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 different signs.
B) x and y must be negative.
C) x and y have the same sign.
D) x and y must be positive.

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 different signs.
B) x and y must be negative.
C) x and y have the same sign.
D) x and y must be positive.

Quizplus · Accepted Answer

For the fraction $\frac{x^3}{y}$ to be greater than 0, both the numerator and the denominator must either be positive or negative, meaning x and y must have the same sign. Since $x^3$ retains the sign of x, if x is positive, $x^3$ is positive, and if x is negative, $x^3$ is negative. Therefore, for the fraction to be positive, y must have the same sign as x.

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 $\frac { x ^ { 3 } } { y } > 0$