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3 years ago

Which rotation about its center will carry a regular decagon onto itself

Mathematics

2 answers:

timofeeve [1]3 years ago

8 0

Answer:

The answer is any multiple of 36.

Step-by-step explanation:

A decagon has 10 sides, and it has 10 exterior angles of 36° as can be seen in the picture.

Therefore, by rotating the decagon about its center by multiples of 36° will carry a regular decagon onto itself.

Any multiple of 36 could be: 36, 72, 108, 144, 180, 216, 252, 288, etc...

snow_lady [41]3 years ago

3 0

A decagon has 10 sides so every 36 degrees, you would encounter another side.
So, the answer is a 36 degree rotation.

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P (6,6) y=2/3x

matrenka [14]

Answer:

$y = -\frac{3}{2}x+15$

Step-by-step explanation:

Given:

Given point P(6, 6)

The equation of the line.

$y = \frac{2}{3}x$

We need to find the equation of the line perpendicular to the given line that contains P

Solution:

The equation of the line.

$y = \frac{2}{3}x$

Now, we compare the given equation by standard form $y = mx +c$

So, slope of the line $m_{1} = \frac{2}{3}$ , and

y-intercept $c=0$

We know that the slope of the perpendicular line $m_{1}\times m_{2} = -1$

$m_{2}=-\frac{1}{m_{1}}$

$m_{2}=-\frac{1}{\frac{2}{3} }$

$m_{2}=-\frac{3}{2}$

So, the slope of the perpendicular line $m_{2}=-\frac{3}{2}$

From the above statement, line passes through the point P(6, 6).

Using slope intercept formula to know y-intercept.

$y=mx+c$

Substitute point $P(x_{1}, y_{1})=P(6, 6)$ and $m = m_{2}=-\frac{3}{2}$

$6=-\frac{3}{2}\times 6 +c$

$6=-3\times 3 +c$

$c=6+9$

$c=15$

So, the y-intercept of the perpendicular line $c=15$

Using point slope formula.

$y=mx+c$

Substitute $m = m_{2}=-\frac{3}{2}$ and $c=15$ in above equation.

$y = -\frac{3}{2}x+15$

Therefore: the equation of the perpendicular line $y = -\frac{3}{2}x+15$

8 0

3 years ago

Correct answer will get brainliest and full ratings.

DochEvi [55]

It's A. I'm pretty sure.

6 0

3 years ago

Read 2 more answers

Use the following function rule to find f(0). f(x)= -9 (3)^x f (0 ) =

AlladinOne [14]

Step-by-step explanation:

Substitute f(0) into the function:

$f(0) = - 9(3)^{0}$

Include exponent:

$f(0) = - 9(1)$

Multiply:

$f(0) = - 9$

7 0

1 year ago

Solve: 3/5y + 3 = 11 + 1/5y

ale4655 [162]

Answer:

Y=20

Step-by-step explanation:

y equals 20 because you simplify both sides of the equation then you have an isolated variable

7 0

2 years ago

Read 2 more answers

What is the image of (2,3)(2,3) after a reflection over the line y=-xy=−x?

otez555 [7]

Answer:

After the reflection over the line y = -x, the image of the point is: (-3,-2)

Step-by-step explanation:

When a given point is reflected over a line the point only changes place but the distance between the point and the line remains same.

Let (x,y) be a point on the plane

and

y = -x be a line on the plane

When a point is reflected over a line y = -x , the coordinates of the point are exchanged which means x becomes y and y becomes x and both are negated

So (x,y) will become (-y,-x)

Given point is:

(2,3)

After the reflection over the line y = -x, the image of the point is: (-3,-2)

4 0

3 years ago