If y^2-x^2=5(y-x)^2 find x:y

x:y = 1:1 or 2:3

Step-by-step explanation:

By a difference of squares, we get:

(y+x)(y-x)=5(y-x)^2

move all to one side:

(y+x)(y-x) - 5(y-x)^2 = 0

take a common factor of (y - x) out and expand and simply the other factor:

(y - x)[y+x-5(y-x)] = 0

(y - x)(-4y + 6x) = 0

By the null factor rule:

x = y

=> x:y = 1:1

or

6x = 4y

=>

x:y = 4:6

x:y = 2:3

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

answer: when you burn wood, the carbon reacts with the oxygen in the air to create ash and smoke. that is a permanent change you cannot undo that.

step-by-step explanation: