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zlopas [31]
3 years ago
9

What is the measure of DBE? A. 120 B. 75 C. 45 D. 60

Mathematics
1 answer:
vladimir1956 [14]3 years ago
8 0

Hi!

The intersecting chords theorem states that when two chords of a circle intersect, they form a pair of vertical angles (in this case angle DBE and ABC), and the measure of those angles (since they're congruent, it's the same) is equal to half of the sum of the two intercepted arcs.

That rule applies here. In this case, the intersecting chords are line AE and DC (you can tell because they end on the circle, and they have two endpoints on it), and the intercepted arcs are arc DE and arc AC, with measures of 45 degrees and 75 degrees (respectively).

So to find the measure of angle DBE (one of the vertical angles), just take the sum of the measures of the two intersected arcs, and then divide by 2. In this case, it's 45 + 75, to get 120 degrees, dividing by 2 gets 60 degrees.

So therefore your answer is 60 degrees, or B.

Hope this helped!

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Enter the correct answer in the box.
Mekhanik [1.2K]

The equation in the vertex form of g(x) is:

g(x) = (x + 1)^2 - 38

<h3>How to get the equation of function g?</h3>

We know that g(x) is a translation of 2 units below and 3 units to the left of f(x).

So first, let's rewrite f(x) to its vertex form:

f(x) = x^2 - 4x - 32

The vertex is at:

x = -(-4)/2*1 = 2

The y-value of the vertex is:

f(2) = 2^2 - 4*2 - 32 = -36

Then the vertex form of f(x) is:

f(x) = (x - 2)^2 - 36

If we move this vertex 2 units below, and 3 units to the left, then we have:

g(x) = f(x +3) - 2\\\\g(x) = (x - 2 + 3)^2 - 36 - 2\\\\g(x) = (x + 1)^2 - 38

That is the equation for g(x) in vertex form.

If you want to learn more about quadratic equations:

brainly.com/question/1214333

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Step-by-step explanation:

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Please help, I keep getting bots. <br> Using front-end estimation, find a reasonable estimate of:
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Answer:

Roughly 18,000

Step-by-step explanation:

When you need to do rough mental math, you can do something like 720 vs 25 or 30 which is pretty simple to do in your head.

If you are very proficient in mental math, you can do something like 720 * 25, which is harder, but if you know the tricks, you can do this quickly.

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50

Add a zero.

500.

17500 + 500 = 18000

5 0
3 years ago
Read 2 more answers
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