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3 years ago

What sequence of transformations, when applied to △XYZ , shows that △XYZ is similar to △X′Y′Z′ ?

Mathematics

2 answers:

jek_recluse [69]3 years ago

8 0

Answer:

dilation with respect to the origin by a scale factor of 2 followed by a translation of 4 units down

Step-by-step explanation:

stiks02 [169]3 years ago

4 0

The coordinates of Δxyz ⇒⇒ x(1,1)     y(2,3)    z(3,2)
The coordinates of Δx'y'z' ⇒⇒ x'(2,-2)   y'(4,2)    z'(6,0)

1. Applying the transformation of the first sentence on Δxyz
The results are ⇒⇒⇒ (2,-2)   (4,2)    (6,0)

2. Applying the transformation of the second sentence on Δxyz
The results are ⇒⇒⇒ (12,14)   (24,38)    (36,28)

3. Applying the transformation of the third sentence on Δxyz
The results are ⇒⇒⇒ (12,-36)   (24,-12)    (36,-24)

4. Applying the transformation of the fourth sentence on Δxyz
The results are ⇒⇒⇒ (2,-6)   (4,-2)    (6,-4)

By comparing the results obtained with the coordinates of Δx'y'z'
So, the correct answer is the first sentence.
<span>dilation with respect to the origin by a scale factor of 2 followed by a translation of 4 units down</span>

You might be interested in

In Exercises 37– 40, BD ⃗ bisects ∠ABC. Find m∠ABD,<br><br>m∠CBD, and m∠ABC.

MrRissso [65]

Answer:

37, ABD = CBD = 44 degrees, and ABC = 88 degrees

38. ABD = CBD = 24 degrees, and ABC = 48 degrees

39. ABD = CBD = 65 degrees, and ABC = 130 degrees

40. ABD = CBD =67 degrees, and ABC = 134 degrees

Step-by-step explanation:

Recall that when a segment bisects an angle, the angle is divided in equal parts then we have:

37.

6 x + 14 = 3 x + 29

3 x = 19 - 14 = 15

x = 15/3

x = 5

then ABD = 6 (5) + 14 = 30 + 14 = 44 degrees

CBD must equal ABD , so CBD = 44 degrees

And the total angle ABC = 88 degrees

38.

3 x + 6 = 7 x - 18

24 = 4 x

x = 24/4 = 6

Then ABD = 3 (6) + 6 = 24 degrees. Also CBD = 24 degrees and ABC = 48 degrees

39.

- 4 x + 33 = 2 x + 81

- 6 x = 81 - 33

-6 x = 48

x = - 48/6

x = -8

Then ABD = -4 (-8) + 33 = 32 + 33 = 65 degrees

The also CBD = 65 degrees, and ABC = 130 degrees

40.

8 x + 35 = 11 x + 23

35 - 23 = 11 x - 8 x

12 = 3 x

x = 12/3

x = 4 degrees

Therefore:

ABD = 8 (4) + 35 = 32 + 35 = 67 degrees.

Then also CBD = 67 degrees, and ABC = 134 degrees

3 0

3 years ago

You have 8,640 grams of a radioactive kind of cesium. If its half-life is 30 years, how much

Vikki [24]

The mass of cesium left afer 120 years if the original mass of cesium is 8640 with an half-life of 30 years, is 540 grams.

This can be defined as the time taken for half the amount of a radioactive substance to decay.

To calculate the amount of cesium left after 120 years, we use the formua below.

Formula:

R' = R/( $2^{T/t}$ )............. Equation 1

Where:

R = Original amount of Cesium
R' = New amount of cesium
T = Total time
t = Half-life

From the question,

Given:

R = 8640
T = 120 years
t = 30 years

Substitute these values into equation 1

R' = 8640/( $2^{120/30}$ )
R' = 8640/ $2^{4}$
R' = 8640/16
R' = 540 grams.

Hence, The mass of cesium left afer 120 years is 540 grams.

Learn more about half-life here: brainly.com/question/25750315

4 0

2 years ago

Find the slope of the line that passes

Veseljchak [2.6K]

Answer:

-1/3 or -2/6

Step-by-step explanation:

First, you pick two points, I did (-5,10) and (1,8). Then, because slope is y(2)-y(1)/ x(2)-x(1), the equation would be 8-10/1-(-5) which equals -2/6 which simplifies into -1/3.

(hope this helps!)

4 0

3 years ago

The cube of the sum of 3 and k

denis23 [38]

3k^3 should be the answer.

7 0

3 years ago

POINTS X, Y and Z are COLLinear. You are given

Anon25 [30]

Answer:

129

Step-by-step explanation:

Collinear means that the points X, Y, and Z are on the same line. The question asks for one possible value of YZ, so for this, let's assume point X is between Point Y and Point Z.

This means...

XY+XZ=YZ

54+75=YZ

YZ=129

5 0

2 years ago