Renae has been playing Tower of Hanoi and has noticed that the minimum number of moves it takes to defeat the game is related to the number of disks she must move. She has recorded her observations below. Write an equation that describes this pattern. Show your work. Number of Disks in the Tower ║Minimum Number of Moves

1 ║1

2║ 3

3 ║7

4 ║15

5 ║31

Step-by-step explanation:

Let the number of disks be x and the minimum number of moves be y.

When x = 1: y = 1

When x = 2: y = 3

When x = 3: y = 7

When x=4: y = 15

When x = 5: y = 31

Notice that for each derived expression of y, the exponent of 2 is being replaced by the value of x.

The general equation is:

42 inches then 10 1/2 deep

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.