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3 years ago

A triangle has the following vertices (-1,1), (6,-2)and (3,5) if the scale factor of 3, what will be the vertices of the image

Mathematics

1 answer:

olga2289 [7]3 years ago

4 0

Answer:

a. (-3,3), (18,-6), (9,15)

Step-by-step explanation:

If the scale factor is 3 and dilation is about the origin, each of the coordinates of the pre-image is multiplied by 3 to get the coordinates of the image.

Multiplying (-1, 1) by 3 gives (-3, 3), which matches choices A and C.

Multiplying (6, -2) by 3 gives (18, -6) which matches choices A and D.

The only viable choice is choice A.

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Find the central angle of a sector of a circle of the area of the sector and the area of the circle are in the proportion of 3:5

abruzzese [7]

Answer:

$\theta = 216$

Step-by-step explanation:

Given

Area of Sector : Area of Circle = 3 : 5

Required

Determine the central angle

The question implies that

$\frac{Area_{sector}}{Area_{circle}} = \frac{3}{5}$

Multiply both sides by 5

$5 * \frac{Area_{sector}}{Area_{circle}} = \frac{3}{5} * 5$

$5 * \frac{Area_{sector}}{Area_{circle}} = 3$

Multiply both sides by Area{circle}

$5 * \frac{Area_{sector}}{Area_{circle}} * Area_{circle} = 3 * Area_{circle}$

$5 * {Area_{sector} = 3 * Area_{circle}$

Substitute the areas of sector and circle with their respective formulas;

$Area_{sector} =\frac{\theta}{360} * \pi r^2$

$Area_{circle} = \pi r^2$

So, we have

$5 * \frac{\theta}{360} * \pi r^2 = 3 * \pi r^2$

Divide both sides by $\pi r^2$

$5 * \frac{\theta}{360} * \frac{ \pi r^2}{\pi r^2} = 3 * \frac{\pi r^2}{\pi r^2}$

$5 * \frac{\theta}{360} = 3$

Multiply both sides by 360

$360 * 5 * \frac{\theta}{360} = 3 * 360$

$5 * \theta = 3 * 360$

Divide both sides by 5

$\frac{5 * \theta}{5} = \frac{3 * 360}{5}$

$\theta = \frac{3 * 360}{5}$

$\theta = \frac{1080}{5}$

$\theta = 216$

Hence, the central angle is 216 degrees

3 0

3 years ago

Need help with homework

zubka84 [21]

Answer:

5. the other angle has to be 2x because of the other lines being equals so

2x+2x+x-15=180

5x-15=180

5x=195

x=19

6. the other two angle is ajacent to the other two so

3x+17+3x+17+x-9+x-9=360

8x+16=360

8x=344

x=43

7. this ones pretty simple

2x-4+3x+5+2x+11=180

7x+12=180

7x=168

x=24

8. this one to

x+x+4+3x-9=90

5x+5=90

5x=85

x=17

Hope This Helps!!!

5 0

2 years ago

Write an equation of the line in slope-intercept from?

netineya [11]

Answer:

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

Step-by-step explanation:

This is for the first question.

Slope-intercept is:

$y=mx+b$

m - slope

b - y-intercept

We are given the slope of $-\frac{3}{2}$ and a y-intercept of 2.

Plug in the values:

$y=mx+b\rightarrow\boxed{y=-\frac{3}{2}x+2}$

Hope this helps.

4 0

3 years ago

Which answer is correct? Please hurry <3

liq [111]

answer is 4

Es tut mir nicht so leid

6 0

3 years ago

Are these lines parallel

raketka [301]

Answer:

yes, they are parallel.

equation form is:

x=6

y=2

Step-by-step explanation:

7 0

3 years ago