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IRISSAK [1]
3 years ago
13

Polygon ABCD is dilated, rotated, and translated to form polygon A′B′C′D′. The endpoints of AB are at (0, -7) and (8, 8), and th

e endpoints of AB are at (6, -6) and (2, 1.5). What is the scale factor of the dilation?
Mathematics
1 answer:
Anton [14]3 years ago
8 0

Rotation and translation are rigid transformations, they don't change figure sizes. Dilation change figure sizes increasing or decreasing them by scale factor.

First, find AB and A'B' by the formula:

AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}= \sqrt{(8-0)^2+(8-(-7))^2}=\sqrt{8^2+15^2}=\sqrt{64+225}=\sqrt{289}=17,\\ \\A'B'=\sqrt{(x_{B'}-x_{A'})^2+(y_{B'}-y_{A'})^2}= \sqrt{(2-6)^2+(1.5-(-6))^2}=\sqrt{4^2+7.5^2}=\sqrt{16+56.25}=\sqrt{72.25}=8.5.

As you can see AB=2A'B'. This means that the segment AB was decreased twice to form segment A'B'. Then the scale factor is 1/2.

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Aleks04 [339]

To get the volume, you need the area of the sides of the square.

The total surface area is 96, with 6 sides. To get the surface area of just one side, divide 96 by 6, which gets you 16. The surface area of a single square is 16. To get one side of the square, divide that by 4 because there are 4 sides.

Now, multiply 16 by 4 to get the volume.

The volume is 64 cubed milllimeters.

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6 0
3 years ago
I need to find the area of these shapes
Wewaii [24]

Answer:

1: 374cm

2: 248mm

3: 69m

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3 years ago
Jin tried to evaluate 5 + 2 x 9 step-by-step.
Zigmanuir [339]

Answer:

5 + 2 x 9

Step 1 = 7 x 9

Step 2 = 63

Step-by-step explanation:

= 5 + 2 x 9

= 5 + ( 2 x 9 )

= 5 + 18

= 23

Step 2 = 7 x 9

= 63

Step 3 = 63

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4 0
3 years ago
A cannon ball shoots out from a cannon that is 28 inches long at 2700 ft s. What is the
Reika [66]

Answer:

a = 1565217.39 ft / s ^ 2

t = 0.001725 seconds

Step-by-step explanation:

The first thing is to use the same system of units therefore we will pass the 28 inches to feet, like this:

28 in * (1 ft / 12 in) = 2.33 ft

Now yes, we can continue, we have the following data:

vi = 0

vf = 2700 ft / s

the equations in this case are as follows:

vf = vi + a * t

vf = a * t

rearranging for a

a = vf / t (1)

now with the position equation we know that:

x = vi * t + (a * t ^ 2) / 2

x = (a * t ^ 2) / 2 (2)

now replacing (1) in (2), we are left with:

x = (vf / t) * (t ^ 2) / 2

knowing that x would be 2.33 ft, which is when the cannonball exits the cannon.

2.33 = 2700 * t / 2

t = 2.33 * 2/2700 = 0.001725 seconds.

and now replace in (1)

a = vf / t = 2700 / 0.001725 = 1565217.39 ft / s ^ 2

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3 years ago
In long division what is 601 divided by 3
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