Interpreting the inequality, it is found that the correct option is given by F.
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- The first equation is of the line.
- The equal sign is present in the inequality, which means that the line is not dashed, which removes option G.
In standard form, the equation of the line is:
Thus it is a decreasing line, which removes options J.
- We are interested in the region on the plane below the line, that is, less than the line, which removes option H.
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- As for the second equation, the normalized equation is:
- Thus, a circle centered at the origin and with radius 2.
- Now, we have to check if the line
, with coefficients
, intersects the circle, of centre
- First, we find the following distance:
- Considering the coefficients of the line and the center of the circle.
- This distance is less than the radius, thus, the line intersects the circle, which removes option K, and states that the correct option is given by F.
A similar problem is given at brainly.com/question/16505684