Karisha drew pentagon A on a coordinate grid. She then performed a rotation followed by a dilation with scale factor 5 to produc
e pentagon B. Which is a true statement about the two pentagons? A. They are similar, but not congruent. B. They are neither congruent nor similar. C. They are similar and congruent. D. They are congruent, but not similar.
1 answer:
Answer:
A.
Step-by-step explanation:
Rotation is a transformation that turns a figure about a fixed point. An object and its rotation image are the same shape and size, but the figures may be turned in different directions. So, rotation gives us two congruent pentagons.
Dilation is a transformation that produces an image that is the same shape as the original (similar to original), but is a different size. So, dilation gives us two similar pentagons.
A sequence of rotation and dilation produces pentagon that is similar to the initial, but not congruent.
In attached diagram you can see the pictorial representation:
- pentagon FGHIJ is the rotation image of pentagon ABCDE
- pentagon KLMNO is dilation image of pentagon FGHIJ
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The first three standard deviation for coSport include;
- 1 standard deviation above and below the mean = 6.9 and 6.1
- 2 standard deviation above and below the mean = 7.3 and 5.7
- 3 standard deviation above and below the mean = 7.7 and 5.3
The first three standard deviation for Blockbuster include;
- 1 standard deviation above and below the mean = 5.2 and 4.0
- 2 standard deviation above and below the mean = 5.8 and 3.4
- 3 standard deviation above and below the mean = 6.4 and 2.8
"<em>Check the image I added for the plot of the normal distribution</em>"
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<u>In the given chart;</u>
sample size of the coSport, = 400
the mean of the coSport, M = 6.5
standard deviation of the coSport, d = 0.4
The first standard deviation above and below the mean for coSport is calculated as;
at 34% of the sample size = 0.34 x 400 = 136
above the mean = M + d = 6.5 + 0.4 = 6.9
below the mean = M - d = 6.5 - 0.4 = 6.1
The second standard deviation above and below the mean for coSport is calculated as;
at 14% of the sample size = 0.14 x 400 = 56
above the mean = M + 2d = 6.5 + 2(0.4) = 7.3
below the mean = M - 2d = 6.5 - 2(0.4) = 5.7
The third standard deviation above and below the mean for coSport is calculated as;
at 2% of the sample size = 0.02 x 400 = 8
above the mean = M + 3d = 6.5 + 3(0.4) = 7.7
below the mean = M - 3d = 6.5 - 3(0.4) = 5.3
<u>Also In the given chart;</u>
- sample size of the Blockbuster, = 600
- the mean of the Blockbuster, M = 4.6
- standard deviation of the Blockbuster, d = 0.6
The first standard deviation above and below the mean for Blockbuster is calculated as;
at 34% of the sample size = 0.34 x 600 = 204
above the mean = M + d = 4.6 + 0.6 = 5.2
below the mean = M - d = 4.6 - 0.6 = 4
The second standard deviation above and below the mean for Blockbuster is calculated as;
at 14% of the sample size = 0.14 x 600 = 84
above the mean = M + 2d = 4.6 + 2(0.6) = 5.8
below the mean = M - 2d = 4.6 - 2(0.6) = 3.4
The third standard deviation above and below the mean for Blockbuster is calculated as;
at 2% of the sample size = 0.02 x 600 = 12
above the mean = M + 3d = 4.6 + 3(0.6) = 6.4
below the mean = M - 3d = 4.6 - 2(0.6) = 2.8
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Answer:
C
Step-by-step explanation:
Use the formula for the discriminant.