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2 years ago

Find all the unknown angle measures in the diagram. Justify your answer for each angle measure.

Mathematics

1 answer:

Jet001 [13]2 years ago

4 0

Answer:

∠1 is 90° because it is a right angle

To find angle 2, we must add the given angles and x then make the equation equal to 180°, which we next solve for x;

x + 90 + 30 = 180

x + 120 = 180

-120 -120

x = 60, ∠2 = 60°

Angle 5 is vertical to angle 1 which equals 90 degrees, and vertical angles are congruent meaning that they measure the same degrees so therefore ∠5 = 90°

Angles 4 and 40° are vertical to angle 2 which measures 60 degrees;

40 + x(where x equals angle 4) = 60

-40 -40

x = 20, ∠4 = 20°

Specified earlier, angles 40° and 4 are equal to 60°, this means that angle three added to angles 40° and 4 will be equal to 90 degrees since angle 1 is 90 degrees and the other three angles will have to equal 90 degrees because they are supplementary.

So we set up the equation;

40 + 20(angle four) + x = 90

60 + x = 90

-60 -60

x = 30, ∠3 = 30°

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Find the argument of the complex number -3–9 in the interval 0°< ϴ < 360°,

Bingel [31]

Answer:

$\theta=251.6^\circ$

Step-by-step explanation:

Complex Numbers

They are expressed as the sum of a real part and an imaginary part:

$Z = a+b\mathbf{ i}$

Complex numbers can also be expressed in polar form:

$Z = r(\cos\theta+\sin\theta \mathbf{ i}) = r. cis(\theta)$

Where r is the modulus of the complex number and θ is the argument.

The argument can be calculated by:

$\displaystyle \tan\theta=\frac{b}{a}$

The angle θ must be calculated in the appropriate quadrant depending on the signs of the real and imaginary parts.

The complex number is given as:

$Z = -3 -9\mathbf{ i}$

Here: a=-3, b=-9

Since both components are negative, the argument lies in the third quadrant (180° < θ < 270°).

$\displaystyle \tan\theta=\frac{-9}{-3}$

$\displaystyle \tan\theta=3$

$\theta=\arctan(3)$

The calculator gives the answer 71.6°, we need to adjust the angle to the third quadrant by adding 180°, thus

$\mathbf{\theta=251.6^\circ}$

6 0

3 years ago

If the volume of sand is increasing at a constant rate, is the height increasing at a constant rate? Explain.

AysviL [449]

It does not necessarily mean that the height will rise although I it could rise.this is because volume is what is inside your shape. It could spread out more and have more volume. If you think I'm smart let me tell you I'm only in 4th grade not bragging

4 0

3 years ago

How do I solve this ?

Anettt [7]

Answer:

Base is 5/6

Step-by-step explanation:

We calculate the area of a triangle by multiplying height to the base and that divided by two

Let's call the base X

5/36 cm^2 = 1/3 × X ÷ 2 multiply both sides of the equation by 2

2 × 5/36 = 1/3 × X ÷ 2 × 2

5/18 = X/3 now divide both sides by 3

5/18 ÷ 3 = X/3 ÷ 3

X = 5/6

3 0

3 years ago

Rewrite this exponential equation as a logarithmic equation. 4e^x=16

lidiya [134]

Answer:

The rewritten equation is: $x = \ln{4}$

Step-by-step explanation:

The inverse operation of the exponential is the natural logarithm, $\ln$ , and the following property is used to solve this question:

$\ln{e^x} = x$

In this question, we have that:

$4e^x = 16$

$e^x = \frac{16}{4}$

$e^x = 4$

Applying the natural logarithm to both sides:

$\ln{e^x} = \ln{4}$

$x = \ln{4}$

The rewritten equation is: $x = \ln{4}$

8 0

3 years ago

Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one anothe

scZoUnD [109]

Answer:

a) P(male=blue or female=blue) = 0.71

b) P(female=blue | male=blue) = 0.68

c) P(female=blue | male=brown) = 0.35

d) P(female=blue | male=green) = 0.31

e) We can conclude that the eye colors of male respondents and their partners are not independent.

Step-by-step explanation:

We are given following information about eye colors of 204 Scandinavian men and their female partners.

Blue Brown Green Total

Blue 78 23 13 114

Brown 19 23 12 54

Green 11 9 16 36

Total 108 55 41 204

a) What is the probability that a randomly chosen male respondent or his partner has blue eyes?

Using the addition rule of probability,

∵ P(A or B) = P(A) + P(B) - P(A and B)

For the given case,

P(male=blue or female=blue) = P(male=blue) + P(female=blue) - P(male=blue and female=blue)

P(male=blue or female=blue) = 114/204 + 108/204 − 78/204

P(male=blue or female=blue) = 0.71

b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=blue) = 78/114

P(female=blue | male=blue) = 0.68

c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=brown) = 19/54

P(female=blue | male=brown) = 0.35

d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=green) = 11/36

P(female=blue | male=green) = 0.31

e) Does it appear that the eye colors of male respondents and their partners are independent? Explain

If the following relation holds true then we can conclude that the eye colors of male respondents and their partners are independent.

∵ P(B | A) = P(B)

P(female=blue | male=brown) = P(female=blue)

or alternatively, you can also test

P(female=blue | male=green) = P(female=blue)

P(female=blue | male=blue) = P(female=blue)

But

P(female=blue | male=brown) ≠ P(female=blue)

19/54 ≠ 108/204

0.35 ≠ 0.53

Therefore, we can conclude that the eye colors of male respondents and their partners are not independent.

7 0

3 years ago