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
Yuki888 [10]
2 years ago
5

Decide !!!!!!!!!!!!!!!!!!!!!!!!

Mathematics
1 answer:
Mama L [17]2 years ago
3 0

Answer:

\displaystyle [CQF]=5

Step-by-step explanation:

Note that [n] refers to the area of some polygon n.

Diagonal \overline{AC} forms two triangles, \triangle ABC and \triangle ADC. Both of these triangles have an equal area, and since the area of parallelogram ABCD is given as 210, each triangle must have an area of 105.

Furthermore, \triangle ADC is broken up into two smaller triangles, \triangle ADF and \triangle ACF. We're given that \frac{DF}{FC}=2. Since DF and FC represent bases of \triangle ADF and \triangle ACF respectively and both triangles extend to point A, both triangles must have the same height and hence the ratio of the areas of \triangle ADF and \triangle ACF must be 2:1 (recall A=\frac{1}{2}bh).

Therefore, the area of each of these triangles is:

[ACF]+[ADF]=105,\\[][ACF]+2[ACF]=105,\\3[ACF]=105,\\[][ACF]=35 \implies [ADF]=70

With the same concept, the ratio of the areas of \triangle AQE and \triangle DQE must be 2:1 respectively, from \frac{AE}{ED}=2, and the ratio of the areas of \triangle DQF and \triangle CQF is also 2:1, from \frac{DF}{FC}=2.

Let [DQE]=y and [CQF]=x (refer to the picture attached). We have the following system of equations:

\displaystyle \begin{cases}2y+y+2x=70,\\y+2x+x=35\end{cases}

Combine like terms:

\displaystyle \begin{cases}3y+2x=70,\\y+3x=35\end{cases}

Multiply the second equation by -3, then add both equations:

\displaystyle \begin{cases}3y+2x=70,\\-3y-9x=-105\end{cases}\\\\\rightarrow 3y-3y+2x-9x=70-105,\\-7x=-35,\\x=[CQF]=\frac{-35}{-7}=\boxed{5}

You might be interested in
Why are parabolsas used for
JulsSmile [24]

Answer:

Parabolas are frequently used in physics and engineering for things such as the design of automobile headlight reflectors and the paths of ballistic missiles. Parabolas are frequently encountered as graphs of quadratic functions.

8 0
3 years ago
Read 2 more answers
PLS HELP IM STUCK ON THIS ONE PROBLEM!! PLEASE SHOW STEPS
natka813 [3]

you have to solve for X is somthnking

3 0
2 years ago
Which graph matches the exponential function f(x) = 2(1.5)x?
Rama09 [41]
The third one pls mark me brainliest
6 0
3 years ago
Find 3x-y-3z x=-2 y=1 and z=-2
mrs_skeptik [129]
Just fill in the problem... 3*-2-1-3*-2
8 0
2 years ago
Read 2 more answers
From Midnight to 6 am the temperature rose 8 degrees C. At 6 am the temperature was -21 degrees C. What was the temperature at m
Alika [10]
Hello!

We know that from midnight to 6am the temperature went up 8° and at 6am it was -21°

To find what it was at midnight we have to work backwards

Since it went up we have to subtract 8 from -21

-21 - 8 = -29

The answer is -29°C

Hope this helps!
7 0
2 years ago
Read 2 more answers
Other questions:
  • The probability that an individual is left-handed is 0.12. in a class of 39 students, what is the probability of finding five le
    9·2 answers
  • 20 Points!<br>please Help Thanks!<br><br>In Return brainliest and special thanks
    13·1 answer
  • Triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up. What are
    8·1 answer
  • Give one real life example of each correlation: positive, negative, and no correlation.
    11·2 answers
  • A shopkeeper sells an article of 400, while he purchases it for 402. Find out loss percent of shop keeper​
    8·1 answer
  • Write about which method you prefer to use to multiply two 2-digit numbers-regrouping,partial products,or breaking apart a model
    12·2 answers
  • Solve for x<br>this is really difficult ​
    8·2 answers
  • ANSWER THIS ASAP DONT SEND A FILE AT ALL !! I NEED THE QUICK ONLY ANSWER IF YOU REALY KNOW !!
    5·1 answer
  • What can you conclude from the information in the diagram
    9·2 answers
  • There are as many vanilla cupcakes as chocolate cupcakes in a bakery. If there are 35 cupcakes in the bakery, how many are choco
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!