If two of the four expressions x + y, x + 5y, x – y, and 5x – y are chosen at random, what is the probability that their product will be of the form of x2 – (by)2, where b is an integer?

  1/6

Step-by-step explanation:

The product will only be of the required form if the two chosen factors are of the form (x +by) and (x -by).

For the factor (x+y), there is also a factor (x-y) on the list. For the factor (x+5y), there is no factor (x-5y) available.

So, of the (4·3)/2 = 6 possible ways to choose two expressions from the four given expressions, only one pair of the 6 will have a product of the required form.

The probability is 1/6.

step-by-step explanation: 2

step-by-step explanation:

at each of the parallel lines adjacent angles are supplementary. the angles have special names identifying their positions with respect to the parallel lines and transversal. they are corresponding angles, alternate interior angles, or alternate exterior angles. an angles is congruent to its matched angle.