Question
The endpoints of a side of rectangle ABCD in the coordinate plane are at A(1,4) and
B(4,1). Find the equation of the line that contains the given segment.
The line segment is AB.
The equation Is y -

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:

169

Step-by-step explanation:

360-[36+160]-36

360-160-72

169

1. The ordered pairs are as follows

(0, 0)

(1, 5)

(2, 10)

(3, 15)

(4, 20)

2. The rules in the pattern of the days count is

n + 1

3. the rule of the pattern of the cost column is

n + 5

4. The relationship between the terms is

y = 5x

5. It will cost $40 to rent a scooter for 8 days

6. The ordered pair is in 1. and the graph is attached

7. It will cost $32.5 to rent a scooter for 6 1/2 days

In mathematics, an ordered pair is a set of two elements arranged in a specific order. The order of the elements in the pair is important, meaning that swapping the elements changes the identity of the pair.

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Answer:

R = (0,-8)

Step-by-step explanation:

Let's look at the difference between S, and the midpoint M.

S(6,0) - M(3,-4) = N(3,4) This will help us find R(x,y)

Next, take M, and subtract N from it.

M(3,-4) - N(3,4) = (0,-8). This is the value of R.

Answer:

I HOPE IT WILL HELP YOU.

Thanks.

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Answer: The number of freshman who chose education as their major is greater than the number of freshman who chose science or other as their major ANSWER- D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using the midpoint formula, the midpoints of the following are:

(4, √2) and (-2, 5√2) --> M(1, 3√2)

(-⅔, ⅘) and (⅓, ½) --> (-1/6, 13/20)

The formula that is used to determine the coordinates of the midpoint of a line segment is called the midpoint formula, and it is expressed as:

M(x, y) = [(x1 + x2)/2, (y1 + y2)/2]

Find the midpoint between (4, √2) and (-2, 5√2):

Let,

(4, √2) = (x1, y1)

(-2, 5√2) = (x2, y2)

Plug in the values

M(x, y) = [(-2 + 4)/2, (5√2 + √2)/2]

M(x, y) = [2/2, (6√2)/2]

M(x, y) = (1, 3√2)

M(1, 3√2)

Find the midpoint between (-⅔, ⅘) and (⅓, ½):

Let:

(-⅔, ⅘) = (x1, y1)

(⅓, ½) = (x2, y2)

Plug in the values

M(x, y) = [(-⅔ + ⅓)/2, (⅘ + ½)/2]

M(x, y) = [(-⅓)/2, (13/10)/2]

M(x, y) = [(-⅓ × ½), (13/10 × ½)]

M(x, y) = (-1/6, 13/20)

In summary, using the midpoint formula, the midpoints of the following are:

(4, √2) and (-2, 5√2) --> M(1, 3√2)

(-⅔, ⅘) and (⅓, ½) --> (-1/6, 13/20)

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The answer that correctly describes the data shown by the box plot is (B) "The interquartile range is 4 and the range is 10." (option-b)

The box plot provides a graphical representation of data that shows the distribution of a dataset, including the median, quartiles, and any outliers. Here, we need to compute the interquartile range (IQR) and range based on the information given in the box plot.

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). Looking at the box plot, we can see that Q1 is 3 and Q3 is 7. Therefore, the IQR is 7 - 3 = 4.

The range is the difference between the maximum and minimum values of the dataset. Looking at the box plot, we can see that the minimum is 0 and the maximum is 10. Therefore, the range is 10 - 0 = 10.

None of the other options (A), (C), or (D) accurately reflects the IQR and range of the dataset shown.(option-b).

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Answer:

Step-by-step explanation:

You want the lengths of the unknown sides in the given trapezoid figure, knowing that the perimeter is 18 units.

The side AB is a vertical line segment, so its length can be found by finding the difference of y-coordinates of its end points.

  AB = (2) -(-4) = 2+4 = 6

The length of AB is 6 units.

The sum of the lengths of vertical and horizontal segments is ...

  AB +BC +CD = 6 +4 +3 = 13

The total distance from A to D along vertical and horizontal segments is 13 units.

The perimeter is the sum of the lengths of all sides.

  perimeter = AB +BC +CD +AD

  18 = 13 + AD . . . . . . substitute known values

  5 = AD . . . . . . . . . subtract 13

The length of segment AD is 5 units.

__

Additional comment

Finding the length of a vertical or horizontal line is no different than finding the distance between two points on a number line.

By looking at the graph of the linear equation, we conclude that the y-value for x = -3, is y = -9

Here we have the graph of a linear equation. What the graph tells us is "what is the value of y for each value of x".

So, if we  want to find the value of y when we have x = -3, then:

Following these steps, you should be able to see that, when x = -3, the value of y is -9

So we conclude that the y-value for x = -3, is y = -9

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Step-by-step explanation:

The probability of selecting a defective watch is 400/10,000 = 2/50.

The probability of selecting 50 defective watches out of 100 selected is given by the binomial distribution:

(100 choose 50) * (2/50)^50 * (1/2)^(100-50) = 0.072.

So the probability that exactly 50 out of 100 selected watches are defective is approximately 0.072.

Answer:

35.625 pounds

Step-by-step explanation:

First, find the weight of the other truck by multiplying 30 by 3/16:

30(3/16)

= 5.625

Then, add this to the weight of the other truck:

30 + 5.625

= 35.625

So, if both trucks were combined, the weight will be 35.625 pounds

Answer:

Step-by-step explanation:

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

75

Step-by-step explanation:

This process required 3 to be subtracted 5 consecutive times, so again we see that 15 ÷ 3 = 5. The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient.

Division is a simple operation in which a number is divided. It's easiest to think of it as a number of objects being divided among a certain number of people.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

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Answer:

das

Step-by-step explanation:

adsasc

Part 5

Use either loading or unloading methods.

Since the two factors are not significant. So, use either loading or unloading methods.

The null and alternative hypotheses can be defined as follows:

The null hypothesis,

H_0: There is no significance difference between two levels of method at 5% level of significance.

Against alternative hypothesis,

H_a: There is significant difference between two levels of method at 5% level of significance.

From the ANOVA table, the P-value for factor A is 0.315.

Since, 0.315 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significant difference between two levels of method of main effect at 5% level of significance.

Part 2

The P-value is 0.315.

There is no significant difference between two levels of method of main effect at 5% level of significance.

Explanation

Since, 0.315 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significant difference between two levels of the method of main effect at 5% level of significance.

Step 3/5

(3)

The null and alternative hypotheses can be defined as follows:

The null hypothesis,

H_0: There is no significance difference between three types of rides at 5% level of significance.

Against alternative hypothesis,

H_a: There is significant difference between three types of rides at 5% level of significance.

From the ANOVA table, the P-value for factor B is 0.687.

Since, 0.687 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significance difference between three types of ride at 5% level of significance.

Part 3

The P-value is 0.687.

There is no significance difference between three types of ride at 5% level of significance.

Since, 0.687 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significant difference between three types of ride at 5% level of significance.

Step 4/5

(4)

The null and alternative hypotheses can be defined as follows:

The null hypothesis,

H_0: There is no significance difference of interaction between method and ride at 5% level of significance.

Against alternative hypothesis,

H_a: There is significance difference of interaction between method and ride at 5% level of significance.

From the ANOVA table, the P-value for integration of factor A and factor B is 0.138.

Since, 0.138 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significant difference that the interaction between loading and unloading method and types of ride at 5% level of significance.

Part 4

The P-value is 0.138.

There is no significant difference that the interaction between loading and unloading method and types of ride at 5% level of significance.

Explanation

Hint for Next Steps

Since, 0.138 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significant difference that the interaction between loading and unloading method and types of ride at 5% level of significance.

Step 5/5

(5)

Since, the two factors are not significant. So, use either loading or unloading methods.

Part 5

Use either loading or unloading methods.

Since the two factors are not significant. So, use either loading or unloading methods.

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Answer:

\(\theta = 148.8\)

Step-by-step explanation:

Given

\(R_x = -419\)

\(R_y = -253\)

\(R = 490\)

Required

Determine the value of \(\theta\)

Since, \(\theta\) is counter clockwise from x axis;

The relationship between \(\theta\), \(R_x\) and R is

\(cos\theta = \frac{R_x}{R}\)

Substitute values for Rx and R

\(cos\theta = \frac{-419}{490}\)

\(cos\theta = -0.8551\)

Take arccos of both sides

\(\theta = cos^{-1}(-0.8551)\)

\(\theta = 148.770784108\)

\(\theta = 148.8\) (Approximated)

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

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

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

$980

Step-by-step explanation:

Answer:

$980

Step-by-step explanation:

This is 980.17 the 17 is the decimal spot. what is 17 rounded to? for tens place it will be 0. The number line pushes the numbers in the tens from 10 to 49. If it gets to 50 then it goes up. however if it stays at 49 or lower the number goes down.

980 is the answer. Hope This Helps!

Using translation concepts, the trigonometric graph is given by:

y = sin(x) + 1 = 1sin(1x) + 1.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The parent function given in this problem is:

y = sin(x).

The dashed line is a shift up one unit of the parent function, hence the definition is:

y = sin(x) + 1 = 1sin(1x) + 1.

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The number that can complete the equation 5y + 2(3y − 1) = ⬜y − (y + 2) is

5y + 2(3y − 1) = 12 y − (y + 2)

The number that can complete the equation is computed by simplifying the equation at the left hand side of the equality sign and comparing with the right side of the equality side

The comparison will show the number that can fit in the blank

Simplifying the equation at the left hand side of the equation

= 5y + 2(3y − 1)

= 5y + 6y − 2

= 11y - 2

Simplifying the equation at the right hand side of the equation

=  ⬜y − (y + 2)

let x represent the missing number

=  xy − (y + 2)

=  xy − y - 2

comparing both equations

11y - 2 =  xy − y - 2

11y =  xy − y

11y + y =  xy

12y = xy

x = 12

The missing value = 12

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Answer: 2.3 round to cent = 2

Step-by-step explanation:

Answer: $24.71 per hour before raise

Step-by-step explanation: 25.74 - 4% or 25.74 x 0.04 since you are trying to figure out the total pay per hour before the 4% raise

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

5/8

Step-by-step explanation:

You can divide both numbers by 2! Thus making 5/8 10/16's lowest term!

Have a great day and remember to take breaks! I'm proud of you! :D

Answer:

im sorry for anwering this question you may now report me im so sorry

Answer:

the square root of 144 is 12

Answer:

\(\large \boxed{\sf \ \ \sqrt{3x^4}\cdot \sqrt{5x^2}\cdot \sqrt{10}=5x^3\sqrt{6} \ \ }\)

Step-by-step explanation:

Hello,

First, of all, as x is positive we know that:

\((\sqrt{x})^2=|x|=x\)

Let's simplify the expression:

\(\sqrt{3x^4}\cdot \sqrt{5x^2}\cdot \sqrt{10}=\sqrt{3}\cdot x^2\cdot \sqrt{5}\cdot x\cdot \sqrt{2\cdot 5}=x^3\cdot \sqrt{3\cdot 5\cdot 5 \cdot 2}\\ \\=5x^3\sqrt{6}\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you