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x-1/(x-2)^2+25=2/17
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07 Aug 2020, 09:33
07 Aug 2020, 09:33
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Question Stats:
61% (02:04) correct
38% (02:13) wrong based on 98 sessions
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\(\frac{x-1}{(x-2)^2+25}=\frac{2}{17}\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Kudos for the right solution and explanation
Quantity A |
Quantity B |
x |
8 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Kudos for the right solution and explanation
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Posts: 6218
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Re: x-1/(x-2)^2+25=2/17
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07 Aug 2020, 10:51
07 Aug 2020, 10:51
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Carcass wrote:
\(\frac{x-1}{(x-2)^2+25}=\frac{2}{17}\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Kudos for the right solution and explanation
Quantity A |
Quantity B |
x |
8 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Kudos for the right solution and explanation
Given: \(\frac{x-1}{(x-2)^2+25}=\frac{2}{17}\)
Cross multiply to get: \((17)(x-1)=(2)[(x-2)^2+25]\)
Expand both sides: \(17x-17=(2)[(x^2-4x+4)+25]\)
Simplify: \(17x-17=(2)[x^2-4x+29]\)
Simplify again: \(17x-17=2x^2-8x+58\)
Add \(17\) to both sides: \(17x=2x^2-8x+75\)
Subtract \(17x\) from both sides: \(0=2x^2-25x+75\)
Factor: \(0 = (2x - 15)(x - 5)\)
If \(x-5=0\), then \(x=5\), in which case Quantity B is greater
If \(2x-15=0\), then \(x=7.5\), in which case Quantity B is greater
In both possible cases, Quantity B is greater
Answer: B
Re: x-1/(x-2)^2+25=2/17
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14 Dec 2021, 00:10
14 Dec 2021, 00:10
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