2x + 3y =5
4x - y = 3

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer: (5,27.734994) and (5,18.734994)

Step-by-step explanation:

there are two answers to this, first 5--2=7 this to find out one of the sides of the Pythagorean Theorem. We already know that it is 20 units away so lets review the Pythagorean Theorem a^2+b^2=c^2 so 20^2=400 and 7^2=49

400-49=351 and the root of 351 is about 18.734994 we're not quite done yet, we have to add or subtract the coordinates 9+18.734994=27.734994 9-18.734994=-9.734994 so the answer is (5,27.734994) and (5,18.734994)

Answer:

There are no numiners below.

Step-by-step explanation:

:)

Answer:

Joe

Step-by-step explanation:

The statement refers to the way that symbols are represented in sequences, a common practice in formal language theory, by employing a notation that makes symbols a part of the sequence.

In formal language theory, a language is often defined as a set of strings over an alphabet. By representing any alphabetic sequence of symbols as a single string using the notation outlined in the statement, we are able to recognise the language that comprises that sequence as a collection of strings. A subset of the language having all possible strings over the alphabet (a, b, and c) is the set of strings abc, which may be used to represent the language including the sequence (a, b, and c). So, this notation offers an easy approach to discuss languages and the sequences that make up such languages.

Hence, the statement relates the symbols and sequences.

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Since there is only one value of x, hence the equation given has only one solution

Equations are expressions separated using mathematical operations. Given the equation below;

2x+5+2x+3x = x

Collect the like terms

2x+2x+3x -x = -2

7x -x = -2

Simplify

6x = -2

x = -2/6

x = -1/3

Since there is only one value of x, hence the equation given has only one solution

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899,452 is greater than 756,451

899,452 > 756,451

Given,

899,451

756,451

We need to compare these numbers.

Consider 967543

3 - ones

4 - tens

5 - hundreds

7 - thousands

6 - ten thousands

9 - hundred thousands

Find the highest place value in 899,452.

-  8 hundred thousands

We can read this as eight hundred ninety-nine thousand four hundred fifty-two.

Find the highest place value in 756,451.

- 7 hundred thousands

Seven hundred fifty-six thousand four hundred fifty one

Thus,

899,452 is greater than 756,451

899,452 > 756,451

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The solution is, the selection can be made in 593775ways

Combination has to do with selection of r objects from a total number of n objects and this can be done in nCr ways. Generally,

nCr = n!/(n-r)!r!

Since the math teacher has to select 6 students from a class of 30, this can be done in 30C6 number of ways to have;

30C6 = 30!/(30-6)!6!

30C6 = 30!/24!6!

30C6 = 30×29×28×27×26×25×24!/24!×6×5×4×3×2

30C6 = 30×29×28×27×26×25/6×5×4×3×2

30C6 = 427,518,000/720

30C6 = 593775ways

This means, the selection can be made in 593775ways.

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The equation for the graph above is y = 5sin(2x/3).

In Mathematics and Geometry, a sine wave is sometimes referred to as a sinusoidal wave, or sinusoid and it can be defined as a fundamental waveform that is typically used for the representation of periodic oscillations, in which the amplitude of displacement at each interval is directly proportional to the sine of the displacement's phase angle.

Mathematically, a sine wave can be represented or modelled by this mathematical equation:

y = asin(bx)

Where:

Based on the graph of this sine wave, we have:

Amplitude, a = 5.

Periodicity, b = 2π/period = 2π/(3π) = 2/3

Therefore, the required sine wave function is given by;

y = asin(bx)

y = 5sin(2x/3)

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Given expression q=p+7

Expression can be defined as contains one or more variables and constants with one or more arithmetic operators.

Simply put the p values in the expression. solve it and get the q values.

q=p+7 in the place of p submit p=0

q=0+7

q=7

q=p+7  in the place of p submit p=2

q=2+7

q=9

q=p+7  in the place of p submit p=3

q=3+7

q=10

Therefore, The values of q are 7,9,10

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The missing numbers are:

7,9 and 10 when 0, 2, and 3 respectively.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

An equation,

q = p + 7.

Substituting the values of p:

When p = 0,

q = 0 + 7

q = 7.

When p = 2,

then q = 9.

And when p = 3,

q = 10

Therefore, all the required values are given above.

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The correct answer is Part 1: The 99% confidence interval for the population proportion is approximately (0.4716, 0.5416).Part 2: With 99% confidence, the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

Part 1:

To construct a 99% confidence interval for the population proportion, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

where the margin of error is determined by the level of confidence and the standard error.

First, let's calculate the sample proportion:

Sample Proportion = (Number of adults who say they have started paying bills online) / (Total number of adults surveyed)

Sample Proportion = 1436 / 2837 ≈ 0.5066 (rounded to four decimal places)

Next, we need to calculate the standard statistics error, which is the measure of the variability in the sample proportion:

Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)

Standard Error = sqrt((0.5066 * (1 - 0.5066)) / 2837) ≈ 0.0136 (rounded to four decimal places)

Now, we can calculate the margin of error:

Margin of Error = Critical Value * Standard Error

The critical value is based on the desired confidence level. For a 99% confidence level, the critical value is approximately 2.576 (obtained from a standard normal distribution table).

Margin of Error = 2.576 * 0.0136 ≈ 0.0350 (rounded to four decimal places)

Finally, we can construct the confidence interval:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.5066 ± 0.0350

Confidence Interval ≈ (0.4716, 0.5416) (rounded to four decimal places)

Part 2:

The correct interpretation is:

C. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

This means that we are 99% confident that the true proportion of adults who have started paying bills online falls within the range of 0.4716 to 0.5416. The survey results suggest that approximately 47.16% to 54.16% of the population of adults have started paying bills online in the last year.

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Answer:

6 3/8 inches

Step-by-step explanation:

let 'x' = distance in 1 hr, 25 minutes (which is 85 minutes)

(3/8 ÷ 5) = x ÷ 85

cross-multiply:

5x = 255/8

40x = 255

x = 6 3/8

Answer:

a. (2, 3).

Step-by-step explanation:

-2x+y=-1

-8x+2y= -10        Multiply the first equation by -2:-

4x - 2y = 2          Adding:

-4x + 0 = -8

x = -8/-4

x = 2

So

-8(2) + 2y = -10

2y = -10 + 16 = 6

y = 3.

The probability that that arrow will land on the part labelled C after the first spin would be = 1/5.

To calculate the probability of the chosen event, the formula for probability should be used which is given as follows:

Probability = possible outcome/ sample space

Where possible outcome = 2

sample space = A,B,B,B,C,C,D,D,D,E = 10

Therefore the probability that the arrow will land on the part labelled C after the first spin = 2/10 = 1/5.

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The presence of a correlation between statistical variables is an indication

of the existence of a relationship variables, it however, does not imply

direct causation.

Part one:

The similarities of the graphs are;

The differences are;

Second part;

The HOA president's petition is in line with the social media post based on the graph.

The graph shows a strong correlation between murder rates and ice cream sales, however, selling ice cream, and murder are unrelated events.

The correlation between the sale of ice cream and murder is an indication of the existence of a common third factor.

Based on the time of the year dependence of the two variables, which corresponds to hot and cold weather, there is a correlation of both the murder rate and ice cream sales with temperature.

Therefore, the HOA president is not right for doing so

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Largest fraction 5/12 and 3/8, 2/5 and 19/45, 5/7, 13/14and 19/21

1) Between 5/12 and 3/8

Lets multiply both the 5/12 with 8/8 and 3/8 with 12/12

Therefore , new equations are  

5/12 x 8/8 = 40/ 96

3/8 x 12/12 = 36/96

So, 5/12 is larger fraction.

2) Between 19/45, 5/7

Lets multiply both the 19/45 with 7/7 and 5/7 with 45/45

Therefore , new equations are  

19/45 x 7/7 = 133/ 315

5/7 x 45/45 = 225/315

So, 5/7 is larger fraction.

3) Between 13/14and 19/21

Lets multiply both the 13/14 with 3/3 and 19/21 with 2/2

Therefore , new equations are  

13/14 x 3/3 = 39/42

19/21 x 2/2 = 38/42

So, 13/14 is larger fraction.

In arithmetic, a number expressed as a quotient, in which a numerator is divided via a denominator. In a easy fraction, both are integers. A complex fraction has a fraction inside the numerator or denominator. In a right fraction, the numerator is much less than the denominator

In arithmetic, a fraction described because the a part of the whole thing. as an instance, a pizza is divided into four identical pieces, then each piece is represented by means of ¼. Fractions help to distribute and choose the numbers easily and make the calculation faster.

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Answer:

1/3 + 3/4 + 4/6 +1/2 =

Step-by-step explanation:

1/6 + 4/6 = 5/6

3/4 + 1/4 = 4/4

5/6 + 4/4 = 9/12

9514 1404 393

Answer:

  5.  70°

  6.  69°

  7.  17°

  8.  37°

Step-by-step explanation:

Problems 5, 7, 8 have the opposite side and adjacent side given. You know that ...

  Tan = Opposite/Adjacent

Then the angle measure is ...

  angle = arctan(Opposite/Adjacent)

__

Problem 6 gives the opposite side and the hypotenuse. The sine relation is involved there:

  Sin = Opposite/Hypotenuse

Then the angle measure is ...

  angle = arcsin(Opposite/Hypotenuse)

__

5. ? = arctan(93/34) ≈ 70°

6. ? = arcsin(42/45) ≈ 69°

7. ? = arctan(11/35) ≈ 17°

8. ? = arctan(22/29) ≈ 37°

The required, general solution for x that satisfies the equation cos(x + 30) = -1 is x = (2n + 1)π - 30.

To find the general solution for the equation cos(x + 30) = -1, we can start by considering the general form of the cosine function. The cosine function has a period of 2π, meaning it repeats every 2π radians.

In this equation, we have cos(x + 30) = -1. Since the cosine function has a maximum value of 1 and a minimum value of -1, the only way for cos(x + 30) to equal -1 is if x + 30 is an odd multiple of π. We can write this as:

x + 30 = (2n + 1)π

Here, n is an integer representing the number of periods of the cosine function. To find the general solution, we can solve for x by subtracting 30 from both sides:

x = (2n + 1)π - 30

This equation gives us the general solution for x that satisfies the equation cos(x + 30) = -1. We can see that for each integer value of n, we have a different solution.

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Answer:

option 1 is true. -1/2=-0.5

Answer:

-1/2

Step-by-step explanation:

-5/6 + 6/18

Simplify the second fraction by dividing the top and bottom by 3 ( then we will have like denominators)

-5/6 + 2/6

Combine the numerators since the denominators are the same

-3/6

Divide the top and bottom by 3

-1/2

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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If the price of each folder is $2.15, and the amount of folders is f, the total price paid for folders is the product of the unitary price by the amount bought.

Similarly, the price paid for notebooks is the unitary price of one notebook ($4.60) multiplied by the amount of notebooks (n).

Finally, the total cost of both products together is the sum of these products.

The supply budget is $150, so the total cost needs to be lesser than or equal this value.

Therefore, we have that:

So the correct option is B.

Answer:

1/4

Step-by-step explanation:

Slope formula =

\( \frac{y2 - y1}{x2 - x1 \\ } \)Therefore, by choosing any 2 points

(-4,0) as 1 and (0,1) as 2

It will be

\( \frac{1 - 0}{0 - - 4} = \frac{1}{4} \)

The narrowest graph of the quadratic function is y = 5x² + 1.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know the graph a quadratic function y = ax² + bx + c is narrower and narrower with an increase in the value of a > 1.

From the given options we conclude that y = 5x²+ 1 has the narrowest graph.

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Answer:

\(y1 = 4 \\ x1 = 3\)

\(y - y1 = m(x - x1)\)

\(y - 4 = 0(x - 3)\)

\(y - 4 = 0\)

\(y = 4\)

Deductive Reasoning.

What's the difference between inductive and deductive reasoning?

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down. Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

Examples-

Inductive Reasoning: The first lipstick I pulled from my bag is red. The second lipstick I pulled from my bag is red. Therefore, all the lipsticks in my bag are red.

Deductive Reasoning: The first lipstick I pulled from my bag is red.

A deductive approach involves the learners being given a general rule, which is then applied to specific language examples and honed through practice exercises. An inductive approach involves the learners detecting, or noticing, patterns and working out a 'rule' for themselves before they practise the language.

A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

Thus ,I know I'll have to work a double shift today because I have a migraine and every time I have a migraine I get stuck pulling a double is and example of Deductive reasoning . Because a  deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.

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Answer:

integer-4

proper fraction-1/10

improper fraction-0/4

Step-by-step explanation:

do not copy in the internet

Answer:

y = 12.5065

Step-by-step explanation:

Answer:7.5 remember a negative divided by a negative (or multipled) is a positive.

Step-by-step explanation:

Check the picture below.

let's recall that, the arc made from 0 to π is just half a circle or namely a semi-circle, so any fraction of π refers to that arc

\(\cfrac{11\pi }{18}\qquad \textit{really means}\qquad \cfrac{11}{18}\qquad \textit{of that semi-circle}\)