How is the product of a complex number and a real number represented on the complex plane?



Consider the product of 2−4i and 3.



Drag a value or phrase into each box to correctly complete the statements

The resulting plot of a circle with its center at (4.2, 2.7) and radius of 7.5 is: Plot of a circle with its center at (4.2, 2.7) and radius of 7.5

To make a plot of a circle with its center at (4.2, 2.7) and radius of 7.5, you can follow these steps:

Step 1: Plot the center point (4.2, 2.7) on a graph paper.

This will be the center of your circle.

Step 2: Draw a line from the center point towards the right side, which is 7.5 units long.

Step 3: Draw a line from the center point towards the left side, which is 7.5 units long.

You can also use a compass to draw the circle.

Step 4: Draw a line from the center point upwards, which is 7.5 units long.

Step 5: Draw a line from the center point downwards, which is 7.5 units long.

Step 6: Join the endpoints of these lines to form a circle.

You can also use a compass to draw the circle.

The resulting plot of a circle with its center at (4.2, 2.7) and radius of 7.5 is:

Plot of a circle with its center at (4.2, 2.7) and radius of 7.5

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Answer: 120

Step-by-step explanation: divide 24 by 5 to get 4.8 so its 4.8 minutes for one question

25 x 4.8 = 120

A sensible original hypothesis that suggests a positive relationship between two variables could be: "Hypothesis: Increased physical exercise is positively associated with improved cardiovascular health."

The hypothesis suggests that there is a positive relationship between increased physical exercise and improved cardiovascular health. This means that as the level of physical exercise increases, it is expected to result in an improvement in cardiovascular health.

To explain further, the hypothesis is based on the understanding that physical exercise has various beneficial effects on the cardiovascular system. Regular exercise can lead to improvements in heart function, increased blood flow, lower blood pressure, improved cholesterol levels, and better overall cardiovascular fitness.

By proposing this hypothesis, we are suggesting that individuals who engage in more physical exercise will experience greater improvements in their cardiovascular health compared to those who engage in less or no exercise. This hypothesis can be tested through research studies, where data on exercise habits and cardiovascular health measures are collected and analyzed to determine if a positive relationship exists between the variables.

It is important to note that while the hypothesis suggests a positive relationship, further research is needed to provide concrete evidence and establish a causal link between increased physical exercise and improved cardiovascular health.

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Answer:

\(\sqrt{50}\) = \(5\sqrt{2}\)

Step-by-step explanation:

Start by factoring the expression:

\(\sqrt{5^{2}*2 }\)

Then you get:

\(\sqrt{5^{2}\) \(\sqrt{2}\)

Now simplify the root:

5\(\sqrt{2}\)

Answer:

Emilio needs less than 1 stick of butter

Step-by-step explanation:

Emilio needs 1/2 stick of butter to make cornbread . He also needs 1/4 stick of butter to make apple muffins . Does Emilio need more than I stick of butter to make both recepes or less than 1 stick of butter ? How do you know?

Cornbread = 1/2 stick of butter

Apple muffins = 1/4 stick of butter

Total sticks of butter = cornbread + apple muffins

= 1/2 + 1/4

= (2+1) / 4

= 3/4 stick of butter

= 0.75 stick of butter

0.75 stick of butter is less than 1 stick of butter

Therefore,

Emilio needs less than 1 stick of butter

Answer:

Division C = 9%

Division E = 10%

Step-by-step explanation:

From the pie chart attached,

Let the missing percentage of division C and E are c% and e% respectively.

Since, division B + division C + division D = 50%

[Divisions on one half of the circle]

23% + c% + 18% = 50%

41% + c% = 50%

c = 50 - 41

c = 9%

Similarly, division A + division F + division E = 50%

27 + 13 + e = 50

40 + e = 50

e = 10%

The average rate of change between hour 4 and hour 8 is equal to the  average rate of change between hour 0 and hour 4.

Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given,

The function f(x)=80(1.5)x

where x is the time in hours

Then,

f(4)=80(1.5)4=480

f(8)=80(1.5)8=960

f(0)=80(1.5)0=0

Then the average rate of change between 4 and 8 hours =\(\frac{960-480}{4}\)

=120 units per hour

The average rate of change between 0 and 4 hours=\(\frac{480-0}{4}\)

=120 units per hour

Hence, the average rate of change between hour 4 and hour 8 is equal to the  average rate of change between hour 0 and hour 4.

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The rate at which the distance from the plane to the station is increasing when it has a total distance of 4 miles away from the station is 317.5 mi/h.

A rate in which a certain number of units of the first quantity are compared to one unit of the second quantity is not the same as a unit rate. In other words, we may state that the comparison's second amount is always 1.

Thus, P denotes the plane's location, R denotes the radar's location, and V denotes the point that is vertical to the radar and at the plane's height.

Assume that h is the height of the plane, s is the separation from the radar, and x is the separation from point V.

The plane travels at 480 miles per hour and has a 3 mile height. Ds-480 miles per hour.

dt By Pythagorean theorem,

x² = h² + s²

x² = 3²+s²

x² = 9 + s²

Differentiate implicitly with respect to t.

2x dx/dt = 2s ds/dt + 0

x dx/dt = s ds/dt

Use (1)

dx/dt = \(\frac{dx}{dt} =\frac{\sqrt{x^2-9} }{x}\)

= √7/4 x 480

= 120√7

≈ 317.49

Hence, the distance increasing at the rate of dx/dt is 317.5 mi/h.

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Answer:

x = -\(\frac{1}{2}\)y + \(\frac{7}{4}\)

Step-by-step explanation:

First, isolate x by subtracting 2y from both sides:

4x + 2y = 7

4x = -2y + 7

Then, divide each side by 4:

x = -\(\frac{1}{2}\)y + \(\frac{7}{4}\) is x in terms of y

The value of x is x= 7/4 - y/2

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation. Look at the image below to understand the parts of an equation.

Given:

4x+ 2y = 7

4x= 7-2y

x= 1/4(7-2y)

x= 7/4-2y/4

x= 7/4 - y/2

Hence, x= 7/4 - y/2

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Answer:a party of fishermen rented a boat for $240. two of the fishermen had to withdraw from the party and, as a result, the share of each of the others was increased by $10. how many were in the original party? provide a numerical answer.

Step-by-step explanation:

Now ,Let original number in party be "x"::

Average cost per person = 240/x

New number in the party:: x-2

New Average cost per person:: 240/(x-2)

Equation::

10 dollars =New average - old average

240/(x-2) - 240/x = 10

240x - 240(x-2) = 10x(x-2)

480 = 10x^2-20x

x^2 - 2x - 48 = 0

X = 8 (ORIGINAL)

the distance from the plane to the radar station is increasing at a rate of approximately 30.84 kilometers per minute.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, A plane flying with a constant speed of 25 km/min passes over a ground radar station at an altitude of 12 km and climbs at an angle of 30 degrees.

We can use the law of cosines to find d:

d² = 12² + (h + 12)² - 2(12)(h + 12)cos(θ)

Since the plane is climbing at an angle of 30 degrees, we can use trigonometry to find h:

sin(30) = h / (25 km/min * 2 min)

h = 25 km/min

Now we can substitute this value of h into the equation for d and simplify:

d² = 12² + (25 + 12)² - 2(12)(25 + 12)cos(θ)

d² = 12² + 37² - 2(12)(37)cos(θ)

d² = 144 + 1369 - 888cos(θ)

d² = 1513 - 888cos(θ)

To find the rate at which d is changing, we can take the derivative of both sides of this equation with respect to time:

2dd/dt = -888(d(cos(θ))/dt)

Since the plane is flying with a constant speed of 25 km/min, we can use trigonometry to find d(cos(θ))/dt:

cos(θ) = 12/d

d(cos(θ))/dt = -(12/d²)(dd/dt)

d(cos(θ))/dt = -(12/d²)(25 km/min)

Now we can substitute these values into the equation for the rate of change of d:

2dd/dt = -888(-(12/d²)(25 km/min))

2dd/dt = (888*12)/(d²)(25 km/min)

dd/dt = (5328)/(d²) km/min

Finally, we can substitute the value we found for d into this equation to get the rate at which d is changing 2 minutes later:

d = sqrt(1513 - 888cos(θ))

θ = 30 degrees

dd/dt = (5328)/(d²) km/min

dd/dt = (5328)/(1513 - 888cos(30)) km/min

dd/dt ≈ 30.84 km/min

Therefore, the distance from the plane to the radar station is increasing at a rate of approximately 30.84 kilometers per minute.

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Answer:

46.08

Step-by-step explanation:

you have to make your percentage a decimal, which 60% will be .60 and 20% will be .20. you then multiply your initial number which is 36 by .60 and add that on because youre adding 60%. After that you will multiply that given number by .20 and you subtract what that product is from your last product you received (36x.60) which if im not mistaken will give you $46.08.

Answer:

C

Step-by-step explanation:

I took the test

Answer:

2/3 i believe

Answer:

2/3 :)

Step-by-step explanation:

Answer:

We conclude that her students, on average, do not take 30 minutes on the quiz, contrary to what the textbook company states.

Step-by-step explanation:

We are given;

Population mean; μ = 30 minutes

Population standard deviation; σ = 3 minutes

Sample size; n = 10

Sample mean; x¯ = 25

Significance level = 5% = 0.05

Let's define the hypotheses;

Null hypothesis; H0: μ = 30

Alternative hypothesis: Ha: μ ≠ 30

Let's find the test statistic;

z = (x¯ - μ)/(σ/√n)

z = (25 - 30)/(3/√10)

z = -5.27

From online p-value from z-score calculator attached using, z = -5.27, significance level = 0.05, two tailed hypothesis, we have;

p < 0.00001

This is less than the significance level, and so we will reject the null hypothesis and conclude that Her students, on average, do not take 30 minutes on the quiz, contrary to what the textbook company stated.

Answer:

A. Her students, on average, do not take 30 minutes on the quiz, contrary to what the textbook company stated.

Answer:

y-(-8)= -6(x-2)

y+8= -6x+12

y = -6x+ 4

you're mistake was you did +8 in 3rd step but you need to -8 both side becoz y-(-8)= y+8

Step-by-step explanation:

brainliest?

The student has incorrectly added 8 on both sides of the equation instead of subtracting it.

The general form of an equation is given as,

(y ₋ y₁)=m(x ₋ x₁)

where (x₁,y₁) is the point through which the line passes and m is the slope of the line.

Given that a line has a slope of -6 and passes through the point (2, –8). Therefore, substitute the slope and point in the above general form of the line and simplify.

(y ₋ y₁)=m(x ₋ x₁)

[y ₋ (-8)] = (-6)(x ₋ 2)

y + 8 = -6x + 12

Subtract 8 from both sides of the equation,

y + 8 - 8 = -6x + 12 - 8

y = -6x + 4

Now, if the steps are compared it can be seen that parenthesis are not opened properly and instead of subtracting 8, it is added to both sides of the equation.

Hence, the student has incorrectly added 8 on both sides of the equation.

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Answer: Your mom?

Step-by-step explanation: Your mom?

The given differential equation is `(27xy + 45y²) + (9x² + 45xy)y' = 0`.We have to solve this differential equation by using integrating factor `u(x, y) = (xy(2x+5y))-1`.The integrating factor `u(x,y)` is given by `u(x,y) = e^∫p(x)dx`, where `p(x)` is the coefficient of y' term.

Let us find `p(x)` for the given differential equation.`p(x) = (9x² + 45xy)/ (27xy + 45y²)`We can simplify this expression by dividing both numerator and denominator by `9xy`.We get `p(x) = (x + 5y)/(3y)`The integrating factor `u(x,y)` is given by `u(x,y) = (xy(2x+5y))-1`.Substitute `p(x)` and `u(x,y)` in the following formula:`y = (1/u(x,y))* ∫[u(x,y)* q(x)] dx + C/u(x,y)`Where `q(x)` is the coefficient of y term, and `C` is the arbitrary constant.To solve the differential equation, we will use the above formula, as follows:`y = [(3y)/(x+5y)]* ∫ [(xy(2x+5y))/y]*dx + C/[(xy(2x+5y))]`We will simplify and solve the above expression, as follows:`y = (3x^2 + 5xy)/ (2xy + 5y^2) + C/(xy(2x+5y))`Simplify the above expression by multiplying `2xy + 5y^2` both numerator and denominator, we get:`y(2xy + 5y^2) = 3x^2 + 5xy + C`This is the general solution of the differential equation.

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The fourth term in the geometric sequence is -81.

What is a geometric sequence?

In mathematics, a geometric progression, also known as a geometric sequence, is a set of non-zero numbers where each term after the first is derived by multiplying the previous one by a fixed, non-zero amount called the common ratio.

We are given a sequence as 3, –9, 27, ...

We can observe that each term is being multiplied by -3.

So, the common ratio i.e. r = -3

Here x = 4 and a₁ = 3.

Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get

⇒a₄ = a₁ r⁽⁴⁻¹⁾

⇒a₄ = a₁ r³

⇒a₄ = 3 (-3)³

⇒a₄ = 3 * -27

⇒a₄ = -81

Hence, the fourth term in the geometric sequence is -81.

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Answer:

$36

Step-by-step explanation:

30/(5/6) = $36

Answer:

$35

Step-by-step explanation:

If Frank has saved $30 which is only 5/6 the total cost, then he is still missing 1/6, so you need to find 1/6 of 30

30 times 1/6 equals 30/6 which is 5

The game costs $35

Answer:

NO

Step-by-step explanation:

they don't form a triangle because a triangle add up to 180°

Hope It Help

Step-by-step explanation:

\(\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}\)

\(\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}\)

\(\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}\)

\(\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}\)

\(\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}\)

\(\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}\)

Taking sin²θ common in both numerator & denominator, We get :

\(\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}\)

\(\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{cot\theta = \dfrac{cos\theta}{sin\theta}}}}\)

\(\mathsf{\implies \dfrac{1 -cot^2\theta}{1 + cot^2\theta}}\)

\(\mathsf{Given :\;cot\theta = \dfrac{1}{\sqrt{5}}}\)

\(\mathsf{\implies \dfrac{1 - \left(\dfrac{1}{\sqrt{5}}\right)^2}{1 + \left(\dfrac{1}{\sqrt{5}}\right)^2}}\)

\(\mathsf{\implies \dfrac{1 - \dfrac{1}{5}}{1 + \dfrac{1}{5}}}\)

\(\mathsf{\implies \dfrac{\dfrac{5 - 1}{5}}{\dfrac{5 + 1}{5}}}\)

\(\mathsf{\implies \dfrac{5 - 1}{5 + 1}}\)

\(\mathsf{\implies \dfrac{4}{6}}\)

\(\mathsf{\implies \dfrac{2}{3}}\)

Hence, option (a) 2/3 is your correct answer.

The percent increase in the cost of the uniform from last year to this year is 25%.

To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.

The difference between this year's price and last year's price is:

$65 - $52 = $13

The original price (last year's price) is $52.

So the percent increase in the cost of the uniform is:

percent increase = (difference / original price) x 100

percent increase = ($13 / $52) x 100

percent increase = 0.25 x 100

percent increase = 25%

Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.

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Maria received 999 votes out of a total of 25, which means that 999/25 = 39.96% of the class voted for her. Therefore, approximately 40% of the class voted for Maria.

To find the percentage of the class that voted for Maria, we need to first find the total number of students who voted:

Total number of students who voted = number who voted for Benjamin + number who voted for Sahil + number who voted for Maria

= 444 + 1212 + 999

= 2655

Now we can calculate the percentage of the class that voted for Maria:

Percentage of class that voted for Maria = (number who voted for Maria / total number of students who voted) x 100%

= (999 / 2655) x 100%

= 37.6%

Therefore, 37.6% of the class voted for Maria, approximately 40% of the class voted for Maria.

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Answer:

X=-8

Step-by-step explanation:

2 #7&"8*_8-*'7&-$(7

X<-8

On the number line, put the dot at -8 and shade to the left.

For a normal distribution, the skewness and kurtosis measures are as follows: Option B. 0 and 3.

Skewness is a measure of the asymmetry of a probability distribution. Skewness is a measure of the degree of asymmetry in the probability distribution of a random variable around its mean.

When the skewness is 0, the normal distribution is symmetrical.

Kurtosis is a measure of the degree of peakiness, or flatness, of a probability distribution.

For a normal distribution, kurtosis equals 3. In comparison to the normal distribution, distributions with kurtosis greater than 3 have a more pointed peak and longer tails, while distributions with kurtosis less than 3 have a less pointed peak and shorter tails.

Therefore, for a normal distribution, the skewness and kurtosis measures are 0 and 3, respectively. Hence, the correct option is B. 0 and 3.

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Answer:

-1280

Step-by-step explanation:

10×(-2)= -20

-20×(-2)= 40

4th term: 40×(-2)= -80

5th term: -80×(-2)= 160

6th term: 160×(-2)= -320

7th term: -320×(-2)= 640

8th term: 640×(-2)= -1280

A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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Answer:

p = 13

Step-by-step explanation:

When a polynomial f(x) is divided by (x + h) then the remainder is f(- h)

Here both polynomials are divided by (x + 1)

Evaluate them both for x = - 1

3(- 1)³ - 5(- 1)² - 4(- 1) + p, that is

- 3 - 5 + 4 + p

= p - 4 → A

6(- 1)³ + p(- 1)² + 9(- 1) + 5, that is

- 6 + p - 9 + 5

= p - 10 → B

Given that A = 3B, then

p - 4 = 3(p - 10)

p - 4 = 3p - 30 ( subtract 3p from both sides )

- 2p - 4 = - 30 ( add 4 to both sides )

- 2p = - 26 ( divide both sides by - 2 )

p = 13

The total erasing cost is 5.

The erasing cost refers to the cost associated with removing or eliminating something. In this case, the question states that the total erasing cost is 5. However, without further context or information, it is unclear what specifically is being erased and what the units of the cost are.

To provide a more detailed explanation, it would be helpful to have additional information about the context or problem at hand. Please provide more details or clarify the question so that I can assist you more effectively in determining the specific meaning and explanation behind the total erasing cost of 5.

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