Question

NO LINKS!!! URGENT HELP PLEASE!!!

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

a. xy
1. positive
2. negative

b. x^2
1. positive
2. negative

c. x/y + x
1. positive
2. negative

d. y - x
1. positive
2. negative

Answer 1

Explanation:

a. The product of a negative number (x < 0) and a positive number (y > 0) is negative. Therefore, xy is negative.

b. Squaring a negative number (x < 0) gives a positive result. Therefore, x^2 is positive.

c. The expression x/y is less than 1, because x < y. Therefore, x/y + x is less than 2x. Since x < 0, the expression x/y + x is negative.

d. The expression y - x is the difference between a positive number (y > 0) and a negative number (x < 0). Therefore, y - x is positive.

Hope this helps

Answer 2

a) 2. negative

b) 1. positive

c) 2. negative

d) 1. positive

Explanation:

If x < 0 then x is negative.

If y > 0 then y is positive.

Part (a)

If a negative value is multiplied by a positive value, the result is always negative. For example, (-2) · 3 = -6. Therefore:

• xy is negative.

Part (b)

If a negative value is squared (multiplied by itself), the result is always positive. For example, (-2)² = (-2) · (-2) = 4. Therefore:

• x² is positive.

Part (c)

If a negative value is divided by a positive value, the result is always negative. For example, -4 / 2 = -2.

If a negative value is added to a negative value, the result is always negative. For example, (-2) + (-2) = (-2) - 2 = -4. Therefore:

• (x/y + x) is negative.

Part (d)

If a negative value is subtracted from a positive value, the result is always positive. For example, 3 - (-4) = 3 + 4 = 7. Therefore:

• (y - x) is positive.