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29 Jul 2024, 03:31
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On the number line shown, the tick marks are equally spaced and the coordinates of points A and B are \(7^{12}\) and \(7^{13}\), respectively. Which of the following coordinates represent the two points that are 2.5 times as far from Point A as Point A is from Point B?
A. \(-2*7^{13}\) and \(16*7^{12}\)
B. \(-2*7^{13}\) and \(15*7^{12}\)
C. \(-2*7^{13}\) and \(10*7^{12}\)
D. \(-2*7^{12}\) and \(16*7^{12}\)
E. \(-2*7^{12}\) and \(15*7^{12}\)
29 Jul 2024, 03:31
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Official Solution:
On the number line shown, the tick marks are equally spaced and the coordinates of points A and B are \(7^{12}\) and \(7^{13}\), respectively. Which of the following coordinates represent the two points that are 2.5 times as far from Point A as Point A is from Point B?
A. \(-2*7^{13}\) and \(16*7^{12}\)
B. \(-2*7^{13}\) and \(15*7^{12}\)
C. \(-2*7^{13}\) and \(10*7^{12}\)
D. \(-2*7^{12}\) and \(16*7^{12}\)
E. \(-2*7^{12}\) and \(15*7^{12}\)
Assuming the coordinate of A is \(a\), then the coordinate of B, in terms of \(a\), is \(7a\). Thus, the distance between the points is \(7a - a = 6a\). So, we are looking for the points which are \(6a * 2.5 = 15a\) distance from \(a\), so the points are at \(a - 15a = -14a\) and \(a + 15a = 16a\). Substituting the actual value of \(a\) we get:
\(-14a = -14 * 7^{12} = -2 * 7^{13}\) and \(16a = 16 * 7^{12}\).
Answer: A
On the number line shown, the tick marks are equally spaced and the coordinates of points A and B are \(7^{12}\) and \(7^{13}\), respectively. Which of the following coordinates represent the two points that are 2.5 times as far from Point A as Point A is from Point B?
A. \(-2*7^{13}\) and \(16*7^{12}\)
B. \(-2*7^{13}\) and \(15*7^{12}\)
C. \(-2*7^{13}\) and \(10*7^{12}\)
D. \(-2*7^{12}\) and \(16*7^{12}\)
E. \(-2*7^{12}\) and \(15*7^{12}\)
Assuming the coordinate of A is \(a\), then the coordinate of B, in terms of \(a\), is \(7a\). Thus, the distance between the points is \(7a - a = 6a\). So, we are looking for the points which are \(6a * 2.5 = 15a\) distance from \(a\), so the points are at \(a - 15a = -14a\) and \(a + 15a = 16a\). Substituting the actual value of \(a\) we get:
\(-14a = -14 * 7^{12} = -2 * 7^{13}\) and \(16a = 16 * 7^{12}\).
Answer: A
19 Nov 2024, 09:02
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I think this is a high-quality question.
