure of the smaller angle formed by the intersection of the lines \(y = kx + b\) and \(y = bx + k\)?
To answer the question, we need to determine the slopes of each line, which are represented by the values of \(k\) and \(b\).
(1) \(b + k = 1\).
This statement alone is not sufficient to determine the slopes of the lines.
(2) \(bk = 0\).
This statement alone is not sufficient to determine the slopes of the lines.
(1)+(2) Combining both statements and solving \(b + k = 1\) and \(bk = 0\), we get two possibilities: \(k = 1\) and \(b = 0\), or \(k = 0\) and \(b = 1\). In either case, one line has a slope of 0 (a horizontal line), and the other has a slope of 1. The intersection of these lines forms a 45-degree angle. Not sufficient.
Answer: C
What is the measure of the smaller angle formed by the intersection of the lines \(y = kx + b\) and \(y = bx + k\)?
To answer the question, we need to determine the slopes of each line, which are represented by the values of \(k\) and \(b\).
(1) \(b + k = 1\).
This statement alone is not sufficient to determine the slopes of the lines.
(2) \(bk = 0\).
This statement alone is not sufficient to determine the slopes of the lines.
(1)+(2) Combining both statements and solving \(b + k = 1\) and \(bk = 0\), we get two possibilities: \(k = 1\) and \(b = 0\), or \(k = 0\) and \(b = 1\). In either case, one line has a slope of 0 (a horizontal line), and the other has a slope of 1. The intersection of these lines forms a 45-degree angle. Not sufficient.
Answer: C
General Discussion
09 May 2023, 12:56
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
