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rosijanka [135]
3 years ago
5

State the postulate or theorem that proves that x is parallel to y

Mathematics
1 answer:
Schach [20]3 years ago
3 0
Converse of the alternate interior angles theorem states the postulate or theorem that proves that x is parallel to y.
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A jogger runs 140 m due west, then changes direction for the second leg of her run. At the end of the run, she is 374 m away fro
USPshnik [31]

Answer:

The length of her second displacement = 247.12 m.

The direction of her second displacement = 31.24° from west.

Step-by-step explanation:

As per the question,

From the figure as drawn below,

Let the starting point be O. After running 140 m due west, she reached at point A.

∴ OA = 140 m

And At the end of the run, she is 374 m away from the starting point at an angle of 20° north of west.

∴ OP = 374 m

We have to find the distance AP = x.

By using the cosine rule in triangle OAP

cos \theta = \frac{OA^{2}+OP^{2}-AP^{2}}{2\times OA\times OP}

After putting the given value, we get

cos 20= \frac{140^{2}+374^{2}-x^{2}}{2\times 140\times 374}

x^{2}=140^{2}+374^{2} - 2\times 140\times 374\times cos 20

  ∴ x = 247.12 m  

Hence,the length of her second displacement = 247.12 m.

Again,

By using the cosine rule in triangle OAP, we get

cos \alpha = \frac{OA^{2}+AP^{2}-OP^{2}}{2\times OA\times AP}

After putting the given value, we get

cos \alpha = \frac{140^{2}+247.12^{2}-374^{2}}{2\times 140\times 247.12}

∴ α = 148.759°

Hence, the  direction of her second displacement = 180° - α = 180° - 148.759 = 31.24° from west.

8 0
3 years ago
Rule: add 1, multiply by 2, first term:2
lesya692 [45]
2+1=3x2=6

Sooo, your answer would be 6



4 0
2 years ago
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kicyunya [14]
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8 0
2 years ago
The integer between - 2.8 and -1.4 is<br> .<br> Check
kolbaska11 [484]

Answer:

Step-by-step explanation:

-2

Integer is a whole number.

7 0
3 years ago
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Find the value of the trigonometric ratio: tan X.
serious [3.7K]

Answer:

The value of the trigonometric-ratio:

  • Tan X = 24 / 7

Step-by-step explanation:

Given the angle X

It is clear that:

  • The opposite of the angle X = 48
  • The adjacent to the angle X = 14

We know that the trigonometric-ratio of Tan X is defined as

Tan X = Opposite / Adjacent

substituting Opposite = 48, and Adjacent = 14

Tan X = 48/14

Tan X = 24 / 7

Therefore, the value of the trigonometric-ratio:

  • Tan X = 24 / 7
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3 years ago
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