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3 years ago

If Z is the centroid of ∆LMN,WZ=4,ZN=14, and ZY = 10, find each missing measure

Mathematics

1 answer:

jeyben [28]3 years ago

7 0

Answer:

ZM = 8

WM = 12

XZ = 7

XN = 21

LZ = 20

Step-by-step explanation:

The centroid of a triangle is the point of intersection of the midpoint of the each of the three sides of a triangle. The centroid of a triangle is located inside the triangle and it is known as the center of gravity.

The centroid theorem for a triangle states that the centroid of a triangle is located at 2/3 of the distance from the vertex of the triangle of the middle of the opposite side.

ZM = (2/3)WM (centroid theorem)

Therefore: WZ = (1/3)WM

WM = 3WZ = 3 * 4 = 12

ZM = (2/3) * WM = 2/3 * 12 = 8

ZN = (2/3)XN (centroid theorem)

XN = (3/2)ZN = 3/2 * 14 = 21

XN = 21

XZ + ZN = XN

XZ + 14 = 21

XZ = 7

LZ = (2/3)LY (centroid theorem)

Therefore: ZY = (1/3)LY

LY = 3ZY = 3 * 10 = 30

LZ = (2/3) * LY = 2/3 * 30 = 20

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Answer:

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Step-by-step explanation:

<u>Probability</u>

The experimental or empirical probability can be defined as the ratio of the number of times an event occurs to the total number of times the random activity was performed.

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3 years ago

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Step-by-step explanation:

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3 years ago

Find the derivative of the function y = sin(tan 4x)

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3 years ago

Over the last 24 months, Wendy has deposited the same amount of money in her bank account each month. If she deposited a total o

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Answer:

Step-by-step explanation:

Assuming she deposited the same amount each month.

Total ÷ Months = Amount Deposited Each Month

1,320 ÷ 24 = 55

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3 years ago

Harper knows he is 50 yards from school. The map on his phone shows that the school is 3/4 inch from his current location. How f

yulyashka [42]

Answer:

Harper is 200 yards away from her home if the map shows 3 inches

Step-by-step explanation:

50 yards = 3/4 inch

3 inches = 3/1

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12/4 = 3 inches

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I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

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3 years ago