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diamong [38]
4 years ago
9

AABC has vertices at A(12, 8), B(4,8), and C(4, 14).

Mathematics
1 answer:
borishaifa [10]4 years ago
3 0

Answer:

<u>Triangle ABC and triangle MNO</u> are congruent. A <u>Rotation</u> is a single rigid transformation that maps the two congruent triangles.

Step-by-step explanation:

ΔABC has vertices at A(12, 8), B(4,8), and C(4, 14).

  • length of AB = √[(12-4)² + (8-8)²] = 8
  • length of AC = √[(12-4)² + (8-14)²] = 10
  • length of CB = √[(4-4)² + (8-14)²] = 6

ΔMNO has vertices at M(4, 16), N(4,8), and O(-2,8).

  • length of MN = √[(4-4)² + (16-8)²] = 8
  • length of MO = √[(4+2)² + (16-8)²] = 10
  • length of NO = √[(4+2)² + (8-8)²] = 6

Therefore:

  • AB ≅ MN
  • AC ≅ MO
  • CB ≅ NO

and ΔABC ≅ ΔMNO by SSS postulate.

In the picture attached, both triangles are shown. It can be seen that counterclockwise rotation of ΔABC around vertex B would map ΔABC into the ΔMNO.

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Usually one will differentiate the function to find the minimum/maximum point, but in this case differentiating yields:
\frac{2\pi}{7(x-5)^{2}}\sin{\frac{2\pi}{7(x-5)}}}
which contains multiple solution if one tries to solve for x when the differentiated form is 0.

I would, though, venture a guess that the minimum value would be (approaching) 5, since the function would be undefined in the vicinity.

If, however, the function is
-1+\cos{\frac{2\pi}{7}(x-5)}}
Then differentiating and equating to 0 yields:
\sin{\frac{2\pi}{7}(x-5)}}=0
which gives:
x=5 or 8.5

We reject x=5 as it is when it ix the maximum and thus,
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3 years ago
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Answer:

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Step-by-step explanation:

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Answer:

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3 years ago
A kitchen measures 3.75 meters by 4.2 meters.
dalvyx [7]

Answer:

a. A_{(kitchen)}=15.75\ m^2

b. A_{(total)}=39.375\ m^2

Step-by-step explanation:

The formula for calculate the area of a rectangle is:

A=lw

Where "l" is the lenght and "w" is the width

a. We know that the kitchen measures 3.75 meters by 4.2 meters; then we can say that:

l=3.75\ m\\\\w=4.2\ m

Therefore, substituting these values into the formula, we get that the area of the kitchen is:

A_{(kitchen)}=(3.75\ m)(4.2\ m)=15.75\ m^2

b. The area of the living room is one and a half times (1.5 times) that of the kitchen, this is:

A_{(living)}=(1.5)(15.75\ m)=23.625\ m^2

Therefore, the total of the living room and the kitchen is:

A_{(total)}=15.75\ m^2+23.625\ m^2=39.375\ m^2

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