What is the length of AC? What is the measure of angle A? What is the measure of angle B?

The value of r and ∅ are (a). r = 10 and ∅ = 2, (b). r = 2 and ∅ = 2 and (c). r = 1/2 and ∅ = 2.

In addition to the rectangular form, a complex number can also be represented in polar form. Typically, we write complex numbers as z = x + iy, where i is an imaginary integer. However, in polar form, complex numbers are modeled as a union of argument and modulus.

We have z = 2 (cos2 + isin2)

And given polar form is r(cos∅ + sin∅), where 0≤∅≤2π

To solve (a):

5z = 5 x 2 (cos2 + isin2)

5z = 10 (cos2 + isin2)

Comparing with the standard form,

r = 10 and ∅ = 2

To solve (b):

\(\bar{z}\) = conjugate of 2 (cos2 + isin2)

\(\bar{z}\) =2 (cos2 - isin2)

Comparing with the standard form,

r = 2 and ∅ = 2

To solve (c):

If z is a non-zero complex number and z=x+iy,

the (multiplicative) inverse of z, denoted by z⁻¹ or 1/z, is When z is written in polar form,

so that

z = r\(e^{(i)(\theta)}\)= r (cos θ+i sin θ), where r ≠ 0,

the inverse of z is (1/r) \(e^{(i)(-\theta)}\) = (1/r)(cos θ−i sin θ).

1/z = 1/2 (cos2 - isin2)

Comparing with the standard form,

r = 1/2 and ∅ = 2

Therefore, the values  (a). r = 10 and ∅ = 2, (b). r = 2 and ∅ = 2 and (c). r = 1/2 and ∅ = 2.

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The quotient of - 3.32 / - 2.2 is 8 ÷5.

Given fraction:

-3.32 / -2.2

First step is to re-write the given fraction which is - 3.52 / - 2.2

3.52 / 2.2

Second step is to convert the decimal to fraction

352 ÷ 100 / 22 ÷10

Third step is to reduce the fraction

reducing 352/100

=(2^5 × 11)/(2^2 × 5^2)

= [(2^5 × 11) ÷ 2^2] / [(2^2 × 5^2) ÷ 2^2]

= (2^3 × 11)/5²

= 88/25

Reducing 22/10

Divide the numerator and denominator by the greatest common divisor

= 22 ÷ 2 / 10 ÷ 2

= 11 /5

Now let determine  or find the quotient

88 ÷ 25 × 11 ÷ 5

= 8 ÷ 5

Therefore we can conclude that 8 ÷ 5 is the quotient.

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Answer:

Step-by-step explanation:

regular decagon = all side equal and all angles congruent, so your answer is 144°

Answer:

It should be 90

Step-by-step explanation:

Because 270 divided by 3 is 90

Answer:

Step-by-step explanation:

The domain is the set of x values and the range is the set of y values.

Answer:

The additional information that needed is m∠ABD = m∠CDB ⇒ C

Step-by-step explanation:

In the given figure

Triangles ADB and CBD are congruent by ASA under these conditions

Let us see the given to find the correct answer

∵ ∠ADB and ∠CBD have the same mark

∴ m∠ADB = m∠CBD ⇒ (1) given

∵ Side DB is a common side in the two triangles

∴ DB = BD ⇒ (2) given

∵ ∠ABD and ∠CDB are the angles at the end of BD

∴ m∠ABD must equal m∠CDB ⇒ (3) to prove the congruency using ASA

∴ The additional information that needed is m∠ABD = m∠CDB

Answer:

To prove that two triangles with three congruent, corresponding angles are congruent, you would need to have at least one set of corresponding sides that are also congruent. You could then use ASA or AAS congruence theorems or rigid transformations to prove congruence.

Step-by-step explanation:

Answer:

The experimental probability depends on how many times you're spinning it and theoretical probability is stating what "would" happen if you're only spinning it once. After you get the theoretical probability, you would multiply that percentage by 25 to get the experimental probability percentage.

Step-by-step explanation:

The experimental probability depends on the number of times the experiment is conducted. The result from a theoretical probability is what would happen if the experiment is done once.

Probability determines how likely a stated event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0. Experimental probability is based on the result of an experiment that has been carried out multiples times

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Since the leading degree of the resulting expression is 2, hence the  polynomial simplifies to an expression that is a quadratic

Polynomial expressions are expressions that has a leading degree of 3 and above.

Given the expression

(-5x² - 2x + 4) + (8x² - x - 1) - (x+2)(x-5)

Expand the polynomial

(-5x² - 2x + 4) + (8x² - x - 1) - (x² -3x - 10)

Collect the like terms

-5x² + 8x² - x² - 2x - x + 3x + 4 - 1 + 10

2x²  + 13

Since the leading degree of the resulting expression is 2, hence the  polynomial simplifies to an expression that is a quadratic

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Approximately 99.7% of housing prices are between a low price of $108,000 and a high price of $162,000.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

As we want the interval with a percentage of 99.7%, the bounds within three standard deviations of the mean are given as follows:

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Answer:

36720 different desserts

Step-by-step explanation:

(1020x3)x12=36720

Answer:

50 °

Step-by-step explanation:

that is the procedure above

Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.

To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.

The formula for the geometric mean is given by:

GM = n√x1 x2 . . . xn

Solving for the geometric mean between 1/5 and 60 using the formula:

GM = n√x1 x2 . . . xn

where n = 2, x1 = 9/16, and x2 = 25/3

GM = √(9/16(25/36)

GM = 0.625

Hence, the geometric mean of 9/16 and 25/36 is 0.625

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Answer:

Train B travels faster

Step-by-step explanation:

See attachment for complete question

Since both trains are travelling at constant speed, we can pick any non zero equivalents of distance and time to calculate the rate at which they both travel.

For Train A

\(Distance = 12.5m\)

\(Time = 1s\)

\(Rate = Distance/Time\)

\(Rate = 12.5m/1s\)

\(Rate = 12.5m/s\)

For Train B

\(Distance = 100m\)

\(Time = 4s\)

\(Rate = Distance/Time\)

\(Rate = 100m/4s\)

\(Rate = 25m/s\)

By comparison:

\(25m/s > 12.5m/s\)

Hence,

Train B travels faster

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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The elevation difference between the valley and sea level is 94 feet.

Given that a valley is 94 feet below sea level.

We need to find that what is the absolute value of the elevation difference between the valley and the sea level,

The absolute value of a number represents its distance from zero on the number line, regardless of whether the number is positive or negative. In this case, the valley is 94 feet below sea level, so its elevation can be represented as -94 feet.

To find the absolute value of -94, you disregard the negative sign and take the magnitude of the number.

Therefore, the absolute value of -94 is 94.

Thus, the elevation difference between the valley and sea level is 94 feet.

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Answer:

28$

Step-by-step explanation:

You subtract 2 from 8 which is 6, you then multiply 6 times 3.50. Then add 7, which you get 28$

Answer:

$28.000000000000000000000000000000000

Step-by-step explanation:

Lol they're called, wait, what are they called again? ;-; no no I really forgot this time.

Onto the Problamo

We purchase 8 books in total. The first two books cost $7. So that 2/8 books purchased. now we need to purchase 6 more. Because It says: $3.50 per book, we do 3.50*6 or 3.50+3.50+3.50+3.50+3.50+3.50. so 7$ from the 2 books from the first statement plus $21 from the leftover 6 books.

7+21=28$

so I owe the school book fair $28 in the end

Answer:

• no

• no

• no

• yes

Step-by-step explanation:

Let's start by solving the inequality.

-8 +5w >32

5w> 32 +8

5w> 40

Divide both sides by 5:

w> 8

This means that the value of w should be greater than 8.

Since w is not ≥8, the value of w does not include 8. -6 and -5 are smaller than 8 and are thus not the value of w either.

9, being greater than 8, is a solution to the inequality.

Answer:

\(y-2=3(x-4)\)

Step-by-step explanation:

We are given a line contains the point (4, 2).

We also know that the line is parallel to y= 3x - 7.

We want to write the equation of this line.

Parallel lines have the same slopes.

First, let's find the slope of y = 3x - 7.

3 is in the place of where m (the slope) is, so that means it is the slope of that line.

It is also the slope of the line whose equation we want to write.

The equation of the line can be written in three ways:

All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.

Substitute 3 as m in \(y-y_1=m(x-x_1)\).

\(y-y_1=3(x-x_1)\)

Now, substitute 4 as \(x_1\) and 2 as \(y_1\).

\(y-2=3(x-4)\)

Topic: parallel and perpendicular lines

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Answer:

A.

Step-by-step explanation:

The vertical line test is a way of finding out if a relation is a function.

Graph the relation.

Then imagine a vertical line moving from left to right over the graph of the relation.

If the vertical line intersects at most one point of the graph in any position you place the vertical line, then the relation is a function.

This function passes the vertical test since it never intersects more than one point on the vertical line at a time.

Answer: A.

The surface area of a cylinder with circular bases of radius r and height h is equal to the sum of the areas of the two circular faces and the area of the rectangular lateral surface:

A = 2πr² + 2πrh

If you know the height h, then you can solve the quadratic equation for r.

Step-by-step explanation:

1. 84 cm^2

2. 616 cm^2

3. 2496 cm^2

Given:

A triangle

l (length) = 12 cm

w (width) is 2 cm less than 3/4 of its length

Find: A (area) - ?

First, let's find the width of the rectangle according to the given information:

\(w = (\frac{3}{4} \times 12) - 2 = 9 - 2 = 7 \: cm\)

Now, we can find the area:

\(a = w \times l\)

.

2. Given:

A circular clock

C (circumference) = 88 cm

π = 22/7

Find: A (area) - ?

\(c = 2\pi \times r\)

First, let's find the radius of the clock:

\(2 \times \frac{22}{7} \times r = 88\)

\( \frac{44}{7} \times r = 88\)

Multiply both sides of the equation by 7 to eliminate the fraction:

\(44r =616\)

Divide both parts of the equation by 44 to make r the subject:

\(r = 14\)

Now, we can find the area:

\(a = \pi {r}^{2} \)

\(a = \frac{22}{7} \times {14}^{2} = 616 \: {cm}^{2} \)

.

3. Given:

A rectangle

l (length) = 52 cm

P = 200 cm

Find: A (area) - ?

First, let's find the width of the rectangle (the perimeter is equal to the sum of all side lengths):

P = 2l + 2w

2w = P - 2l

2w = 200 - 2 × 52

2w = 96 / : 2

w = 48 cm

Now, we can find the area:

A = w × l

A = 48 × 52 = 2496 cm^2

Answer:

Its D

Step-by-step explanation:

Answer:

14. 5

15. 12

16. 9

17. 13

18. 14

19. 20

20. 19

21. 15

22. 600

23. -1

24. 4

25. -18

26. 25

hope this helped

Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

Answer:

The percentage of 18 people out of 50 is 36 %

Step-by-step explanation:

The percentage refers to the per hundred or hundredths and is ended with the symbol %.  By dividing two amounts, ratios and percentages are both used to compare the two amounts.

so,

Therefore the percentage of 18 people out of 50 people is 36 %.

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Answer: The insurance company will pay for $3,000 in damage to the light pole

Step-by-step explanation:

Step 1: Jimmy's deductible is $500, so he will have to pay the first $500 of the repair costs.

Step 2: Since the damage to the light pole is less than $25,000, Jimmy's property damage insurance policy will cover the remaining repair costs for the light pole.

Step 3: The insurance company will pay for the remaining $3,000 ($3,500 - $500) to repair the light pole.

Answer:

20

Step-by-step explanation:

area = length * breadth

320cm² = length * 16cm

divide both sides by 16cm to isolate length

20cm = length

The area between z = -1.71 and z = 0.08 is 0.4883, in median .

What is median ?

The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the centre of a sequence to determine its value.

=> P(-1.71 < Z < 0.08 ) = P(Z < 0.08 ) - P(Z < -1.71)

= 0.5319 - [1 - P(Z < 1.71)]

= 0.5319- [1 - 0.9564]

= 0.4883

Hence, the area between z = -1.71 and z = 0.08 is 0.4883.

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The Dividend per Shareholder in 2017 is $20.

As, Dividend per Shareholder = Profit / Number of Shareholders

Since the number of shareholders is assumed to have remained unchanged during the period 2017-2020, we can calculate the dividend per shareholder in 2017 using the profit value for that year.

Based on the given table, the profit for 2017 is $7,000.

Dividend per Shareholder in 2017

7000/x = 15500 / 44.29

7000/x = 349.966

x = 7000/349.966

x= 20.01

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