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just olya [345]
3 years ago
6

A figure is reflected over the y-axis. Which of the following are true? The pre-image and image are congruent. The y-coordinates

' signs change. The x-coordinates' signs change. The x-axis is the line of reflection.
Mathematics
1 answer:
serg [7]3 years ago
3 0
When a reflection occurs, the original graph and the reflected graph are mirror images of each other. So, when the graph is reflected about the y-axis, think of the y-axis as the mirror. When you fold the graph length-wise, you will see that both graphs would coincide. Thus, their y-coordinate would not change. It would only change to the opposite quadrant, thereby changing the signs of the x-coordinates. So, as a rule, during reflection, the coordinates (x,y) is changed to (-x,y).

Therefore, the answer is:<span>The x-coordinates' signs change..</span>
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2 years ago
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Answer:

c.negative

True, by definition since the variance take in count the differences around the mean squared, then we can't have a negative value for a sum of square values.

Step-by-step explanation:

We need to remember that the variance is a measure of dispersion for a dataset respect to a measure of central tendency called the mean. The mean is defined as:

\bar x = \frac{\sum_{i=1}^n X_i}{n}

And the population mean is given by:

\mu= \frac{\sum_{i=1}^n X_i}{N}

The population variance is defined by:

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And the sample variance is defined as:

s^2= \frac{\sum_{i=1}^n (X_i -\bar x)}{n-1}

Now if we analyze the options we have this:

a.zero

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b.larger than the standard deviation

False, if the population standard deviation is \sigma=2 then the variance would be \sigma^2 = 4 and as we can see is higher than the standard deviation

c.negative

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d.smaller than the standard deviation

False, if the population standard deviation is \sigma=0.1 then the variance would be \sigma^2 = 0.01 and as we can see is lower than the standard deviation

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