sarah joined three squares at their vertices to create the figure shown in the diagram. She then covered each of the three squares with square centimeter tiles.

Question

Based on the information, which statement is true?
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A) The number of tiles needed to cover both Region P and Region R is greater than the number of tiles needed to cover Region S.The number of tiles needed to cover both Region P and Region R is greater than the number of tiles needed to cover Region S
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B) The number of tiles needed to cover Region R is the same as the number of tiles needed to cover both Region P and Region S.The number of tiles needed to cover Region R is the same as the number of tiles needed to cover both Region P and Region S .
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C) The number of tiles needed to cover Region S is greater than the number of tiles needed to cover both Region P and Region R.The number of tiles needed to cover Region S is greater than the number of tiles needed to cover both Region P and Region
R
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D) The number of tiles needed to cover Region S is the same as the number of tiles needed to cover both Region P and Region R.

Answer 1

D) The number of tiles needed to cover Region S is the same as the number of tiles needed to cover both Region P and Region R.

Answer 2

Point P is located at (7, 4) on a coordinate grid. Point P is translated 4 units to the left and 8 units down to create point P’.
Which measurement is closest to the distance between point P and point P’ in units?

A) 8.98.9
B) 4040
C) 16.216.2
D) 2.652.65

Answer 3

To find the distance between point P and point P', we can use the distance formula:

d = √((x2-x1)^2 + (y2-y1)^2)

For point P, (x1, y1) = (7, 4), and for point P', (x2, y2) = (7-4, 4-8) = (3, -4)

So, the distance between point P and point P' is:

d = √((3-7)^2 + (-4-4)^2) = √((-4)^2 + (-8)^2) = √(16 + 64) = √80 ≈ 8.94

The closest measurement to this distance is 8.9.

Therefore, the answer is A) 8.9.

Answer 4

Which transformations do not preserve congruence? (Choose 2)
Responses
A) (x, y) → (x+2, y–1)( x , y ) → ( x +2, y– 1)
B) (x, y) → (1/8x, 1/8 y)
C) (x, y) → (–x, –y)( x , y ) → (– x , – y )
D) (x, y) → (x, –y)( x , y ) → ( x , – y )
E) (x, y) → (2.5x, 2.5y)( x , y ) → (2.5 x , 2.5 y )
F) (x, y) → (y, –x)

Answer 5

The transformations that do not preserve congruence are:

E) (x, y) → (2.5x, 2.5y)
F) (x, y) → (y, –x)

Both of these transformations involve scaling or rotating the points, which changes the shape and size of the figures.

Answer 6

Which table shows a proportional linear relationship between x and y?
A)
x | y
6 | 4
12 | 10
18 | 16
24 | 22
28 | 26
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B)
x | y
7 | 15
8 | 17
14 | 29
16 | 33
17 | 35
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C)
x | y
-9 | 54
-6 | 36
0 | 0
5 | -30
7 | -42
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D)
x | y
-15 | -14
-13 | -12
-11 | -10
-9 | -8
-7 | -6

Answer 7

The table that shows a proportional linear relationship between x and y is:

A)
x | y
6 | 4
12 | 10
18 | 16
24 | 22
28 | 26

In this table, as the value of x increases, the value of y also increases, and the ratio between the two remains constant. Therefore, the relationship is proportional and linear.

Answer 8

Match each data set with its mean absolute deviation.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
1.456
1.728
3.333
2.741

A) 0,1,2,3,4,5,6
B)1,2,2,3,3,6,7,8,10
C)0,0,1,2,3,3,8,910
D)0,2,23,34,5,6,7

Answer 9

To find the mean absolute deviation (MAD), we need to calculate the average of the absolute differences between each data point and the mean of the data set.

Calculating the MAD for each data set:

A)
Data set: 0,1,2,3,4,5,6
Mean: (0+1+2+3+4+5+6)/7 = 21/7 = 3
Absolute differences: |0-3|, |1-3|, |2-3|, |3-3|, |4-3|, |5-3|, |6-3| = 3, 2, 1, 0, 1, 2, 3
Mean absolute deviation = (3+2+1+0+1+2+3)/7 = 12/7 = 1.714 (approximately)

B)
Data set: 1,2,2,3,3,6,7,8,10
Mean: (1+2+2+3+3+6+7+8+10)/9 = 42/9 = 4.667 (approximately)
Absolute differences: |1-4.667|, |2-4.667|, |2-4.667|, |3-4.667|, |3-4.667|, |6-4.667|, |7-4.667|, |8-4.667|, |10-4.667| = 3.667, 2.667, 2.667, 1.667, 1.667, 1.333, 2.333, 3.333, 5.333
Mean absolute deviation = (3.667+2.667+2.667+1.667+1.667+1.333+2.333+3.333+5.333)/9 = 24/9 = 2.667 (approximately)

C)
Data set: 0,0,1,2,3,3,8,9,10
Mean: (0+0+1+2+3+3+8+9+10)/9 = 36/9 = 4
Absolute differences: |0-4|, |0-4|, |1-4|, |2-4|, |3-4|, |3-4|, |8-4|, |9-4|, |10-4| = 4, 4, 3, 2, 1, 1, 4, 5, 6
Mean absolute deviation = (4+4+3+2+1+1+4+5+6)/9 = 30/9 = 3.333 (approximately)

D)
Data set: 0,2,23,34,5,6,7
Mean: (0+2+23+34+5+6+7)/7 = 77/7 = 11
Absolute differences: |0-11|, |2-11|, |23-11|, |34-11|, |5-11|, |6-11|, |7-11| = 11, 9, 12, 23, 6, 5, 4
Mean absolute deviation = (11+9+12+23+6+5+4)/7 = 70/7 = 10

Matching each data set with its mean absolute deviation:

A) 1.714
B) 2.667
C) 3.333
D) 10