Find the product of z1 and z2, where z1 = 5(cos 60° + i sin 60°) and z2 = 7(cos 210° + i sin 210°)

Write in a + bi form

Answer:

576

Step-by-step explanation:

If its helpful please mark me brainiest :>

Thanks ;p

Answer:

576

Step-by-step explanation:

12x6 = 72

72x8=576

576

Answer:

= 80πcm²

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer:

Given the information:

=> Area of base = π(6²) = 36π cm²

=> Area of the hole = πr² = π(4²) = 16πcm²

As we know that, the surface area of the piece of wood has to be painted at base:

= Base area - area of hole

= 36π cm² - 16πcm²  

= 20πcm²

For the curved surface area can be determined by the following formula:

Area = πrl where l is the slant height

Applying Pythagoras theorem, we have:

[tex]l^{2} = r^{2} + h^{2}[/tex]

<=> [tex]l^{2} = 6^{2} + 8^{2}[/tex]

<=> [tex]l^{2} =100[/tex]

<=> l =10

=> the curved surface area is: π*6*10 =60πcm²

Hence the total surface area to be painted is

= the curved surface area + he surface area of the piece of wood has to be painted at base

=  60πcm² +20πcm²

= 80πcm²

Hope it will find you well.

To find the surface area to be painted, calculate the total surface area of the cone and subtract the area of the cylindrical hole.

To find the surface area to be painted, we need to calculate the total surface area of the cone and then subtract the area of the cylindrical hole.

The total surface area of a cone is given by the formula A = πr(r + l), where r is the radius of the base and l is the slant height.

In this case, the radius of the cone is the same as the radius of the base of the hole, which is 4 cm. We need to find the slant height of the cone, l.

By applying the Pythagorean theorem to the right triangle formed by the height of the cone, the slant height, and the radius of the cone, we can calculate the slant height as l = sqrt( h^2 + 4^2 ), where h is the height of the cone.

Since the height of the cone is not given, we will not be able to find the exact value for the surface area to be painted. However, we can provide the general formula based on the given information:

Surface area to be painted = (π * r1 * (r1 + sqrt( h^2 + r1^2 ))) - (2 * π * r2 * h),

where r1 is the radius of the base of the hole and r2 is the smaller radius of the hole.

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To graph y=4x-9, plot the y-intercept at (0,-9), then for each increase in x, y increases by 4. Draw a line through these points to describe the equation.

To graph the equation y=4x-9, we need to identify the slope and the y-intercept. In this case the slope is 4, which means for each increase in x by 1, y increases by 4. The y-intercept is -9, which is the point where the line crosses the y-axis.

Start by plotting the y-intercept at (0,-9) on the graph. Then, for each unit increase in x, move up 4 units on the y-axis from the previous point. Drawing a line through these points will visualize the equation y=4x-9.

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Answer:

Area of Shaded Region: ( About ) 19.6

Step-by-step explanation:

~ To find the area of the shaded region, let us calculate the area of the circle, and the area of the hexagon, subtracting it's area from the area of the circle ~

1. Given a radius of 6 cm, let us calculate the area of the circle provided the area formula πr^2. Substitute the value of the radius, but keep π in terms of π until the end ⇒ π * ( 6 )^2 = 36π ⇒ ( About ) 113.1 units^2

2. To find the area of the hexagon, let us divide the hexagon into 6 triangles. All 3 of the sides of each triangle is 6 cm, provided these are equilateral triangles. We should calculate the area of each triangle, so let us draw an altitude for each of these Δs. Doing so, through Coincidence Theorem we split the segment drawn to the altitude into two ≅ parts, or 3 units each. That means that the altitude must be 3√3, by properties of 60-60-60 triangles. That being said, the area of one of the triangles: 1/2 * base * height ⇒ 1/2 * 6 * 3√3 ⇒ 9√3 units^2.

3. Knowing that all the 6 triangles are ≅, let us simply multiply the area of a of the triangles * 6 to recieve the area of the hexagon ⇒ 9√3 * 6       ⇒ 54√3 units^2

4. The area of the shaded region is now ⇒ 113.1 - 54√3 ⇒

Area of Shaded Region: ( About ) 19.6

By subtracting the area of the hexagon, from the area of the circle. The area of the shaded region is 19.6.

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the circle = [tex]\pi r^{2}[/tex]

Given a radius of 6 cm,

The area of the circle = [tex]\pi r^{2}[/tex]

Substitute the value of the radius,

[tex]\pi ( 6 )^2 \\= 36 \times 3.14\\= 113.1 units^2[/tex]

The area of the circle is 113.1 units^2.

To find the area of the hexagon, let us divide the hexagon into 6 triangles. All 3 of the sides of each triangle are 6 cm, provided these are equilateral triangles.

The area of one of the triangles

 [tex]=1/2 \times base \times height\\ \\= 1/2 \times 6 \times3\sqrt3 \\\\ =9\sqrt{3} units^2.[/tex]

The area of the triangles 6 times to receive the area of the hexagon

[tex]9\sqrt{3} \times 6 \\ \\54\sqrt{3} units^2[/tex]

The area of the shaded region = 113.1 - 54√3

                                                       =  19.6

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A member customer need to pay for the sweater during the sale if the customer paid the stores credit card is $ 15.30.

Credit card is defined as a kind of credit product offered by banks that enables users to take out loans up to a pre-approved credit limit. Earn benefits like cashback or mileage points. security from credit card theft. Free credit score information. Absence of foreign transaction costs increased capacity to spend.

Costumer is defined as a person or organization that acquires goods or services from another corporation. Positive customer experiences are extremely important for brand awareness because they frequently result in word-of-mouth promotion.

Given the market price = $24

The percent initial discount = 25%

The percent final discount = 15%

The customer paid the stores credit card

= 24 x 0.75 = 18

= 18 x 0.85 = 15.3

Thus, a member customer need to pay for the sweater during the sale if the customer paid the stores credit card is $ 15.30.

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Answer:

d 68

Step-by-step explanation:

do not know hope it maybe might help you sorry wish i could help

Answer: probably D but i dont know could be A, B, or C

Step-by-step explanation:

Answer:

B=4

Step-by-step explanation:

Answer:

b=-1

Step-by-step explanation:

To find the value of b, we need to isolate it.

This means moving all the numerical values to one side, and the variables to the toher.

First, we can add 6 to both sides

-3=1-4b

Subtract 1 from both sides

-4=-4b

Divide both sides by -4

-1=b

b=-1

Answer:

B. exponential

Step-by-step explanation:

By visual inspection, determine the best-fitting regression model for the scatterplot is Quadratic.

The graph reveals that,

The scatter plot behaves like a quadratic equation would.

The graph therefore begins and ends in the same direction.

Moreover, the scatter plot's points increase first until they reach a maximum value, then they start to decline.

As a result, A quadratic equation can be seen visually in the scatter plot.

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Answer:

  B. f(x) = 2x-3

Step-by-step explanation:

The first point in the table tells you there will be an added constant of -3. All answer choices agree on this.

The x-values are evenly spaced, so we can examine the f(x) values to see what sort of function it is. It usually works well to consider the differences of adjacent values. Here, we see they are ...

  -1 -(-3) = 2

  1 -(-1) = 2

  3 -1 = 2

  5 -3 = 2

  7 -5 = 2

All of the differences are the same value, 2, so this is a linear function. There is only one answer choice that is a linear function:

  f(x) = 2x -3

Final answer:

The correct function that represents the data in the table is B. f(x)= 2x-3. This linear function consistently provides the correct f(x) values for each x when compared to the data given.

Explanation:

In order to choose the function that represents the data given in the table, we will analyze each option provided against the data.

For x=0, the value of f(x) should be -3.

For each increase of 1 in x, the value of f(x) increases by 2.

Now let's evaluate the given options:

Option A: f(x)= 2/x-3 does not satisfy the values for any x in the table.

Option B: f(x)= 2x-3 consistently satisfies the value of f(x) for each x in the table. For example, if x=2, f(x) = 2*2 - 3 = 1, which matches the table data.

Option C: f(x)= x^2-3 gives incorrect values for all x other than 0 and 1.

Option D: f(x)= 2x^2-3 also provides incorrect values since it increases much more rapidly than the data in the table.

Therefore, the correct answer is Option B, f(x)= 2x-3.

Answer:

She need 7 bags to cover the garden

Step-by-step explanation:

Diameter of circular garden = 16 feet

Radius of circular garden =[tex]\frac{16}{2} = 8 feet[/tex]

Area of circular garden =[tex]\pi r^2 = \frac{22}{7} \times 8^2 =200.96ft^2[/tex]

30 sq.feet covered by no. of bags = 1

200.96 sq.feet covered by no. of bags = [tex]\frac{200.96}{30}=6.69[/tex]

Hence She need 7 bags to cover the garden

Jane will need 7 bags to cover her garden.

First, we need to find the area of Jane's garden. The formula for the area of a circle is A = πr², where r is the radius.

Next, we determine how many bags of fertilizer are needed:

Since Jane can't purchase a fraction of a bag, she will need to round up to the nearest whole number. Therefore, Jane will need 7 bags of fertilizer to cover her garden.

Answer:

9/50 or 0.18

Step-by-step explanation:

If you divide both 9/10 and 5 by 5, you get 9/50 of a mile in 1 minute. Hope this helps!

Answer:

[tex]\frac{9}{50}[/tex] miles per minute.

Step-by-step explanation:

To solve this, you will need to divide the total amount run by 5 to find the amount of miles run per minute.

This can be done by dividing by 5 or multiplying by 1/5 to get:

[tex]\frac{9}{10} *\frac{1}{5} = \frac{9}{50}[/tex] miles in 1 minute.

Answer:

Step-by-step explanation:

First of all we all should know about a geometric progression to solve this question.

A geometric progression is a series in which there is a first term a and all the next terms are calculated by multiplying the previous term by a common number r.

where a is known as first term and

r is known as common ratio.

In the question we are given a as 20 and we have to find out 2 terms after 20 and 4th term is given as 2500.

Formula for [tex]n^{th}[/tex] term in a geometric progression is:

[tex]a_{n} = a\times r^{n-1}[/tex]

Here [tex]a_{4}[/tex] = 2500

As per formula of [tex]n^{th}[/tex] term:

[tex]a\times r^{3} = 2500\\\Rightarrow 20 \times r^{3} =2500\\\Rightarrow r^{3} = 125\\\Rightarrow r = 5[/tex]

Now, 2nd term:

[tex]a_{2} = a \times r\\\Rightarrow a_{2} = 20 \times 5\\\Rightarrow a_{2} = 100[/tex]

Now, 3rd term:

[tex]a_{3} = a \times r^{2} \\\Rightarrow a_{3} = 20 \times 5^{2}\\\Rightarrow a_{3} = 500[/tex]

So, the two geometric means between 20 and 2500 are 100 and 500.

Answer:

105

Step-by-step explanation:

the middle angle is 75 degrees

co interior angles add up to 180 so 75 +105 = 180

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Answer:

3/5 of 1 page in 45  min

Step-by-step explanation:

Answer:

Step-by-step explanation: the awnser on edge is C the solution is for combinations, but the situation calls for permutations. Hope this helped :)

The error that is made in the work shown below is C. The solution is for combinations, but the situation calls for permutations.

It should be noted that permutations simply mean the ways that the objects from a set can be selected.

In this case, the error that is made in the work shown below is that the solution is for combinations, but the situation calls for permutations.

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Answer:

c

Step-by-step explanation:

you start with $45 then for each number of days you pay $3

The volume of the traffic pylon is 7.26 cubic feet.

To find the volume of the cone-shaped pylon, we'll use the formula for the volume of a cone, which is [tex]\( \frac{1}{3} \pi r^2 h \),[/tex]  where ( r ) is the radius of the base and ( h ) is the height.

Given that the height ( h ) of the pylon is 2.4 feet and the radius ( r ) is 1.7 feet, we can plug these values into the formula:

[tex]\[\text{Volume} = \frac{1}{3} \pi \times (1.7)^2 \times 2.4\][/tex]

Let's calculate this:

[tex]\[\text{Volume} \approx \frac{1}{3} \times 3.14159 \times (1.7)^2 \times 2.4\][/tex]

[tex]\[\text{Volume} \approx \frac{1}{3} \times 3.14159 \times 2.89 \times 2.4\][/tex]

[tex]\[\text{Volume} \approx \frac{1}{3} \times 3.14159 \times 6.936\][/tex]

[tex]\[\text{Volume} \approx \frac{1}{3} \times 21.78\][/tex]

[tex]\[\text{Volume} \approx 7.26 \text{ cubic feet}\][/tex]

So, the volume of the cone-shaped pylon is approximately 7.26 cubic feet.

Answer:

-3

Step-by-step explanation:

Slope = change of x over change of y

6 over 2

3

line goes down so slope is negative

-3

The slope of the line passing through the given points (-1, 4) and (1, -2) is -3.

Given the following points:

To find the slope of the line passing through the given points (-1, 4) and (1, -2):

The slope of a line is simply the gradient of a line and it is typically used to describe both the direction and steepness of an equation of a straight line.

Mathematically, the slope of a line is given by the following formula;

[tex]Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Substituting the given points into the formula, we have;

[tex]Slope. \;m = \frac{-2 \;- \;4}{1\; - \;[-1]}\\\\Slope. \;m = \frac{-6}{2}[/tex]

Slope, m = -3

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Answer:

x=8, x=-6

Step-by-step explanation:

D.

it's D the answer is d

Answer:

Option 1

Step-by-step explanation:

The points where the two functions intersect are the solutions.

Answer:

The missing height is 5 units

Step-by-step explanation:

Mathematically, the area of a parallelogram can be found using the formula below;

A = Base× Height

From the parallelogram diagram, we can identify that the base has a length of 7 units, a height of h units and an area of 35 square units

Substituting these values in the equation above, we have

35 = 7 × h

h = 35/7

h = 5 units

Answer:

5 real

Step-by-step explanation:

Answer:

I think the answer is 42.

Step-by-step explanation:

I estimated 23.1 to 23 miles then I estimated 19.24 to 24 and added 23+19=42. But I don't know if that is correct because there was no specification if we round to the whole number.

The actual distance is 42.34 miles. The total distance Pablo drove, is sum of distance of aunt's house an friend's house.

Pablo drove 23.1 miles to his aunt's house and then 19.24 miles to his friend's house.

To estimate the total distance driven, he can round the numbers to the nearest mile or to the nearest tenth to make the calculation easier. If rounding to the nearest mile, he can estimate 23 + 19 miles, which is 42 miles.

If rounding to the nearest tenth, he can estimate

23.1 + 19.2= 42.3 miles.

The actual total distance driven is 23.1 + 19.24 = 42.34 miles.

Answer:

The most correct option is;

(B) 958.2 ft.²

Step-by-step explanation:

From the question, the dimension of each square = 3 ft.²

Therefore, the length of the sides of the square = √3 ft.

Based on the above dimensions, the dimension of the small semicircle is found by counting the number of square sides ti subtends as follows;

The dimension of the diameter of the small semicircle = 10·√3

Radius of the small semicircle = Diameter/2 = 10·√3/2 = 5·√3

Area of the small semicircle = (π·r²)/2 = (π×(5·√3)²)/2 = 117.81 ft.²

Similarly;

The dimension of the diameter of the large semicircle = 10·√3 + 2 × 6 × √3

∴ The dimension of the diameter of the large semicircle = 22·√3

Radius of the large semicircle = Diameter/2 = 22·√3/2 = 11·√3

Area of the large semicircle = (π·r²)/2 = (π×(11·√3)²)/2 = 570.2 ft.²

Area of rectangle = 11·√3 × 17·√3 = 561

Area, A of large semicircle cutting into the rectangle is found as follows;

[tex]A_{(segment \, of \, semicircle)} = \frac{1}{4} \times (\theta - sin\theta) \times r^2[/tex]

Where:

[tex]\theta = 2\times tan^{-1}( \frac{The \, number \, of \, vertical \, squrare \, sides \ cut \, by \ the \ large \, semicircle}{The \, number \, of \, horizontal \, squrare \, sides \ cut \, by \ the \ large \, semicircle} )[/tex]

[tex]\therefore \theta = 2\times tan^{-1}( \frac{10\cdot \sqrt{3} }{5\cdot \sqrt{3}} ) = 2.214[/tex]

Hence;

[tex]A_{(segment \, of \, semicircle)} = \frac{1}{4} \times (2.214 - sin2.214) \times (11\cdot\sqrt{3} )^2 = 128.3 \, ft^2[/tex]

Therefore; t

The area covered by the pavers = 561 - 128.3 + 570.2 - 117.81 = 885.19 ft²

Therefor, the most correct option is (B) 958.2 ft.².

Answer:AC=AD•AB over AE

Step-by-step explanation:

Answer:

$5,040

Step-by-step explanation:

Answer:

The answer is 45,000

Step-by-step explanation:

I hope this helps

Answer:

The answer is 45,000

Step-by-step explanation:

Every second, the number of harmful bacteria remaining in the body decays by a factor of approximately .

To determine the rate of change in the number of harmful bacteria remaining in the body every second, we need to convert the time in the given function from minutes to seconds. The function provided is

⇒ [tex]H_{minute}[/tex](t) = 500,000,000 · [tex](0.2)^t[/tex].

A minute has 60 seconds, so we need to express the decay factor for a second. By letting t = [tex]t_{seconds}[/tex] ÷ 60, we can rewrite the function in terms of seconds:

⇒ [tex]H_{second}[/tex](t) = 500,000,000 · [tex](0.2)^\frac{t}{60}[/tex].

For every passing second, the decay factor is [tex](0.2)^\frac{1}{60}[/tex]. Using a calculator, we find:

⇒ [tex](0.2)^\frac{1}{60}[/tex] ≈ 0.98855,

rounded to two decimal places.

Therefore, every second, the number of harmful bacteria remaining in the body decays by a factor of approximately 0.99.

Complete question:

After a certain medicine is ingested, the number of harmful bacteria remaining in the body declines rapidly.

The relationship between the elapsed time t, in minutes, since the medicine is ingested, and the number of harmful bacteria remaining in the body, [tex]H_{minute}[/tex](t), is modeled by the following function:

[tex]H_{minute}[/tex](t) = 500,000,000 · [tex](0.2)^t[/tex]

Complete the following sentence about the rate of change in the number of harmful bacteria remaining in the body in seconds.

Round your answer to two decimal places.

Every second, the number of harmful bacteria remaining in the body decays by a factor of            .

Answer:

Step-by-step explanation:

24√3

The area of the regular hexagon with radius length 4 m will be 24√3 square meters.

The polygon which is having six sides and each side are congruent. And each internal angle of the hexagon will be of 120 degrees.

The area of the regular hexagon is six times area of the equilateral triangle.

Area of regular hexagon = 6 x Area of the equilateral triangle.

The regular hexagon with radius length 4 m.

The area of the equilateral triangle will be

Area = (√3 / 4) x (side)²

Area = (√3 / 4) x 4²

Area = 4√3 square meters

Then the area of the regular hexagon with radius length 4 m will be

Area of regular hexagon = 6 x 4√3

Area of regular hexagon = 24√3 square meters

The area of the regular hexagon with radius length 4 m will be 24√3 square meters.

The diagram is attached below.

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Answer:

10

Step-by-step explanation:

All you have to do is count the number of answers imputed. Simple as that. If its a dot plot then just count the number of dots or x's

Step-by-step explanation:

[tex]Volume = \frac{4}{3} \pi r^3[/tex]

[tex]V = \frac{4}{3} \pi (\frac{1}{2} )^3[/tex]

[tex]V=\frac{4}{3}\pi (\frac{1}{8})[/tex]

[tex]V= 0.5233..[/tex]

So, the volume of the sphere would be 0.523.