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lord [1]
3 years ago
15

Polygons ABCD and EFGH are similar. Find the length of CD.

Mathematics
1 answer:
CaHeK987 [17]3 years ago
3 0

Answer:

there is no image?

Step-by-step explanation:

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What is the area of the triangle shown below?
Effectus [21]

Answer:

42 sq. Units

Step-by-step explanation:

I took the test

7 0
3 years ago
Write the rule of the nth term of each sequence 7,4,1,-2
Zarrin [17]

Answer:

a_{n} = 10 - 3n

Step-by-step explanation:

the terms 7, 4, 1, - 2 form an arithmetic sequence with n th term

a_{n} = a_{1} + (n - 1)d

where d is the common difference and a_{1} the first term

here d = - 2 - 1 = 1 - 4 = 4 - 7 = - 3 and a_{1} = 7, hence

a_{n} = 7 - 3(n - 1) = 7 - 3n + 3 = 10 - 3n


8 0
3 years ago
Folding a rectangle along one diagonal results in a shape whose area is 2/3 that of the original
Charra [1.4K]

Answer:

  • 60°

Step-by-step explanation:

<em>Refer to attached picture</em>

Given rectangle ABCD. Its folded shape is given as well.

It has sides a and b and diagonal d, with the angle BCD marked as α.

We need to find the value of angle AOC or BOD.

This is going to be 2α, which is easy to find out. BOD is cut by the angle bisector, each of the angles is α.

Let the area of the rectangle is A, then the folded shape has area 2/3A.

<u>The area of rectangle ABCD:</u>

  • A = ab

<u>From the triangle CBD we get:</u>

  • a/d = sin α ⇒ a = d sin α
  • b/d = cos α ⇒ b = d cos α

<u>Then</u>

  • A = d sin α * d cos α = d²sin α cos α

Now, lets find the area of the folded shape.

It is the area of the rectangle minus the area of the triangle CMB as this part  is lost as part of overlap.

<u>Area of the triangle:</u>

  • A = 1/2dh

<u>Since h/(d/2) = tan α ⇒ h = 1/2d tan α, the area is:</u>

  • A = 1/2d*1/2d tan α = 1/4d² tan α

<u>We have the difference of the areas which is 1/3 of the area of the rectangle:</u>

  • 1/3(d²sin α cos α) = 1/4d² tan α
  • sin α cos α = 3/4 tan α
  • sin α cos α = 3/4 sin α / cos α
  • cos² α = 3/4
  • cos α = √(3/4)
  • cos α = √3/2
  • α = arccos (√3/2)
  • α = 30°

<u>The acute angle formed by the two diagonals of the rectangle is:</u>

  • 2α = 2*30° = 60°

3 0
2 years ago
collen family plans to paint the window of their house. her father will paint twice as many window as her mother, and collen and
saw5 [17]

Answer:

21 windows

Step-by-step explanation:

colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?

Answer: Let the number of window Colleen father would paint be x while that of her mother be y. Since her father will paint twice as many window as her mother, therefore the number of windows painted by the father x = 2y

Let the number of windows each painted by Colleen and her 2 brothers be z since they would paint the same number of windows. The total number of windows to be painted = 2y + y + z + z + z = 3y + 3z = 3(y + z).

Then number of windows needed to be painted by Colleen and her mother is given as z + y. Since Colleen painted 7 windows as her share and her mother share i.e. y + z = 7

Therefore the total number of windows = 3(y + z) = 3(7) = 21 windows

5 0
3 years ago
Factor completely: y6 - 1.
RUDIKE [14]

Answer:

(y times 6) -1

Step-by-step explanation:

I don't know what to say it is already simplified

7 0
3 years ago
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