HURRY PLEASE! The difference between two positive numbers is 4 and the sum of their squares is 170. What are the numbers? Do not guess or check. Show your work.

x = 11

y = 7

Step-by-step explanation:

Let x and y be the unknown numbers.

"The difference between two positive numbers is 4..." (1)

x - y = 4

Assuming that:

x and y ≥ 0

"...the sum of their squares is 170" (2)

x² + y² = 170

Arrange the first equation (1):

x - y = 4

x = 4 + y

Now substitute x to equation (2):

x² + y² = 170

(4 + y)² + y² = 170

y² + 8y + 16 + y² = 170

y² + y² + 8y + 16 = 170

2y² + 8y + 16 = 170

2y² + 8y = 170 - 16

2y² + 8y = 154

2y² + 8y - 154 = 0

Quadratic:

= 7

= -11

Recall that:

x and y ≥ 0 or that it is only positive.

So y = 7

Now solve for x in equation (1):

x = 4 + y

x = 4 + (7)

x = 11

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following