Question

NO LINKS!!

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

Answer 1

A) negative B)Positive C) Negative D) Positive

Explanation:

A) Negative

Since x is negative and y is positive, negative*positive is negative.

B) Positive

Since x is negative, when squared, it will be positive so the product is positive.

C) Negative

Since x is negative, when it is divided by positive, it will still be negative. And adding itself, makes it more low.

D) Positive

Since y is positive, and x is negative, it is positive+positive, so positive.

Answer 2

(a) negative

(b) positive

(c) negative

(d) positive

Explanation:

Given:

• x < 0 ⇒ x is negative.
• y > 0 ⇒ y is positive.

`\begin{aligned}\sf (a)\quad xy &= \sf negative * positive \\ &= \sf negative \end{aligned}`

`\begin{aligned}\sf (b)\quad x^2y & \sf= xxy\\ & \sf= negative * negative * positive\\& \sf= positive * positive\\ & \sf= positive\end{aligned}`

`\begin{aligned}\sf (c)\quad (x)/(y)+x&=\sf (negative)/(positive)+negative\\ &= \sf negative+negative\\ &= \sf negative \end{aligned}`

`\begin{aligned}\sf (a)\quad y - x &= \sf positive - negative \\ &= \sf positive + positive \\ & = \sf positive\end{aligned}`

Information:

• When a negative number is multiplied/divided by a positive number, the product/quotient is always negative.
• When a positive number is multiplied/divided by a negative number, the product/quotient is always negative.
• When a negative number is multiplied/divided by a negative number, the product/quotient is always positive.
• When a positive number is multiplied/divided by a positive number, the product/quotient is always positive.
• When a negative number is added to a negative number, the result is always negative.
• When a negative number is subtracted from a positive number, the result is always positive.