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brilliants [131]

3 years ago

9

P is the centroid of triangle ABC. AE=21,CD=14, and BF=11 What is the length of AP

1 answer:

allsm [11]3 years ago

8 0

The length of AP is 14 units

Step-by-step explanation:

The centroid point of a triangle is:

The point of intersection of the three medians of the triangle
The centroid point divides each median into two segments at a ratio 2 : 1 from its vertex
The length of the segment from the vertex to the centroid is $\frac{2}{3}$ of the length of the median
The length of the segment from the centroid to the base is $\frac{1}{3}$ of the length of the median

Look to the attached figure

In Δ ABC

∵ D is the mid-point of AB

∵ E is the mid-point of BC

∵ F is the mid-point of AC

∵ AE , BF and CD are the medians of the triangle

∵ AE , BF and CD are intersected at P

∴ P is the centroid of the triangle

- By using the rule above

∴ AP = $\frac{2}{3}$ AE

∵ AE = 21 units

∴ AP = $\frac{2}{3}$ × 21

∴ AP = 14 units

The length of AP is 14 units

Learn more:

You can learn more about the triangles in brainly.com/question/3358617

#LearnwithBrainly

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Answer:

145 yards squared

Step-by-step explanation:

So the area of the base is area of a square with side length of 5 yards $5*5=25$

The area of one triangular face base times height divided by two and then simply multiplied by 4 because there are 4 triangular faces.

$(\frac{5*12}{2} )*4 = 120$

So the total surface area is $25+120=145$ yards squared

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Solve for w, where w is a real number.<br> √w+9=5

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3 years ago

Generate the nest three terms of each arithmetic sequence shown below.

o-na [289]

Answer:

A)2,6,10

B)2,-6,-18

C)-1,-3,-5

Step-by-step explanation:

<u>A)a1=-2 and d=4</u>

We know that the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{2}=a_{1}+(2-1)d$

$a_{2}=a_{1}+(1)d$

Substituting the given value we get

$a_{2}= -2+(1)4$

$a_{2}= -2+4$

$a_{2}= 2$

------------------------------------------

Similarly

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the given value we get

$a_{3}= -2+(2)4$

$a_{3}= -2+8$

$a_{3}= 6$

-------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the given value we get

$a_{4}= -2+(3)4$

$a_{4}= -2+16$

$a_{4}= 10$

-------------------------------------------------------------------------------------------

<u>B</u><u> $a_n=a_{(n-1)}-8$ with $a_1=10$ </u>

$a_2=a_{(2-1)}-8$

$a_2=a_{1}-8$

Substituting the given value

$a_2= 10-8$

$a_2=2$

---------------------------------------------------------------------

$a_3=a_{(3-1)}-8$

$a_3=a_{2}-8$

Substituting the value

$a_3=2-8$

$a_3= -6$

---------------------------------------------------------------------

$a_4=a_{(4-1)}-8$

$a_4=a_{3}-8$

Substituting the value

$a_4= -6-8$

$a_4= -14$

-------------------------------------------------------------------------------------------

<u>C) $a_1=3, a_2=1$ </u>

Here the difference is -2

the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the value we get

$a_{3}= 3+(2)-2$

$a_{3}= 3-4$

$a_{3}= -1$

------------------------------------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the value we get

$a_{4}= 3+(3)-2$

$a_{4}= 3-6$

$a_{4}= -3$

----------------------------------------------------------------------------------

$a_{5}=a_{1}+(5-1)d$

$a_{5}=a_{1}+(4)d$

Substituting the value we get

$a_{5}= 3+(4)-2$

$a_{5}= 3-8$

$a_{5}= -5$

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3 years ago