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EastWind [94]
3 years ago
7

ABCD is a parallelogram such that AB is parallel to DC and DA parallel to CB. The length of side AB is 20 cm. E is a point betwe

en A and B such that the length of AE is 3 cm. F is a point between points D and C. Find the length of DF such that the segment EF divide the parallelogram in two regions with equal areas

Mathematics
2 answers:
Firdavs [7]3 years ago
5 0
The length of DF will be 17 cm.
seraphim [82]3 years ago
5 0

Answer:

\therefore DF=17cm

Step-by-step explanation:

The easiest way to solve this, it's by graphing.

By given, we know that

AB=20cm, and AE=3cm.

By sum of segments, we have

AE+EB=AB\\3cm+EB=20cm\\EB=20cm-3cm\\EB=17cm

Additionally, we know that segment EF divides the parallelogram in two equal areas, that is, in two equal trapezoids, that means their bases are congruent.

So,

EB=DF

\therefore DF=17cm

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A shelf contains n separate compartments. There are r indistinguishable marbles.
densk [106]

Answer:\frac{n!}{r!(n-r)!}

ways

Step-by-step explanation:

Given that a shelf contains n separate compartments. There are r indistinguishable marbles

The marbles are identical so they can be placed in any order.

Let us consider the places available for placing these r marbles

No of compartments available =n

Marbles to be placed = r

Since marbles are identical and order does not matter

number of ways the r marbles can be placed in the n compartments

= nCr

=\frac{n!}{r!(n-r)!}

8 0
4 years ago
The graph of a function f(x) is shown below:
Ber [7]
I wold say it is b <span>integers from −3 < y ≤ 3 </span>

6 0
3 years ago
Find the value of x in the isosceles triangle shown below.<br> T<br> r<br> 8<br> 12
Anna11 [10]
The correct answer is 8
5 0
3 years ago
I REALLY NEED HELP PLEASE!!
rjkz [21]

Answer:

4588 [in²].

Step-by-step explanation:

1) the given octagon can be imagined as 8 triangles (see the attachment). In order to calculate the required area of the octagon, it is enough to calculate the area of one triangle then increase it 8 times:

2) area of one triangle is:

37*31/2 [in²].

3) the required area of the octagon is:

31*37*8/2=31*37*4=4588 [in²].

8 0
3 years ago
A stainless steel patio heater is a square pyramid. The length of one side of the base is 23.8 in. The slant height of the pyram
vovangra [49]
The height of the heater is about 89.3 in.

You can solve this problem with the Pythagorean Theorem. The base is a square. So half way across the middle will the right under the tip of the pyramid. We can use the measurement with the slant height to write and solve the equation below.

23.8^2 + x^2 = 90.1^2
x will be about 89.3.
4 0
3 years ago
Read 2 more answers
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