Algebraically determine if the relation x = y2 – 100 is symmetrical with respect to the x-axis, y-axis, or the origin.
1 answer:
Answer: Option D: x-axis symmetry
Step-by-step explanation:
The symmetry concept can be explained as below:
- If any point say, (x,y) on the graph, then (x,-y) is also on the graph, it shows x- axis symmetry.
- If any point say, (x,y) lies on the graph, then, (-x,y) should also lie on the same graph, then is shows y-axis symmetry.
Now, here the graph is for x = y^{2}-100 is attached.
Suppose, (x,y) = (-100,0)
then, solving this point satisfies the equation of given graph.
Also, (x,-y) = (-100,0) satisfies the equation of the given graph.
Hence, the relation x = y^2 – 100 is symmetrical to x-axis.
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We're given the Arithmetic Progression <em>-24, -4, 16, 36 ...</em> .
We know that a term in an AP is generally represented as:
where,
- a = the first term in the sequence
- n = the number of the term/number of terms
- d = difference between two terms
We need to find .
From the given progression, we have:
- a = -24
- n = 23
- d = (-24 - (-4) = -20
Using these in the formula,
Therefore, the 23rd term in the AP is -464.
Hope it helps. :)