All categories

2 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]2 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

You might be interested in

How do uou do this problem

Ronch [10]

The first step to solving an equation like this is to find the slope of a line that will be perpendicular to the line given. The slope of a line that's perpendicular to another line is the negative reciprocal. The negative reciprocal of -1/5 is 5. So, so far our equation is y = 5x + b. Now, to find what b is equal to, we should substitute the values of x and y from the point (1,2) since we know that our line goes through the point. Our equation becomes:

2 = 5 + b
b= -3

That means that the equation of our new line is y = 5x - 3

4 0

3 years ago

Change 72 out of 123 to a percentage

Elanso [62]

Answer:

72 / 123 * 100 = 58.53658537 per cent

Step-by-step explanation:

4 0

3 years ago

Vertical analysis (common-size) percentages for Vallejo Company’s sales, cost of goods sold, and expenses are listed here.

dybincka [34]

Cost of goods sold - expenses = net income
do this for each year and compare.

6 0

2 years ago

The prism has a surface area of 1312 mm2.

777dan777 [17]

So each dimention is 32 by 8 by 10
so the surface area=2 times(8 times 10)+(2 times (32 times 10))+(2 times (8 times 32))=2 times 80+2 times 320+2 times 256=1312

if halved
just divide each by 2
(2 times 4 times 5)+(2 times 16 times 5)+(2 times 4 times 16)=(2 times 20)+(2 times 80)+(2 times 64)=40+160+128=328
the new surface area is 328 mm^2

4 0

2 years ago

That you're positive that you should be trying out these difficult math questions, let’s get right to it! The answers to these q

Lemur [1.5K]

Answer:

that you're positive that you should be trying out these difficult math questions, let’s get right to it! The answers to these questions are in a separate section below, so you can go through them all at once without getting spoiled.

#1:

body_ACT_0506_-_56

#2:

body_ACT_0506_-_59

#3:

body_ACT_0809_-_38_J

#4:

body_ACT_0809_-_54

#5:

body_ACT_0809_-_55-1

#6:

body_ACT_0809_-_56

#7:

body_ACT_0809_-_57-1

#8:

body_ACT_0809_-_60

#9:

body_ACT_1112_-__48-1

#10:

body_ACT_1112_-_45

#11:

body_ACT_1112_-_51-1

#12:

body_ACT_1112_-_52

#13:

body_ACT_1112_-_53

#14:

body_ACT_1112_-_58

#15:

body_ACT_1314_-_55-1

Step-by-step explanation:

5 0

2 years ago