Question

NO LINKS!! URGENT HELP PLEASE!!!

If x < 0 and y > 0, determine the sign of the real number.

a. x/y
1. positive
2. negative

b. xy^2
1. postive
2. negative

c. (x - y)/xy
1. positive
2. negative

d. y(y - x)
1. positive
2. negative

Answer 1

From the question it is given that x<0 and y>0 or in other words x is negative and y is positive.

(a)x y : x is negative and y is positive

⇒negative x positive = negative

Therefore, xy is negative

(b)x : x is negative and is positive

⇒negative x positive = negative

Therefore, x is negative

(c) (x − y)xy : x is negative and is positive

⇒(x − y) is negative and xy is negative {from (a)}

⇒negative x negative = positive

Therefore, (x-y)xy is negative

(d) y(y − x): x is negative and y is positive

here y - x is positive

⇒positive x positive = positive

Therefore, (y-x)y is negative

Answer 2

a. 2. negative

b. 2. negative

c. 1. positive

d. 1. positive

Explanation:

Given that x < 0 and y > 0, we can use the rules of signs to determine the sign of the given expressions.

a. x/y

The expression x/y is negative because the quotient of a negative number and a positive number is always negative. Therefore, the answer is 2. negative.

b. xy^2

The expression xy^2 is negative because the product of a negative number and a positive number squared is always negative. Therefore, the answer is 2. negative.

c. (x - y)/xy

The expression (x - y)/xy is positive because the numerator, (x - y), is negative and the denominator, xy, is positive. The quotient of a negative number and a positive number is always negative, but since there is a negative sign in the numerator and another in the denominator, they cancel each other out, resulting in a positive value. Therefore, the answer is 1. positive.

d. y(y - x)

The expression y(y - x) is positive because the product of two factors, both of which are positive or both of which are negative, is always positive. In this case, y and (y - x) are both positive, so their product is positive. Therefore, the answer is 1. positive.