1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alexandr1967 [171]
4 years ago
8

Triangle $abc$ has vertices at $a(5,8)$, $b(3,-2)$, and $c(6,1)$. the point $d$ with coordinates $(m,n)$ is chosen inside the tr

iangle so that the three small triangles $abd$, $acd$ and $bcd$ all have equal areas. what is the value of $10m + n$?
Mathematics
1 answer:
Usimov [2.4K]4 years ago
4 0

Answer:

10m + n = 49

Explanation:

Point D will be the centroid of ABC. To find the centroid we use formula.

Given the coordinates of the three vertices of a triangle ABC,

the centroid D coordinates are given by -

m = (x₁ + x₂ + x₃)/3      &      n = (y₁ + y₂ + y₃)/3

m = \frac{5 + 3 + 6}{3}

m = \frac{14}{3}

and

n = \frac{8-2+1}{3}

n = \frac{7}{3}

Now we will find the value of 10m+n

= 10*\frac{14}{3} + \frac{7}{3}

= \frac{140}{3} + \frac{7}{3}

= \frac{147}{3}

= 49

So, 10m + n = 49

That's the final answer.


You might be interested in
The sub shop is keeping track of the number of pounds of turkey sold each day the amount of turkey sold on Saturday is about how
jeka57 [31]
Is that the full question? Theres no numbers
3 0
3 years ago
Ben has a piece of plywood that measures 1 yard on each side.He cuts the wood into 6 equal pieces.Each piece is 1/3 yard wide an
mash [69]

Answer:

The area is "\bold{\frac{1}{6}}".

Step-by-step explanation:

In this question, to understand the problem we use the model, that  Begins with drawing squares from each side which is 1 yard, and divides these as defined throughout the problem. To fix the issue, using the given model, please find the attached file.

Calculating the area of the one-piece:

=\frac{1}{2} \times \frac{1}{3}\\\\=\frac{1}{2\times 3}\\\\=\frac{1}{6}\\\\

5 0
3 years ago
What happens when supply exceeds demand?
Dvinal [7]

Answer:

A

Step-by-step explanation:

Price lowers so more people end up buying the product when it exceeds the demand.

8 0
2 years ago
3 + 2(2x + 8) = 1 is equivalent to
Vedmedyk [2.9K]
3+2 ( 2x + 8 ) = 1 is equivalent to ...


fraction : X = -9/2
Decimal -4.5

8 0
4 years ago
3. Elena can make 15 pizzas in 3 hours. If the number of pizzas is represented by p and time is represented by t, Write an equat
zhuklara [117]

Answer:

Your answer is 3x = 15

Step-by-step explanation:

3x = 15

Since 3 is being multiplied by x, we divide both sides by 3.  3x/3 cancels out, and you're left with x.

15/3 = 5

x = 5

This is my take using algebraic methods.

6 0
3 years ago
Other questions:
  • The sum of three consecutive odd integers if the first inteher is x
    12·1 answer
  • Write a sentence using the verb ser that describes a food commonly found at un asado or barbecue.
    15·1 answer
  • Dori and Nemo go to Taco Bell for lunch. Dori orders three soft tacos and three double Deckers $11.25. Nemiah pays $10 for four
    9·1 answer
  • 2/3 of 864 squarr feet
    10·1 answer
  • On tuesday and wednesday, cab fare cost $7.75 total. on monday and thursday, cab fare cost $6.30 on each day. on friday, cab far
    15·1 answer
  • Write each ratio as a rate
    9·1 answer
  • Find the fifth degree Taylor polynomial approximation of T _{5}(x) centered at a=0 to the function f(x)=cos(x);f(x)=sin(x);f(x)=
    6·1 answer
  • How do you get on the daily Brainiest users?<br> Please put a serious answer in!
    13·2 answers
  • What are the values of m and 0 in the diagram below?
    15·2 answers
  • I need help real bad please help
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!