If x and y are reciprocals of each other, then their product always equals
A. 1
B. x^2
C. y^2
D. 1/x^2
Well, it seems like x and y have a special relationship going on - they're reciprocals of each other! So, if we multiply them together, we'd end up with... drumroll, please... 1! Yup, A is the correct answer here. It's always a party when x and y are reciprocals!
If x and y are reciprocals of each other, then their product is always equal to 1.
This means that if x and y are reciprocals, then x * y = 1.
Therefore, the correct answer is:
A. 1
If x and y are reciprocals of each other, it means that they are numbers such that their product is always equal to 1. In other words, x * y = 1.
To understand why their product is always equal to 1, let's look at the definition of reciprocal. The reciprocal of a nonzero number x is defined as 1 divided by x. Mathematically, we can represent the reciprocal of x as 1/x.
So, if x and y are reciprocals, we can say that x = 1/y and y = 1/x.
Now, let's substitute the value of y in terms of x into the equation x * y = 1:
x * (1/x) = 1
This simplifies to:
1 = 1
Therefore, the product of x and y is always equal to 1.
Hence, the correct answer is: A. 1.