Elena works in an animal

Need urgent help anyone?! The dilation DO,2.5 is applied to triangle ABC below. Use the dilation of triangle ABC and its image t

zavuch27 [327]

A dilation $D_{O,\,k}$ is a dilation with a scale factor, k centered at the origin.

A scale factor, k means that the distance of the image from the the center of dilation is k times the distance of the pre-image from the center of dilation and the size of the image is k times the size of the pre-image.

Given triangle ABC with vertices A(-2, 2), B(1, 2) and C(1, -1), a dilation $D_{O,\,k}$ will result in the image with vertices A'2.5(-2, 2) = A'(-5, 5), B'2.5(1, 2) = B'(2.5, 5) and C'2.5(1, -1) = C'(2.5, -2.5)

Now, consider line AC, the equation of the line is given by

$\frac{y-2}{x-(-2)} = \frac{-1-2}{1-(-2)} \\ \\ \Rightarrow \frac{y-2}{x+2} = \frac{-3}{1+2} = \frac{-3}{3} =-1 \\ \\ \Rightarrow y-2=-(x+2)=-x-2 \\ \\ \Rightarrow y=-x$

Notice that line y = -x is a line passing through the origin which is the center of dilation.

Consider line A'C', the equation of the line is given by

$\frac{y-5}{x-(-5)} = \frac{-2.5-5}{2.5-(-5)} \\ \\ \frac{y-5}{x+5} = \frac{-7.5}{2.5+5} = \frac{-7.5}{7.5} =-1 \\ \\ \Rightarrow y-5=-(x+5)=-x-5 \\ \\ \Rightarrow y=-x$

As an be seen the line AC and the line A'C' is the same line.

5 0

4 years ago

Please give me the answer ASAP.

wel

Answer:

-t+2>10

Step-by-step explanation:

Just ask.

Hope this helps! :D

7 0

2 years ago

The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 m

jeka94

9514 1404 393

Answer:

8000π mm^3/s ≈ 25,133 mm^3/s

Step-by-step explanation:

The rate of change of volume is found by differentiating the volume formula with respect to time.

V = 4/3πr^3

V' = 4πr^2·r'

For the given numbers, this is ...

V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s

_____

<em>Additional comment</em>

By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.

4 0

3 years ago

Help please! will give brainliest! and can please explain.

storchak [24]

Answer: 150

We know that cos Ф = sin (90 - Ф)

If Ф = 150, then:

cos 150 = sin (150 - 90)

cos 150 = sin 60

Using the equation they gave us:

cos 150 = sin ( $\frac{150}{3}$ - 10)

cos 150 = sin 60

4 0

3 years ago

Please Help!!! Its math!

Veronika [31]

Answer:

$159

Step-by-step explanation:

All your doing is adding 45% and a percentage is out of 100 so to put it in decimal form it would be 0.45 added onto 159 which would give you $159.45 rounded to the nearest dollar would be $159

3 0

3 years ago