Question 1021146
i would say selection D.


that is:


(-y-2) / x


you are given that y > 0.


you are also given that xy < 0.


if y > 0, and xy < 0, then x < 0.


has to be because a negative times a positive is a negative which is less than 0.


so, if y is positive, x must be negative in order for x times y to be negative.


of all your options, the only one that has to be positive is eelction D.


this is because y is positive, therefore -y - 2 has to be negative.


since x also has to be negative, you get a negative divided by a negative which has to be positive.


none of the others have to be positive.
we'll go through each one to show you why.


A.x-y


if y is positive and x is negative, then x - y will have to be negative because when you subtract a positive you are adding a negative and a negative (x) plus a negative (-y) is a negative.


B.2x+3y


whether thi is positive or negative depends on the values of x and y.
if x is -20 and y is + 1, then the sum will be negative.


C.x+10/y+2


this also depends on the values of x and y.
if x is more negative than -10, then the numerator will be negative and the denominator will be positive, resulting in a negative.


D.(-y-2)/x


y is positive and so -y is negative.
the numerator has to be negative.
the denominator has to be negative.
the result is positive.


E.2y^2+x 


if x is large enough, then the result will be negative.
for example, y is 1 and x is - 100.
y^2 is 1.
add 1 and -100 and you get a negative number.


the only one that has to be positive is selection D.