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
djverab [1.8K]
3 years ago
14

In △ABC, CM is the median to AB and side BC is 12 cm long. There is a point P∈ CM and a line AP intersecting BC at point Q. Find

the lengths of segments CQ and BQ , if P is the midpoint of CM

Mathematics
1 answer:
Licemer1 [7]3 years ago
4 0

Answer:

4 cm

Step-by-step explanation:

Draw the line MD that is parallel to AQ. Consider triangles BMD and BAQ. These triangles are similar, because they have three pairs of congruent angles (angles BMD and BAQ are corresponding, angles BDM and BQA are corresponding and angle B is common). The coefficient of similarity is \dfrac{1}{2}, because point M is midpoint of AB. Then

\dfrac{BD}{BQ}=\dfrac{1}{2}\Rightarrow BQ=2BD.

Since BQ=BD+DQ, then DQ=2BD-BD=BD.

Consider triangles CPQ and CMD. These triangles are similar, because they have three pairs of congruent angles (angles CPQ and CMD are corresponding, angles CQP and CDM are corresponding and angle C is common). The coefficient of similarity is \dfrac{1}{2}, because point P is midpoint of CM. Then

\dfrac{CQ}{CD}=\dfrac{1}{2}\Rightarrow CD=2CQ.

Since CD=CQ+DQ, then DQ=2CQ-CQ=CQ.

Hence you get CQ=DQ=BD=\dfrac{BC}{3}=\dfrac{12}{3}=4\ cm.

You might be interested in
John is hiking in the San Juan National Forest. Every 4 hours his elevation increases between 140 and 210 feet. 36 hours ago, Jo
Ksju [112]

Answer D. It is the closets answer to my calculations so im sorry if im wrong

8 0
2 years ago
How many terms are in the arithmetic sequence 9, 2, −5, . . . , −187?
Fantom [35]
9, 2, -5... so is going down by 7 each time, meaning the "common difference" is -7.

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=9\\
d=-7\\
a_n=-187
\end{cases}
\\\\\\
-187=9+(n-1)(-7)\implies -187=9-7n+7
\\\\\\
7n=9+7+187\implies 7n=203\implies n=\cfrac{203}{7}\implies \boxed{n=29}
4 0
3 years ago
Please help I am having a really bad day and crying all the time.
polet [3.4K]

Answer:

7 dollars

Step-by-step explanation:

I hope this helps and i hope you have better days and stop crying because life is way to short for all of that and i dont know you but you dont deserve to cry all the time you should be happy if you want to talk about anything im here!

5 0
3 years ago
If the side of a square is 3 feet, the unit of it's area will be ______
sveta [45]

Answer:

9

Step-by-step explanation:

Given,

Side of square = 3 feet.

To find : Area of square = ?

Formula : -

Area of square = ( side )²

Area of square

= 3²

= 3 x 3

= 9 feet²

Therefore,

The unit of it's area will be 9 feet².

6 0
2 years ago
567898765456787654567876567876+9999999999999999999999999999999
KonstantinChe [14]

Answer:

1.05678988E31

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Other questions:
  • This question is based on the following circle graph.
    9·2 answers
  • Jon invests $2300 at 7.5% annual interest, compounded continuously. How long will it take this money to double in value?
    9·1 answer
  • Find the general solution of the given differential equation. y''' − 2y'' − 4y' + 8y = 0
    9·1 answer
  • How do i do this:<br>6 ( 5 )<br> -4
    9·2 answers
  • IN the 30-60-90 triangle below, side s has a length of ? and side q has a length of ?
    6·1 answer
  • 3) Malik deposited $1.050 in a savings account, and it earned $241.50 in
    11·1 answer
  • Simplify: power with a power 5^8*7^8
    15·1 answer
  • Deloria says she can find the relative frequency of nuts based on another relative frequency. What might she be doing?
    5·1 answer
  • Trucker's Heaven Diner uses hundreds of plates, glasses, and cups each day. The dishwashers start a new load of dishes every 1 1
    13·1 answer
  • Find the dimensions of a cube with a
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!