<u><em>Answers:</em></u>
The corresponding angles of the triangles are congruent
The image is a reduction of the pre-image
Neither the dilation nor the rotation change the shape of the triangle
<u><em>Explanation:</em></u>
<u>For shapes to be similar:</u>
1- there should be a ratio between the sides
2- angles in first shape should be congruent to angles in second shape
Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes
<u>Let's check the choices:</u>
<u>1- </u><span><u>The corresponding sides of the triangles are congruent:</u>
This option is incorrect as dilation changes the lengths of the sides
<u>2- </u></span><span><u>The corresponding angles of the triangles are congruent:</u>
This option is correct as neither dilation nor rotation alters the measures of the angles
<u>3- </u></span><span><u>The corresponding sides of the image are 5 times as long as those of the pre-image:</u>
This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image
<u>4- </u></span><span><u>The image is a reduction of the pre-image:</u>
This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced
<u>5- </u></span><span><u>Neither the dilation nor the rotation change the shape of the triangle:</u>
This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)
<u>6- </u></span><u>The rotation reduces the size of the triangle:</u>
This option is incorrect as rotation does not alter the size of the shape. It only changes its position
Hope this helps :)
<h3>
Answer: Mean = 218.9.</h3><h3>Median = 229</h3><h3>Mode = Zero mode.</h3>
Step-by-step explanation:
Given blood cholesterol level was measured for each of 8 adults (in mg/dL) are:
264, 191, 160, 148, 262, 212, 268, 246
In order to find the mean, we need to add all those 8 numbers and divide by 8.
Therefore, mean = 
<h3>Mean = 218.9.</h3>
In order to find the median, we need to arrange them in ascending order:
148, 160, 191, 212, 246, 262, 264, 268.
The middle most two values are 212 and 246.
Therefore, median = 
<h3>Median = 229.</h3>
<h3>Therefore, Mode = Zero mode.</h3>
Given:
The function that represents how the amount of fuel changes as a function of distance flown is
where x represents miles flown, and f(x) represents the amount of fuel remaining.
To find:
The rate of change for this scenario.
Solution:
The slope intercept form of a linear function is
...(i)
Where, m is the slope or rate of change and b is the y-intercept.
We have,
...(ii)
On comparing (i) and (ii), we get
Therefore, the rate of change for this scenario is -0.9. It means, the amount of fuel in the airplane is decreasing by 0.9 gallons per mile.
