The expression 90 y 5 - 54 y 4 is equivalent to r y 4 15 y - 9 ,

Question

The expression 90 y 5 - 54 y 4 is equivalent to r y 4 15 y - 9 , where r is a constant. What is the value of r ?

Accepted Answer

The correct answer is 6 . Applying the distributive property to the expression r y 4 15 y - 9 yields 15 r y 5 - 9 r y 4 . Since 90 y 5 - 54 y 4 is equivalent to r y 4 15 y - 9 , it follows that 90 y 5 - 54 y 4 is also equivalent to 15 r y 5 - 9 r y 4 . Since these expressions are equivalent, it follows that corresponding coefficients are equivalent. Therefore, 90 = 15 r and - 54 = - 9 r . Solving either of these equations for r will yield the value of r . Dividing both sides of 90 = 15 r by 15 yields 6 = r . Therefore, the value of r is 6 .

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