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SajjadAhmad
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

(-6)*a = -60

-6a(-6 + 4) = -60

36a - 24a = -60

12a = -60

a = -5

Answer: B
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Given that \(x♦ y=xy(x+4)\) and \((-6) ♦ a = -60,\) and we need to find the value of a

To find (-6) ♦ a we need to compare what is before and after ♦ in (-6) ♦ a and x♦ y

=> We need to substitute x with -6 and y with a in x♦ y to get the value of (-6) ♦ a

=> \(-6♦ a=-6*a(-6+4)\) = -6a*-2 = 12a = -60 (given)
=> a = \(\frac{-60}{12}\) = -5

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

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-6*a = 60
-6(a) (-6+4) = 60
Since x*y = xy(x+4)

Which implies
12a = 60
a= 5

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x♦y=xy(x+4)x♦y=xy(x+4)

(−6)♦a=−60=(−6)a(−6+4)=12a(−6)♦a=−60=(−6)a(−6+4)=12a

a = -5
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