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3 years ago

Which diagram shows possible angle measures of a triangle?

Mathematics

2 answers:

gavmur [86]3 years ago

7 0

Hello!

the angles in a triangle add to 180°
------------------------------------------------------------------------------------------------------
Triangle 1
115 + 35 + 25 = 175

Since it does not equal 180 it is not triangle 1
------------------------------------------------------------------------------------------------------
Triangle 2
115 + 32 + 33 = 180

Since it does equal 180 it is triangle 2
------------------------------------------------------------------------------------------------------
The answer is triangle 2

Hope this helps!

Deffense [45]3 years ago

4 0

The second triangle is the answer

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Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

BartSMP [9]

By using De Moivre's theorem:

If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴ $\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )$
k= 0, 1 , 2, ..... , (n-1)

For The given complex number ⇒ z = 81(cos(3π/8) + i sin(3π/8))


Part (A) find the modulus for all of the fourth roots

∴ The modulus of the given complex number = l z l = 81

∴ The modulus of the fourth root = $\sqrt[4]{z} = \sqrt[4]{81} = 3$

Part (b) find the angle for each of the four roots

The angle of the given complex number = $\frac{3 \pi}{8}$
There is four roots and the angle between each root = $\frac{2 \pi}{4} = \frac{\pi}{2}$
The angle of the first root = $\frac{ \frac{3 \pi}{8} }{4} = \frac{3 \pi}{32}$
The angle of the second root = $\frac{3\pi}{32} + \frac{\pi}{2} = \frac{19\pi}{32}$
The angle of the third root = $\frac{19\pi}{32} + \frac{\pi}{2} = \frac{35\pi}{32}$
The angle of the fourth root = $\frac{35\pi}{32} + \frac{\pi}{2} = \frac{51\pi}{32}$

Part (C): find all of the fourth roots of this

The first root = $z_{1} = 3 ( cos \ \frac{3\pi}{32} + i \ sin \ \frac{3\pi}{32})$
The second root = $z_{2} = 3 ( cos \ \frac{19\pi}{32} + i \ sin \ \frac{19\pi}{32})$

The third root = $z_{3} = 3 ( cos \ \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})$
The fourth root = $z_{4} = 3 ( cos \ \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})$

7 0

3 years ago

8. A company makes electronic components for TV's. 95% pass final inspection (and 5% fail and need to be fixed). 120 components

Taya2010 [7]

Using the binomial distribution, it is found that the variance of the number that pass inspection in one day is 5.7.

For each component, there are only two possible outcomes, either it passes inspection, or it does not. The probability of a component passing inspections is independent of any other component, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability, and has variance given by:

$V(X) = np(1 - p)$

In this problem:

95% pass final inspection, hence $p = 0.95$

120 components are inspected in one day, hence $n = 120$ .

The variance is given by:

$V(X) = np(1 - p) = 120(0.95)(0.05) = 5.7$

The variance of the number that pass inspection in one day is 5.7.

To learn more about the binomial distribution, you can take a look at brainly.com/question/24863377

3 0

2 years ago

Which choice correctly shows rounding to the hundredths place?

Romashka-Z-Leto [24]

Choice A is false because they are rounding to the nearest tenth (one decimal place) and not nearest hundredth (two decimal places)

Choice B is false as well because 3.825 should round to 3.83. The 5 at the end tells you to round up.

Choice C is false too. The value 3.824 should round to 3.82. Not sure how they got 3.81, so it seems like a deliberate trick question or silly answer.

Choice D is true. The three decimal values are rounded properly to the correct number of decimal places.

Therefore choice D is the answer

4 0

3 years ago

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How can you explain the answer 4 divided by 5

Sergio [31]

Answer:

4 divided by 5 is equal to 0.8. This decimal can also be written as a fraction. 0.8 = eight tenths or 8/10 (4/5 in its reduced form).

Step-by-step explanation:

3 0

3 years ago

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You and three friends own a paint shop. The shop's profit was $536 in the first month. You always divide the profits equally. In