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Alex73 [517]
3 years ago
7

Can someone please help me?

Mathematics
1 answer:
Fynjy0 [20]3 years ago
7 0

Answer:

x ≈ 50.8°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = \frac{opposite}{hypotenuse} = \frac{JK}{IK} = \frac{6.2}{8} , then

x = sin^{-1} (\frac{6.2}{8} ) ≈ 50.8° ( to the nearest tenth )

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In triangle $ABC$, let angle bisectors $BD$ and $CE$ intersect at $I$. The line through $I$ parallel to $BC$ intersects $AB$ and
Umnica [9.8K]

Answer:

41

Step-by-step explanation:

If you work through a series of obscure calculations involving area and the radius of the incircle, they boil down to a simple fact:

... For MN║BC, perimeter ΔAMN = perimeter ΔABC - BC = AB+AC

.. = 17+24 = 41

_____

Wow! Thank you for an interesting question with a not-so-obvious answer.

_____

<em>A little more detail</em>

The point I that you have defined is the incenter—the center of an inscribed circle in the triangle. Its radius is the distance from I to any side, such as BC, for example.

If we use "Δ" to represent the area of the triangle and "s" to represent the semi-perimeter, (AB+BC+AC)/2, then the incircle has radius Δ/s. The area Δ can be computed from Heron's formula by ...

... Δ = √(s(s-a)(s-b)(s-c)) . . . . where a, b, c are the side lengths

For this triangle, the area is Δ = √38480 ≈ 196.1632 units². That turns out to be irrelevant.

The altitude to BC will be 2Δ/(BC), so the altitude of ΔAMN = (2Δ/(BC) -Δ/s). Dividing this by the altitude to BC gives the ratio of the perimeter of ΔAMN to the perimeter of ΔABC, which is 2s.

Putting these ratios and perimeters together, we get ...

... perimeter ΔAMN = (2Δ/(BC) -Δ/s)/(2Δ/(BC)) × 2s

... = (2/(BC) -1/s) × BC × s = 2s -BC

... perimeter ΔAMN = AB +AC

8 0
3 years ago
In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older
earnstyle [38]

Answer:

Step-by-step explanation:

In the past, mean of age of employees

i.e. \mu = 40

Recently sample was taken

n = sample size = 60

Mean of sample = 45

Std dev of sample s = 16

H_0: \bar x = 40\\H_a: \bar x >40

(Right tailed test)

Since only population std deviation is known we can use t test only

Std error = \frac{s}{\sqrt{n} } \\=\frac{16}{\sqrt{61} } \\=2.049

Mean difference = 45-40 =5

Test statistic t=\frac{5}{2.049} \\=2.441

df = 60

p value =0.008739

Since p < 0.05 we reject null hypothesis

The mean age has increased.

5 0
3 years ago
Farmer George is painting 3 chicken coops. He started painting this morning. Now he only has 3/4 of a chicken coop left to paint
mariarad [96]
If Farmer George starts painting in the morning, and only has 3/4 of a chicken coop left to paint:
3-3/4=
12/4-3/4=9/4 painting in the morning
To put it in a mixed number,  2 1/4 (aka 2.25)
3 0
3 years ago
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The product of the first 3 positive whole numbers
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Answer:

If you mean by 1*2*3=6

Step-by-step explanation:

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3 years ago
1. Consider the figure below.
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Answer:

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  1. m<A= 16
  2. m<M=90
  3. m<N= 52
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2 years ago
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