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Determine the dimensions of the first rectangle.

Mathematics

ScanSolve AI Answer

Answer

(12, 3)
(19, -3)

Step-by-step solution

3 steps
  1. Determine the dimensions of the first rectangle.

    The top-left corner of the first rectangle is (5,9)(5, 9).
    The top-right corner of the first rectangle is (12,9)(12, 9).
    The width of the rectangle is the difference in x-coordinates:

    Width=12−5=7\text{Width} = 12 - 5 = 7

    The point (12,3)(12, 3) is given, which is the bottom-right corner of the first rectangle.
    The height of the rectangle is the difference in y-coordinates:

    Height=9−3=6\text{Height} = 9 - 3 = 6
  2. Determine the coordinates of point A.

    Point A is the bottom-right corner of the first rectangle. From the given information, this point is (12,3)(12, 3).

    A=(12,3)A = (12, 3)
  3. Determine the coordinates of point B.

    The problem states that the two rectangles are identical. This means the second rectangle also has a width of 7 units and a height of 6 units.
    Point A (12,3)(12, 3) is the top-left corner of the second rectangle.
    To find the coordinates of point B, which is the bottom-right corner of the second rectangle:
    The x-coordinate of B will be the x-coordinate of A plus the width:

    xB=12+7=19x_B = 12 + 7 = 19

    The y-coordinate of B will be the y-coordinate of A minus the height (since the rectangle extends downwards from A):

    yB=3−6=−3y_B = 3 - 6 = -3

    So, the coordinates of point B are (19,−3)(19, -3).

    B=(19,−3)B = (19, -3)

    The coordinates are:
    A is (12,3)\boxed{(12, 3)}
    B is (19,−3)\boxed{(19, -3)}

    For the second part of the question:
    n stands for a whole number.
    n is greater than 30, which means n>30n > 30.
    n is less than 100, which means n<100n < 100.
    Combining these conditions, we have 30<n<10030 < n < 100.
    Since n is a whole number (non-negative integer), the possible values for n are integers strictly between 30 and 100.
    The numbers that n stands for are 31,32,33,…,9931, 32, 33, \dots, 99.

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