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4 years ago

12

What if you divide the hexagon into 3 equal parts? Write a sentence that compares the area of each equal part of the hexagon to

each equal part of the trapezoid

1 answer:

borishaifa [10]4 years ago

7 0

I have no idea. I cannot answer all of these questions??!!!?!?!?!

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After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(6,3), B'(-2, 1)

topjm [15]

Rotation 90° counterclockwise about the origin

The coordinates of the pre-image are A (3 , -6) , B (1 , 2) , C (7 , -1)

Rotation 90° clockwise about the origin

The coordinates of the pre-image are A (-3 , 6) , B (-1 , -2) , C (-7 , 1)

Step-by-step explanation:

Let us revise the rotation

1. If point (x , y) rotated about the origin by angle 90° counter-clockwise

then its image is (-y , x)

2. If point (x , y) rotated about the origin by angle 90° clock wise

then Its image is (y , -x)

The given is:

After a rotation of 90° about the origin, the coordinates of the vertices

of the image of a triangle are A' (6 , 3), B' (-2 , 1) and C' (1 , 7)

We need to find the coordinates of the pre-image

There is no mention about the rotation counterclockwise or clockwise,

then we will do both

∵ The rotation is 90° counterclockwise about the origin

∵ Point A (x , y) and its image A' (-y , x)

∵ A' = (6 , 3)

∴ -y = 6 and x = 3

∵ -y = 6 ⇒ multiply both sides by -1

∴ y = -6

∴ Point A is (3 , -6)

∵ Point B (x , y) and its image B' (-y , x)

∵ B' = (-2 , 1)

∴ -y = -2 and x = 1

∵ -y = -2 ⇒ multiply both sides by -1

∴ y = 2

∴ Point B is (1 , 2)

∵ Point C (x , y) and its image C' (-y , x)

∵ C' = (1 , 7)

∴ -y = 1 and x = 7

∵ -y = 1 ⇒ multiply both sides by -1

∴ y = -1

∴ Point C is (7 , -1)

The coordinates of the pre-image are A (3 , -6) , B (1 , 2) , C (7 , -1)

∵ The rotation is 90° clockwise about the origin

∵ Point A (x , y) and its image A' (y , -x)

∵ A' = (6 , 3)

∴ y = 6 and -x = 3

∵ -x = 3 ⇒ multiply both sides by -1

∴ x = -3

∴ Point A is (-3 , 6)

∵ Point B (x , y) and its image B' (y , -x)

∵ B' = (-2 , 1)

∴ y = -2 and -x = 1

∵ -x = 1 ⇒ multiply both sides by -1

∴ x = -1

∴ Point B is (-1 , -2)

∵ Point C (x , y) and its image C' (y , -x)

∵ C' = (1 , 7)

∴ y = 1 and -x = 7

∵ -x = 7 ⇒ multiply both sides by -1

∴ x = -7

∴ Point C is (-7 , 1)

The coordinates of the pre-image are A (-3 , 6) , B (-1 , -2) , C (-7 , 1)

Learn more:

You can learn more about rotation in brainly.com/question/3779181

#LearnwithBrainly

3 0

4 years ago

An equation of an ellipse is given. x2 16 + y2 25 = 1 (a) Find the vertices, foci, and eccentricity of the ellipse. vertex (x, y

eimsori [14]

Answer:

(a)

The vertices are at (0,-5) and (0,5).
The coordinates of the foci are (0,-3) and (0,3).
Eccentricity=3/5

(b)Length of the major axis=10

Step-by-step explanation:

When the major axis of an ellipse is parallel to the y-axis.The standard form of the equation of an ellipse is given as:

$\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1$

Given the equation:

$\dfrac{x^2}{16}+\dfrac{y^2}{25}=1$

(I)The coordinates of the vertices are $(0, \pm a)$

$a^2=25\\a^2=5^2\\a=5$

Therefore, the vertices are at (0,-5) and (0,5).

(II)The coordinates of the foci are $(0, \pm c)$ where c^2=a^2-b^2$

$c^2=a^2-b^2\\c^2=25-16\\c^2=9\\c=3$

The coordinates of the foci are (0,-3) and (0,3).

(III)Eccentricity

This is the ratio of the distance c between the center of the ellipse and each focus to the length of the semi major axis.

Simply put, Eccentricity =c/a

Eccentricity=3/5

(b)Length of the major axis

The length of the major axis=2a

=2(5)=10.

4 0

3 years ago

The ratio of men to women working for a company is 7 to 5 . if there are 105 men working for the company, what is the total numb

babunello [35]

There are 42 males and 70 females

4 0

3 years ago

Jordan needs to write a 20-page

____ [38]

The answer is 2 pages.

5 0

3 years ago

I need the answer ASAP! Please help me!

masha68 [24]

Answer:

Please check the explanation.

Step-by-step explanation:

<u>Determining the length of BC</u>

From the diagram, it is clear that

The point B is located at (-8, 10) and point C is located at (8, 10)

Since points A and C are located on a horizontal straight line. Thus, the length of BC can be determined by counting the x-axis units from reaching x = -8 to x = 8. i.e. 8-(-8) = 8+8 = 16

Thus, the length of BC = 16 units

<u>Determining the length of CD</u>

Given

C (8, 10)

D (2, -2)

The distance between C(8, 10) and D(2, -2)

$\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$CD=\sqrt{\left(2-8\right)^2+\left(-2-10\right)^2}$

$=\sqrt{6^2+12^2}$

$=\sqrt{36+144}$

$=\sqrt{180}$

$=\sqrt{36\times 5}$

$=6\sqrt{5}$

Thus, the length of CD $=6\sqrt{5}$ units

<u>Determining the length of ED</u>

Given

E (-8, -4)

D (2, -2)

The distance between E(-8, -4) and D(2, -2)

$ED=\sqrt{\left(2-\left(-8\right)\right)^2+\left(-2-\left(-4\right)\right)^2}$

$=\sqrt{10^2+2^2}$

$=\sqrt{100+4}$

$=\sqrt{104}$

$=\sqrt{26\times \:4}$

$=2\sqrt{26}$

Thus, the length of ED $=2\sqrt{26}$ units

<u>Determining the length of EB</u>

From the diagram, it is clear that

The point E is located at (-8, -4) and the point B is located at (-8, 10)

Since points E and B are located on a vertical straight line. Thus, the length of EB can be determined by counting the y-axis units from reaching y = -4 to y = 10. i.e. 10-(-4) = 10+4 = 14

Thus, the length of EB = 14 units

4 0

3 years ago