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.
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.
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.
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
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.
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)
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.
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
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.
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
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
To determine which statement is true, we need to analyze the figure and the information given.
First, let's look at the figure and analyze the regions:
- Region P: It consists of one square formed by joining the vertices of two squares.
- Region R: It also consists of one square formed by joining the vertices of two squares.
- Region S: It is the remaining square after regions P and R are formed.
Now, let's consider the number of tiles needed to cover each region:
- Region P: Since it consists of one square, we need to cover it with square centimeter tiles.
- Region R: Similarly, since it also consists of one square, we need to cover it with square centimeter tiles.
- Region S: Since it is a square formed from the remaining area, we can assume it is larger than Region P or R.
Now, let's reexamine the statements:
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.
Since both Region P and Region R consist of only one square each, the total number of tiles needed to cover both of them is equal to the number of tiles needed to cover just one square. However, we already established that Region S is larger. Therefore, statement A is not true.
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.
Statement B suggests that the number of tiles needed to cover Region R is equal to the combined number of tiles needed to cover both Region P and Region S. As we established earlier, Region R consists of only one square, so this statement is not true.
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.
Since Region S is larger than either Region P or R, it logically follows that the number of tiles needed to cover Region S would be greater than the combined number of tiles needed for Region P and Region R. Therefore, statement C is true.
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.
Since Region S is larger than either Region P or R, it cannot require the same number of tiles as the combined number of tiles needed for Region P and Region R. Therefore, statement D is not true.
Therefore, the correct statement is:
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.