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Bunuel
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The operation ⊗ is defined by x⊗y = x^2y + xy for all numbers x and y 07 Jul 2020, 00:55
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B
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77% (01:24) correct 23% (01:22) wrong based on 123 sessions

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The operation \(\otimes \) is defined by \(x \otimes y = \frac{x^2}{y} + \frac{x}{y}\) for all numbers \(x\) and \(y\), when \(y \neq 0\). What is the value of \((9 \otimes (-9))+((-9) \otimes 9 )\) ?

A. -4
B. -2
C. 0
D. 2
E. 4
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B
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The operation ⊗ is defined by x⊗y = x^2y + xy for all numbers x and y 07 Jul 2020, 01:28
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(9⊗(−9))+((−9)⊗9) = \(\frac{9^2}{-9} + \frac{9}{-9} + \frac{(-9)^2}{9} + \frac{-9}{9}\) =
\(-9 - 1 + 9 -1 = -2\)
ans: B
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The operation ⊗ is defined by x⊗y = x^2y + xy for all numbers x and y 07 Jul 2020, 01:40
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IMO B

x⊗y=x^2/y+x/y, when y≠0

(9⊗(−9))+((−9)⊗9) ?

9⊗(−9) = 9^2/(-9) + 9/(-9) = -9 -1= -10
(−9)⊗9 = (-9)^2/9 + (-9)/9 = 9 -1 = 8

(9⊗(−9))+((−9)⊗9) = -10+8 = -2

B. -2
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The operation ⊗ is defined by x⊗y = x^2y + xy for all numbers x and y 07 Jul 2020, 22:07
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Ans - B

Use given X x Y relation for
Solve for 1st term
(9 x (-9))= (9)^2/(-9) + 9/(-9))= -9-1= -10

Solve for second term
((-9) x 9) = ((-9^2)/9 + (-9)/9) = 9-1= 8

Add 1+2
-10+8= -2

So its B

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The operation ⊗ is defined by x⊗y = x^2y + xy for all numbers x and y 07 Jul 2020, 22:15
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x ⊗ y = (x^2/y) + (x/y)

Simplifying, x ⊗ y = (x/y)(x + 1)

There 9 ⊗ (-9) = -10 and (-9) ⊗ 9 = +8

Therefore, the Answer is -2.

Answer (B)
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The operation ⊗ is defined by x⊗y = x^2y + xy for all numbers x and y 20 Nov 2021, 07:40
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Bunuel Can you please give links for questions similar to this for practice
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The operation ⊗ is defined by x⊗y = x^2y + xy for all numbers x and y 21 Nov 2021, 02:38
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ishwan
Bunuel Can you please give links for questions similar to this for practice
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Check below:

13. Functions



For more check below:
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The operation ⊗ is defined by x⊗y = x^2y + xy for all numbers x and y 28 Sep 2022, 11:03
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Given that \(x \otimes y = \frac{x^2}{y} + \frac{x}{y}\) and we need to find the value of \((9 \otimes (-9))+((-9) \otimes 9 )\)

Let's start by finding the value of \(9 \otimes (-9)\)

To find \(9 \otimes (-9)\) we need to compare what is before and after \(\otimes\) in \(9 \otimes (-9)\) and \(x \otimes y\)

=> We need to substitute x with 9 and y with -9 in \(x \otimes y = \frac{x^2}{y} + \frac{x}{y}\) to get the value of \(9 \otimes (-9)\)

=> \(9 \otimes (-9) = \frac{9^2}{-9} + \frac{9}{-9}\) = -9 -1 = -10

Similarly, \(-9 \otimes 9 = \frac{(-9)^2}{9} + \frac{-9}{9}\) = 9 -1 = 8

\((9 \otimes (-9))+((-9) \otimes 9 )\) = -10 + 8 = -2

So, Answer will be B
Hope it helps!

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