Amystery number is greater than 50 and less than 100. you can make exactly five different rectangles with the mystery number of tiles. (hint: this means the mystery number is a square number). its prime factorization consists of only one prime number. what is the mystery number?

81

Step-by-step explanation:

We know the number is between 50 and 100.  The prime factorization consists of only one prime number, so the number must be a perfect square.  The possible numbers are 64 and 81.

The rectangles that can be made with 64 tiles are:

1×64, 2×32, 4×16, 8×8, 16×4, 32×2, 64×1

The rectangles that can be made with 81 tiles are:

1×81, 3×27, 9×9, 27×3, 81×1

There are 7 rectangles that can be made with 64 tiles.  There are only 5 rectangles that can be made with 81 tiles.  Therefore, the mystery number is 81.

chad should not have included the values (1, 2) and (3, 6) because that would mean he only had half a healing card.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)