I may be wrong. But the way I would think would be like that:
Let's consider
statement (1) "products of the x-intercepts is positive" and possible variants of slopes:
Variant 1. Negative slope*positive slope=
negativeX-intercept product is positive, y-intercept product is negativeVariant 2. Negative slope * negative slope =
positiveX-intercept product is positive, y-intercept product is positiveVariant 3. Positive slope*positive slope=
positiveX-intercept product is positive, y-intercept product is positiveVariant 4. Positive slope*positive slope=
positiveX-intercept product is positive, y-intercept product is positiveHence, the product of slopes can be either positive or negative. Not sufficient.
Now
statement (2) "product of y-intercepts is negative". This can happen in two cases.
Variant 1. Negative slope*positive slope=
negativeX-intercept product is positive, y-intercept product is negativeVariant 2. Positive slope*positive slope=
positiveX-intercept product is negative, y-intercept product is negativeSo, from statement (2) we get that positive and negative products of slopes are possible. So, insufficient.
However, when we
combine the two statements,
we need both two conditions to be true, that is: product of x intercepts should be positive and product of y-intercepts should be negative. There is only one case when the above conditions are true among all our charts. Only one variant (Variant 1) overlaps. Hence, we can conclude that the product is negative. Therefore, C.
My guess. May be wrong.
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