.........................

Answer:

[tex]2[/tex]

Step-by-step explanation:

Let [tex][n][/tex] denote the area of some polygon [tex]n[/tex].

The sum of the area of quadrilaterals BCDE and MNDE is equal to [tex][ABC]-([MBE]+[NDC]+AMN])[/tex] (big triangle subtracting the three smaller triangles that aren't part of BCDE or MNDE).

Let the area of triangle ABC be [tex]\alpha[/tex].

Triangle AMN is similar to triangle ABC. Because their side lengths are in ratio 1:2 respectively, the ratio of the area of triangle AMN to triangle ABC is [tex]1:2^2=1:4[/tex].

Therefore, [tex]\displaystyle [AMN]=\frac{1}{4}[ABC]=\frac{1}{4}\alpha[/tex].

Now for triangle NDC, NDC is similar to triangle AMC. Since M is the midpoint of AB, AMC is half the area of ABC. The ratio of the side lengths between triangle NDC and triangle AMC is [tex]1:2[/tex] because the D is the midpoint of MC, so it follows the ratio of their areas must be [tex]1:4[/tex], respectively.

Therefore, [tex]\displaystyle[NDC]=\frac{1}{4}[AMC]=\frac{1}{8}[ABC]=\frac{1}{8}\alpha[/tex].

We can use the same concept for triangle MEB. Triangle MEB is similar to triangle ANB, and the ratio of their sides is also [tex]1:2[/tex], since E is the midpoint of BN. Their areas are in the ratio [tex]1:2^2=1:4[/tex] and we have [tex]\displaystyle [MBE]=\frac{1}{4}[ANB]=\frac{1}{8}\alpha[/tex].

Thus,

[tex]\displaystyle \frac{[ABC]}{[BCDE]+[MNDE]}=\frac{\alpha}{\alpha-\frac{1}{4}\alpha-\frac{1}{8}\alpha-\frac{1}{8}\alpha}=\frac{\alpha}{0.5\alpha}=\frac{1}{\frac{1}{2}}=\boxed{2}[/tex]

Calculate the volume of a cuboid whose dimensions are 3.6cm 8.2cm 11cm

Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions. The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist. how many miles does the second cyclist bike in 45 mins?

According to Newton's Law of Cooling, the temperature T(t) of a hot object, at time t after being placed in an environment with a constant temperature C, is given by T(t)=C+(To-C)e^-kt, where To is the temperature of the object at time t = 0 and k is a constant that depends on the object. If a hot cup of coffee, initially at 190°F, cools to 125°F in 5 minutes when placed in a room with a constant temperature 75°F, how long will it take for the coffee to reach 100°F?​

which of the following represents a function?
x -10 -9 0 5
y 19 17 25 19

can somebody tell me the answer to this?

can anyone help with this, please

U.
15. How many correct answers would be
needed to get a score of 85% on a math
test that has forty questions?
A. 32
B. 34
C. 36
D. None of the above

TASK 2 - Calculate the averages for the data sets below (19 marks).
Sun
protection
factor
0
30
Thickness Count on rate-meter (counts per minute)
of lead
Kk
2
3 Average
(cm)
0
446 444 449
1
231 238
240
113
111
110
3
65
63
65
4
34
31
35
Time for UV bead to change colour
(seconds)
1
2
3 Average
31 28
123 122 119
244 247 246
333 331 329
5
2.
10
15
20
448
456
449
Height from
which marble
dropped (cm)
10
1
Crater width (mm)
2
3
10
12
Heart rate (bpm)
2 3
Number of
steps
Average
1
Average
13
10
70
75
73
20
19
19
21
20
90
96
94
30
33
31
31
40
30
49
44
46
95
98
99
50
64
67
68
40
127
130
125

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Simplify (-2)^4(-2) =
(3st)^2 =
7^0=

The 4:25 bus to the metro airport has a travel time of 1 hour and 45 minutes. The bus is running late today though. What will be the arrival time to the airport?

right ANSWERS only plz i need help on how to do it also not just the answer plz and thank u

A pattern maker uses 526 yards of muslin cloth each month. The cloth comes on bolts, or rolls, that hold 15 yards each.



How many bolts of muslin cloth does the pattern maker use each month?

Use the figure below to find the values of x and y

Three classes at a junior high school raised money to buy new computers

bueno round in the number three hundred ninety eight thousand six hundred twenty two wat is the answer​

Solve the system of equations using the substitution method.

5x−4y=−15
x−3y=−3

(3, 0)

(0, -4)

(-3, 0)

(0, -3)

Prove: The square of an even number is even

A shadow 12 meters long is cast by a water tower that is 16 meters tall. What is the length of the shadow cast by a nearby utility pole that that is 12 meters tall?

A. 6
B. 9
C. 13
D.16

PLEASE HELP ME WILL MARK BRAINLIEST AND PLZ EXPLAIN

answerrrrrrrrrrrr plssssssssssssssssssssssssssssssss

Please help me ASAP please I need help

Kevin has copays of $30 per office visit, $150 emergency room without
hospitalization and $250 for hospitalization. He had to go to a physician's office 5 times
this year and went to the ER once with no hospitalization. His medical bills totaled
$2,826. How much did Kevin save by being insured? Make sure you show your
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The combined amount of ingredients are sugar, brown and white 8 cups, write an addition equation to solve how many cups of brown sugar was added if the chef used 4 cups of sugar

Select the correct answer.
When graphing an inequality, the boundary line needs to be graphed first. Which graph correctly shows the boundary line of the inequality?
y <1/3x+ 1

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