The figure below is composed of squares and semi-circles. Find the perimeter of this shape. Show your work.

We have the following equation to solve

Where E, I, and Z are complex numbers, therefore let's put it in numbers

We can solve it directly into the rectangular form by doing the distrutive

Then

Remember that

Then

Now we have completely solved the problem!

______________________

The second solution (usual)

When we have real engineering problems, we like to do multiplication and division with the polar form, then let's convert Z and I to the polar form

Now to do the multiplication we multiple the magnitude and sum the phases (angles)

We already have the result, now just put it in the rectangular form

We will have the following expressions for store A and B respectively:

From this, we can see that after certain ammount of flowers the price will be better if we arrage it as follows:

When we are given a straight line drawn on the cartesian graph, i.e, having x and y coordinates, the gradient/slope is the change on the y-axis relative to change on the x-axis.

The x-axis is the horizontal axis and the y-axis is the vertical axis.

To get the gradient, we simply pick two points on the line and name them points 1 and 2. Thus, they will have the following attributes:

The gradient of a straight line is:

So, in our question, we can pick our points 1 and 2 at

Point 1 = (-2, 6), (1,-3),

Point 2 = (0, 0), (2,-6)

Applying our formulae, we get:

The gradient is -3.

As for the intercept on the y-axis, this is the point on the vertical axis where the graph cuts the graph. It can be visibly seen from our graph as occurring at y = 0.

However, it can be calculated via a formula to give us the form: y = mx + c.

where: m is the gradient/slope and c is the intercept on the y axis.

Formulae for getting conventional line equation is:

The line equation is therefore: y = -3x + 0

Slope = -3 AND

y-intercept = 0

The shape of the distribution A is Negatively skewed.

What is a negatively skewed distribution?\

A negatively skewed distribution sometimes referred to as a left-skewed distribution, is a type of distribution where more values are concentrated on the right side (tail) of the distribution graph and the left tail of the distribution graph is longer.

The idea of skewness is used in finance to analyze the distribution of investment returns. An investor may anticipate frequent tiny wins and a few significant losses, according to the distribution's negative skewness. In fact, traders frequently use trading methods that are based on distributions that are negatively skewed.

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A rhombus is a two-dimensional shape and is also characterized as a special parallelogram. It has four equal sides, with the opposite angles being equal to each other, whereas its adjacent angles are supplementary.

A rectangle is a also two-dimensional shape. It has four equal angles and four vertices. All the four angles of a rectangle measure 90°.

Rhombuses and Rectangles have the following differences:

1) A rhombus has four equal sides while in a rectangle, the opposite sides are equal.

2) The diagonals of a rhombus bisect each other at 90° while the diagonals of a rectangle bisect each other at different angles.

Given

So, we have that

Therefore, the expression given is

Apply the laws of exponents

Answer:

Answer: -86

Given:

If we consider x+4 as a factor of the given polynomial, this would mean that x=-4. For an x- value to be a factor of a polynomial, P(x) must be equal to 0. With that, we will have:

Therefore, the answer is -86

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

point 01 (4 , 2)

point 02 (6 , 5)

Step 02:

equation of the line:

slope:

Point-slope form of the line

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

The answer is:

y = 3/2 x - 4

Graphing the triangle DEF, we have:

Now, translating the triangle 4 units right and 3 units down, we have the new vertices:

Graphing the triangle D'E'F', we have:

After solving the given equation for f(x) the resultant answer is f(x)=1.

So, find f(x):

Now, calculate as follows:

Therefore, after solving the given equation for f(x) the resultant answer is f(x)=1.

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Answer:

150 degrees

Explanation:

Given: m∠8=150 degrees

Angles 8 and 5 are vertically opposite angles.

Vertical angles are equal, therefore:

Next, angles 1 and 5 are corresponding angles.

Corresponding angles are equal, therefore:

The measure of angle 1 is 150 degrees.

Calculate the area of the square JKLM if KM = 42 mm.

given that KM=42 mm

KM is also the diagonal of the square.

Also, the diagonal KM is the hypotenuse of a right triangle with sides JK and JM the Pythagoras theorem.

Now , let's remember that the angle formed by two sides of a square is equal to 90 degrees, this means, that the angle formed by the diagonal and any side must be the half, it is 45 degrees

so, if we solve the right triangle MLK we will find the length of the s

Now, is it a square, so the sides are equal, and the area is given by

so, the answer is 882 square millimeters

Let us calculate the slope of the line. We get two points (0,7) and (3,5)

given the slope we have that

so the function is:

a. In order to determine how much soap material is used for each bar of soap, consider that the shape of the bar is a cylinder, then, use the folowing formula for the volume of a cylinder:

V = π r² h

where r is the radius of the base and h is the height.

The diameter is 5 cm, then, the radius is r = d/2 = 5 cm/2 = 2.5 cm

The height is h = 2 cm

replace the previous values into the formula for V:

V = (3.14)(2.5 cm)²(2 cm)

V = 39.25 cm³

Hence, 39.25 cm³ of soap material is used to make each bar.

b. In this case it is necessary to calculate the suface area of the plastic used. As before, take into account that the bar has a cylindrical shape. Then, use the following formula for the surface area of a cylinder:

S = 2πr² + 2πrh

replace the values of the parameters to find S:

S = 2π(2.5 cm)² + 2π(2.5cm)(2cm)

S = 70.68 cm²

Hence, 70.68 cm² of plastic is required to wrap each bar

c. Take into account that the soap must be stacked no more than 5 bars high, and that the company wants to ship a minimum of 60 bars.

If there are 5 bars high x 3 bars length, in one face of the box you have 15 bars. Moreover, if there are 4 bars width, then, you have a total of 15x4 = 60 bars in one box, which is what the company wants.

The height of the box is given by 5 times the height of one bar (because there are 5 bars high). The length is given by 3 times the diameter of one bar and the width of the box is given by 4 times the diameter of one bar:

height of the box = 5(2 cm) = 10 cm

length of the box = 3(5 cm) = 15 cm

width of the box = 4(5 cm) = 20 cm

d. First, calculate the volume of the box, as follow:

V = h x l x w = (10 cm)(15 cm)(20 cm) = 3,000 cm³

take into account the conversion 1,000 cm³ = 1 L, then, the capacity of the box is:

V = 3,000 cm³ = 3L

3 seconds

Explanation

we have a graph where

x-axis: indicates the time

y-axis:indicates the height

to solve this we need to find the time, where the maximum heigth is reached

Step 1

check the coordinate where the maximum heigth is reached

and go down vertically to intersect the x-axis:

so, we have , it took around 3 seconds to reach the maximum heigth

I hope this helps you

Rate of Jenny = 1/ 8.4 minutes

Rate of Mofor = 1/13.3 minutes

We know time and rate are inverses of each other.

So, if they work together, their rates would be:

The time they will take will be the inverse of this, thus:

So, let's calculate it:

That is around 5.15 minutes.

Given:

a1 = 4

a3 = 1

r = ½

Let's find the S3 of the sum of the geometric series.

Apply the sum of geometric series formula below:

Let's solve for S3.

Substitute the values into the equation.

Where: n = 3

Thus, we have:

Solving further:

Therefore, the S3 of the sum of the given geometric series is 7

ANSWER:

7

Answer:

Explanation:

We know that the ratio of Helga's savings to Maurice's savings is 8:3 and the ratio of Maurice's savings to Nora's savings is 3:4.

It means that if Helga has $8, Maurice has $3 and Nora has $4

In the same way, we can multiply one quantity by 2, and all the quantities will be multiplied by 2, so if Helga has $16, Maurice has $6 and Nora has $8

Because:

$8 x 2 = $16

$3 x 2 = $6

$4 x 2 = $8

So, following the same logic, we can complete the table as:

Therefore, the complete table is:

SOLUTION:

Case: Enlargement

Method:

Scale factor: The scale factor is the 3, because the image is three times the size of the object.

From the tracing, the center of dilation is at C(-2, -2).

Final answer:

Center = (-2, 2)

Scale factor = 3

So the 100% percent is equal to $60 and is decreasing $40 so is:

So is decreasing $20. now we can made a rule of 3 to finde the percentage so:

and the ecuation will be:

So in total the decrese a 33%

S = {x ∈ R : 3≤x≤12}

1) To solve a compound inequality, we must do it one by one.

Let's start with

1.1) 0≤1/3x -1

1≤1/3x-1+1

1≤1/3x Multiplying both sides by 3

3≤x Flipping it

x≥3

1.2) 1/3x -1≤3

1/3x -1+1≤3+1

1/3x≤4

x≤12

2) Let's find out the solution, by graphing on three lines. The first one for the first solution, the second for the second inequality's solution, and the third for the intersection of the above:

So the Solution set is S = {x ∈ R : 3≤x≤12}

Explanation:

If there are H horses and 6 are taken into the yard, then we have 6 horses less in the stable.

Answer:

There are (H - 6) horses left in the stable

Answer: Letter Z.

The notation Z for the set of integers comes from the German word Zahlen, which means "numbers". Integers strictly larger than zero are positive integers and integers strictly less than zero are negative integers.

First let's find the profit for each t-shirt, by subtracting the selling price and the buying price:

So they have a profit of $17.5 per t-shirt sold.

Now, to find the number of t-shirts they have to sell to break even, we just need to divide the right cost of $740 by the profit value of one t-shirt:

So they need to sell approximately 43 t-shirts to break even.

First i will draw the original point in red

the rotation of 180° will give us the point (3,-4) the blue point

next, we reflect this point in the y-axis, the green point

if we see only the red point and the green point the transformation is equivalent to a reflection in the x-axis

the correct answer is 1

1 and ∠2 are complementary angles. The measure of ∠1 is 14°. The measure of ∠2 is 4x°. Find the value of x.

Remember that

the sum of complementary angles is 90 degrees

so

<1+<2=90

substitute given values

14+4x=90

solve for x

4x=90-14

4x=76

SOLUTION

From the question, let the total number of minutes billed on the phone bill be m

Splitting this into 3 phones, we have

Hence the answer is m/3

Answer:

Step-by-step explanation:

We know supplementary angles add up to 180°:

Find the missing one:

Correct choice is C.

Answer

a = b

a + c = b + c (Addition Property of Equality)

This operation is True.

Explanation

If we are told that

a = b

Adding the same number to both sides of an equation is called the Addition Property of Equality.

And it produces the same number on both sides after this operation.

a = b

Add c to both sides

a = b

a + c = b + c (Addition Property of Equality)

This operation is True.

Hope this Helps!!!