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28 Aug 2024, 10:55
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
75% (03:11) correct
25% (01:43) wrong based on 4 sessions
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Points A, B, C, and D are on the number line above, and AB = CD = 1/3 (BC). What is the coordinate of C?
A. 13/30
B. 9/20
C. 11/24
D. 7/15
E. 29/60
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21 Oct 2024, 12:12
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OE
From the fgure you can see that since the coordinate of A is 1/3, it follows that the coordinate of C is 1/3 + AB + BC. Since you are given that AB = 1/3 (BC), the coordinate of C can be rewritten in terms of AB as follows: 1/3 + AB + BC = 1/3 + AB + 3(AB) = 1/3 + 4(AB).
To find the coordinate of C, you need to know AB. From the fgure, you know that AD = AB + BC + CD = AB + 3(AB) + AB = 5(AB). On the other hand, since the coordinate of A is 1/3 and the coordinate of D is 1/2, it follows that \(AD = \frac{1}{2}- \frac{1}{3} = \frac{1}{6}.\)
Therefore you can conclude that 1/6 = 5(AB) and AB = 1/30. Tus the coordinate of C is \(\frac{1}{3} + 4(AB) = \frac{1}{3} + 4(\frac{1}{30})\), or \(\frac{7}{15}\).
The correct answer is Choice D.
From the fgure you can see that since the coordinate of A is 1/3, it follows that the coordinate of C is 1/3 + AB + BC. Since you are given that AB = 1/3 (BC), the coordinate of C can be rewritten in terms of AB as follows: 1/3 + AB + BC = 1/3 + AB + 3(AB) = 1/3 + 4(AB).
To find the coordinate of C, you need to know AB. From the fgure, you know that AD = AB + BC + CD = AB + 3(AB) + AB = 5(AB). On the other hand, since the coordinate of A is 1/3 and the coordinate of D is 1/2, it follows that \(AD = \frac{1}{2}- \frac{1}{3} = \frac{1}{6}.\)
Therefore you can conclude that 1/6 = 5(AB) and AB = 1/30. Tus the coordinate of C is \(\frac{1}{3} + 4(AB) = \frac{1}{3} + 4(\frac{1}{30})\), or \(\frac{7}{15}\).
The correct answer is Choice D.
