Answer:
The measure of 
:
Step-by-step explanation:
The measurement of is also 
, because both and the angle with the measure of are congruent.
Let 3<em>n</em> + 1 denote the "number" in question. The claim is that
(3<em>n</em> + 1)² = 3<em>m</em> + 1
for some integer <em>m</em>.
Now,
(3<em>n</em> + 1)² = (3<em>n</em>)² + 2 (3<em>n</em>) + 1²
… = 9<em>n</em>² + 6<em>n</em> + 1
… = 3<em>n</em> (3<em>n</em> + 2) + 1
… = 3<em>m</em> + 1
where we take <em>m</em> = <em>n</em> (3<em>n</em> + 2).
12/51 x 100 = 23.53%
Answer: 23.53%
The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
<h3>What is the equation of the ellipse associated with the coordinates of the foci?</h3>
By <em>analytical</em> geometry we know that foci are along the <em>major</em> axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the <em>standard</em> form of the equation of the ellipse is of the following form:
(x - h)² / a² + (y - k)² / b² = 1, where a > b (1)
Where:
- a - Length of the major semiaxis.
- b - Length of the minor semiaxis.
Now, we proceed to find the vertex and the lengths of the semiaxes:
a = 10 units.
b = 8 units.
Vertex
V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)
V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)
V(x, y) = (1.5, 1) + (- 4.5, 1)
V(x, y) = (- 3, 2)
The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
To learn more on ellipses: brainly.com/question/14281133
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