SOLUTION: if xy<0 and y>0 which of the following must be positive? A.x-y B.2x+3y C.x+10/y+2 D.(-y-2)/x E.2y^2+x

Question 1021146: if xy<0 and y>0 which of the following must be positive?
A.x-y
B.2x+3y
C.x+10/y+2
D.(-y-2)/x
E.2y^2+x
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

RELATED QUESTIONS
If x and y are negative integers, which of the following expressions must be negative ? (answered by palanisamy)

Which of the following expressions has a positive value for all x > 0 and y < 0? A)... (answered by josgarithmetic)

If x and y are odd integers, which of the following must be an odd integer? (A) x + y... (answered by vksarvepalli)

If x and y are integers, which of the following is equivalent to... (answered by Alan3354)

If x and y are positive consecutive odd integers, where y > x, which of the following is... (answered by ankor@dixie-net.com)

If x and y are positive consecutive odd integers, where y > x. which of the following is... (answered by ankor@dixie-net.com)

1.) which of the following points are inside the graph of the circle (x-3)^2 + (y-2)^2 =... (answered by stanbon)

If the product of 3 and x is equal to 2 less than y which of the following must be true? (answered by checkley77)

MUST question if p and x are non negative numbers and y is a non positive number, which... (answered by richard1234)