Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$\frac { x ^ { 3 } } { y } 0$$
A) x and y have the same sign.
B) x and y must be positive.
C) x and y must be negative.
D) x and y have different signs.

Question

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$\frac { x ^ { 3 } } { y } > 0$$
A) x and y have the same sign.
B) x and y must be positive.
C) x and y must be negative.
D) x and y have different signs.

Quizplus · Accepted Answer

Since $x^3$ preserves the sign of $x$ (a negative number cubed is negative, and a positive number cubed is positive), for the fraction to be greater than 0, $y$ must have the same sign as $x^3$ (and thus the same sign as $x$). This means $x$ and $y$ must either both be positive or both be negative.

Determine What Signs on Values of X and Y Would x3y>0\frac { x ^ { 3 } } { y } > 0yx3​>0

Determine What Signs on Values of X and Y Would $\frac { x ^ { 3 } } { y } > 0$