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For all numbers x and y the definition of the operation
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08 Feb 2020, 05:51
08 Feb 2020, 05:51
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Question Stats:
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For all numbers \(x\) and \(y\) the definition of the operation \(♦\) is \(x♦ y=xy(x+4)\). If \((-6) ♦ a = -60,\) then what is the value of \(a\) ?
A. -20
B. -5
C. 2.5
D. 5
E. 10
A. -20
B. -5
C. 2.5
D. 5
E. 10
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
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Re: For all numbers x and y the definition of the operation
[#permalink]
08 Feb 2020, 06:42
08 Feb 2020, 06:42
1
GeminiHeat wrote:
For all numbers \(x\) and \(y\) the definition of the operation \(♦\) is \(x♦ y=xy(x+4)\). If \((-6) ♦ a = -60,\) then what is the value of \(a\) ?
A. -20
B. -5
C. 2.5
D. 5
E. 10
A. -20
B. -5
C. 2.5
D. 5
E. 10
Given: \(x♦y=xy(x+4)\)
So: \((-6)♦a=(-6)(a)[(-6)+4]\)
Simplify to get: \((-6)♦a=(-6)(a)(-2)\)
Simplify again to get: \((-6)♦a=12a\)
We are also told that: \((-6) ♦ a = -60,\)
This means we can write: \(12a =-60\)
Divide both sides by 12 to get: \(a =-5\)
Answer: B
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Re: For all numbers x and y the definition of the operation
[#permalink]
09 Feb 2020, 09:13
09 Feb 2020, 09:13
2
GeminiHeat wrote:
For all numbers \(x\) and \(y\) the definition of the operation \(♦\) is \(x♦ y=xy(x+4)\). If \((-6) ♦ a = -60,\) then what is the value of \(a\) ?
A. -20
B. -5
C. 2.5
D. 5
E. 10
A. -20
B. -5
C. 2.5
D. 5
E. 10
We know that: \(x♦ y=xy(x+4)\)
Thus: \((-6) ♦ a = -60\)
\(=>(-6)(a)(-6+4) = -60\)
\(=>12a = -60\)
\(=>a = -5\)
Answer B
