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Lelechka [254]
2 years ago
10

4. will give brainliest

Mathematics
1 answer:
saul85 [17]2 years ago
8 0

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

#SPJ1

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If M is the centroid of triangle GHI, HL=45, JI=63, and KG=60, find the missing measures
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Answer:

Part a) ML=15\ units

Part b) HM=30\ units

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Step-by-step explanation:

see the attached figure to better understand the problem

we know that

A <u><em>centroid</em></u> of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle.

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Part a) Find ML

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ML=\frac{1}{3}HL

substitute the given value

ML=\frac{1}{3}(45)

ML=15\ units

Part b) Find HM

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HL=45\ units

we know that

HM=\frac{2}{3}HL

substitute the given value

HM=\frac{2}{3}(45)

HM=30\ units

Part c) Find JM

we have

JI=63\ units

we know that

JM=\frac{1}{3}JI

substitute the given value

JM=\frac{1}{3}(63)

JM=21\ units

Part d) Find MI

we have

JI=63\ units

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MI=\frac{2}{3}JI

substitute the given value

MI=\frac{2}{3}(63)

MI=42\ units

Part e) Find GM

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we know that

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substitute the given value

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GM=40\ units

Part f) Find MK

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substitute the given value

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En la figura, la suma de las medidas p + q + r + s =/In the figure, the sum of the measures p + q + r + s =
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Answer:

I think its 300

Step-by-step explanation

This is from my understanding, so I may be a bit wrong.

1. First observe the amount of triangles that form, you have two main triangles and one isosceles triangle that forms in the middle by how these are joined together.

2. Using this idea we will come up  with the equations of  each triangle that has been formed.

3. We can observe that almost all angles are named with a variable except the one in the middle, being an isosceles we will name the missing variable y.

4. Triangle 1(left side) or T1 equals 180 degrees but what angles form this triangle, these would be p+q+y = 180, T2(right side) = r+s+y = 180

5. After creating these two triangles we notice that we have not taken into account the triangle in the middle, we are given 1 angle of this isosceles. There is a mathematical property which I don't remember the name, but essentially the angle below is the same as the angle above, this being 120 degrees. This will result in T3 = 2y + 120 = 180

6. Solve for y, which gives us y=30, *<em>simple triangle math you know*</em>

7. Finally we fix our equations for p+q+r+s, essentially T1 and T2 will transform into p+q = 180-y and r+s = 180-y, we add them up forming p+q+r+s = 2(180-y)

8. Solve the equation p+q+r+s = 360 - 2y which when adding y becomes p+q+r+s = 360-60 = 300

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