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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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here only one angle is equal the other one is not

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malfutka [58]

Answer:

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Step-by-step explanation:

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3 years ago

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Serggg [28]

Answer:

The answer is (B).

Step-by-step explanation:

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g(x) = $\frac{x+9}{6}$ is inverse function of f(x) and ≠ $\frac{x+2}{6}$ - 3

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3 years ago

Can someone help me with this please?

AVprozaik [17]

Answer:

y=70°

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Step-by-step explanation:

Since the two triangles are similar, we know that all of the corresponding angles must be the same. On the triangle on the left, we can see that the angle formed between sides AB and AC is 60°. This means that the same angle is formed at Z, which is in the same location on the triangle to the right. From there, we can find the missing angle, W, from the difference of 180°.

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