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insens350 [35]
3 years ago
14

Which sequence of transformations carries ABCD onto HGFE

Mathematics
2 answers:
trasher [3.6K]3 years ago
7 0
If you look closely at the options, the first 3 options will not produce an image that will be in Quadrant II with the vertices coinciding HGFE.
But if you look at the 4th option, translating the points 8 units to the left will produce an image in Quadrant III. Reflecting the image across the x-axis will produce triangle HGFE.
Lady_Fox [76]3 years ago
4 0

Answer:

The correct option is D.

Step-by-step explanation:

It is given that the after transformation figure ABCD onto HGFE. It means HGFE is image of ABCD after transformation.

From the figure it is noticed that A(2,-1) and H(-6,1).

Rotation of 90 degree clockwise about the origin followed by the reflection across the x-axis is expressed as

(x,y)\rightarrow (y,-x)\rightarrow (y,x)

Therefore the image of A(2,-1) is (-1,2), which are not the coordinates of H. Option A is incorrect.

Translation 3 unit up followed by the reflection across the y-axis is expressed as

(x,y)\rightarrow (x,y+3)\rightarrow (-x,y+3)

Therefore the image of A(2,-1) is (-2,2), which are not the coordinates of H. Option B is incorrect.

Reflection across the x-axis followed by rotation of 90 degree counterclockwise about the origin is expressed as

(x,y)\rightarrow (x,-y)\rightarrow (y,x)

Therefore the image of A(2,-1) is (-1,2), which are not the coordinates of H. Option C is incorrect.

Translation 8 unit left followed by reflection across the x-axis is expressed as

(x,y)\rightarrow (x-8,y)\rightarrow (x-8,-y)

Therefore the image of A(2,-1) is (-6,1), which are the coordinates of H. Option D is correct.

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According to an article in Newsweek, the rate of water pollution in China is more than twice that measured in the US and more th
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Answer:

(a) 0.119

(b) 0.1699

Solution:

As per the question:

Mean of the emission, \mu = 11.7 million ponds/day

Standard deviation, \sigma = 2.8 million ponds/day

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(b) The probability when the water pollution is in between 6.2 and 9.3 million pounds/day:

P(6.2 < X < 9.3) = P(\frac{6.2 - 11.7}{2.8} < \frac{X - \mu}{\sigma} < \frac{9.3 - 11.7}{2.8})

P(6.2 < X < 9.3) = P(- 1.96 < Z < - 0.86)

P(6.2 < X < 9.3) = P(- 1.96 < Z < - 0.86)

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