In the diagram, m ∥ n and m and n are cut by transversal p. Which angle pairs are congruent? Check all that apply. ∠1 and ∠5 ∠3
and ∠8 ∠6 and ∠4 ∠8 and ∠2 ∠4 and ∠7
2 answers:
Answer:
<h2>∠1 and ∠5</h2><h2>∠6 and ∠4</h2><h2>∠8 and ∠2</h2>Step-by-step explanation:
The image is attached.
According to geometry, when a transversal crosses one pair of parallels, that set-up give 8 angles which are related each other, we know these angles as
- Alternate interior angles
- Alternate exterior angles.
- Corresponding angles.
- Vertical Angles.
These pair of angles are characterized for being congruent.
According to the graph, ∠1 and ∠5 are congruent, they are corresponding angles, because they are in the same side of the transversal, one interior to parallels, one exterior to parallel.s
Also, ∠6 and ∠4 are congruent, because they are alternate interior angles, they are on different sides of the transversal and inside parallels.
∠8 and ∠2 are congruent, because they are alternate exterior angles, they are on different sides of the transversal and outside parallels.
Therefore, the right choices are ∠1 and ∠5, ∠6 and ∠4, and ∠8 and ∠2
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Answer as an inequality:
Answer in interval notation:
Answer in words: Set of positive real numbers
All three represent the same idea, but in different forms.
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Explanation:
Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is
For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.
Because of this, has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.
The domain of is x > 0 which in interval notation would be
. This is the interval from 0 to infinity, excluding both endpoints.
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The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.
So,
allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.
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In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.