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Elanso [62]
3 years ago
8

On the coordinate plane, ΔABC ≅ ΔDEF by SSS. ΔABC translates 2 units to the left and 3 units down. Do the triangles remain congr

uent? Explain why or why not.
Mathematics
2 answers:
MrRissso [65]3 years ago
8 0
Yes because you are simply translating the shape and moving it and not changing the shape.
elena55 [62]3 years ago
4 0

Answer: Yes, they are congruent.

Step-by-step explanation:

Given: On the coordinate plane, ΔABC ≅ ΔDEF by SSS...........(1)

ΔABC translates 2 units to the left and 3 units down.

Let ΔA'B'C' be the translated image of ΔABC.

  • A translation is rigid transformation that maps every point of a figure by the same distance in a given direction.

Since, all the rigid transformations create congruent images.

Hence, ΔA'B'C'≅ΔABC.........................(2)

From (1) and (2), we have

A'B'C'≅ΔDEF   [Transitive property of equality]

Therefore, the triangles remains congruent.

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He was confirmed as a justice in the year 1973.

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3 years ago
Assume that a computer was used to generate the given confidence interval for the population mean. Find the sample mean or margi
stealth61 [152]

Answer:

The sample mean is

b.3.55

The margin of error is

0.32

Step-by-step explanation:

Deep explanation about a confidence interval

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

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M = z*\frac{\sigma}{\sqrt{n}}

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M = 1.645*215 = 353.675

The lower end of the interval is the mean subtracted by M. So it is 6.4 - 0.3944 = 6.01 hours.

The upper end of the interval is the mean added to M. So it is 6.4 + 0.3944 = 6.74 hours.

In this problem:

The deep explanation is not that important.

We just have to recognize that the interval has a lower end and an upper end. The distance from both the upper and the lower end to the mean is M. This means that the sample mean is the halfway point between the lower end and the upper end.

The margin of error is the distance of these two points(lower and upper end) to the mean.

In our interval

Lower end: 3.23

Upper end: 3.87

Sample mean

M = \frac{3.23 + 3.87}{2} = 3.55

So the correct answer is:

b.3.55

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3 years ago
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vlabodo [156]
K+3=-9
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