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3 years ago

Through which angle of rotation does the image of a regular pentagon coincide with its preimage?

1 answer:

4 0

Answer: 72° or any muliple of it: 72°, 144°, 216°, 288°, 360°, ...

It can be either clockwise or counterclockwise.

Explanation:

Thi is because a regular pentagon has 5 congruent sides.

Then you determine the angle of rotation by dividing 360° (a complete turn) by the number of sides (5)

360° / 5 = 72°.

Then every 72° the segments of the image will overlap those of the preimage.

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Skylar wanted to show the proportional relationship between the dollar value of the original investment, x, and its value after

suter [353]

After checking the information of the table, it is to notice that the table fulfills the behavior of a direct relationship described by the linear equation y = 0.9 · x. #SPJ1

<h3>How to analyze a relationship between the two variables</h3>

Let be x and y the original investment and the value after applying the change, both in monetary units. A direct relationship is observed by following this model:

y = (1 + r/100) · x (1)

Where r is change rate, in percentual units.

<h3>Remark</h3>

The table of the change in investment with respect to initial investment is missing and is now introduced below:

(x₁, y₁) = (75, 7.5), (x₂, y₂) = (100, 10), (x₃, y₃) = (200, 20), (x₄, y₄) = (300, 30), (x₅, y₅) = (400, 40)

To learn more on direct relationships, we kindly invite to check this: brainly.com/question/14293770 #SPJ1

6 0

2 years ago

Find the length of AC round to the nearest hundred

Nataly [62]

Answer:

Option B. 9.11

Step-by-step explanation:

To find the length of line AB, we must first of all calculate the value of θ as shown in the attached photo.

The value of θ can be obtained as follow:

θ + 39° + 120° = 180° (sum of angles in a triangle)

θ + 159° = 180°

Collect like terms

θ = 180° – 159°

θ = 21°

Thus, we can obtain the length of line AB by using sine rule as illustrated below:

b/Sine B = c/Sine C

b = 16

Angle B = 39°

Sine C = 21°

c =?

b/Sine B = c/Sine C

16/Sine 39° = c/Sine 21°

Cross multiply

c × Sine 39° = 16 × Sine 21°

Divide both side by Sine 39°

c = (16 × Sine 21°) / Sine 39°

c = 9.11

Therefore, the length of line AB is 9.11

7 0

2 years ago

Please help me!!!!!!!!!!

Alex

The answer is C. 20.3 miles per hour.

In order to solve this, we have to first convert our time into hours. We start with 11 seconds, but need to convert to hours. Since there are 3600 seconds in an hour, we need to divide by that unit rate.

11 seconds/3600 = .00305 hours

Now we need to convert our meters into miles. The problem lets us know that there are 1609 meters in a mile, so we need to divide the 100 meters by 1609.

100 meters/1609 = .0621 miles.

Now to find miles per hour, we divide the miles we got by the hours.

.00305 miles/ .0621 miles = 20.3 miles per hour.

5 0

2 years ago

Find all values of x that make the triangles congruent. Explain your reasoning.

RSB [31]

Answer:

x = $\frac{4}{5},5$

Step-by-step explanation:

If both the triangles ΔABC and ΔBCD are congruent,

Corresponding sides of both the triangles will be proportional.

$\frac{AB}{BD}=\frac{AC}{CD}$

$\frac{5x}{3x+10}=\frac{5x-2}{4x+3}$

5x(4x + 3) = (5x - 2)(3x + 10)

20x² + 15x = 15x² + 50x - 6x - 20

20x² + 15x = 15x² + 44x - 20

20x² - 15x² = 44x - 15x - 20

5x² = 29x - 20

5x² - 29x + 20 = 0

5x² - 25x - 4x + 20 = 0

5x(x - 5) - 4(x - 5) = 0

(5x - 4)(x - 5) = 0

$x=\frac{4}{5},5$

3 0

2 years ago

Find the mode, median, and mean of the following data and match them with their appropriate result provided below 3,12,11,7,5,5,

WARRIOR [948]

Answer:

Mean: 6.6

Mode: 5

Median: 5.5

7 0

2 years ago