Pleaseee i need help!! and the working!
1 answer:
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When you represent intervals on the number line, you're including full dots, excluding empty dots, and you're considering numbers highlighted by the line.
In the first case, you've highlighted everything before -2 (full dot, thus included), and everything after 1 (empty dot, excluded). So, the set would be
or, in interval notation,
In the second case, you are looking for all numbers between -3 and 5. This interval is symmetric with respect to 1: you're considering all numbers that are at most 4 units away from 1, both to the left and to the right.
This means that the difference between your numbers at 1 must be at most 4, which is modelled by
where the absolute values guarantees that you'll pick numbers to the left and to the right of 1.
The graph is a circle, centered at the origin, with radius=4.
We know that we can write the equation of a circle with radius r and center (a,b) as :
.
Thus, substituting (a, b) with (0, 0) and r with 4, we have:
.
The solutions of this equation are all the points forming the circle shown in the picture. The solutions of this equation are still the same even if we multiply both sides of the equation by 2, because rewriting the equation as:
,
we would still have the same roots.
Thus, the equation of the circle can be written as :
.
Answer: B
We know that we can write the equation of a circle with radius r and center (a,b) as :
Thus, substituting (a, b) with (0, 0) and r with 4, we have:
The solutions of this equation are all the points forming the circle shown in the picture. The solutions of this equation are still the same even if we multiply both sides of the equation by 2, because rewriting the equation as:
we would still have the same roots.
Thus, the equation of the circle can be written as :
Answer: B