10) if the pattern indicated below is continued, what would be the total number of cubes in the 5th stage of the pattern?
a) 55
b) 36
c) 45
d) 30

Option A. 55

Step-by-step explanation:

From the diagram given above, we discovered that the number of cubes in each stage is simply the addition of the squares of the number from 1 to the stage number i.e

1st Stage = 1² = 1 cube

2nd Stage = 1² + 2² = 1 + 4 = 5 cubes.

3rd Stage = 1² + 2² + 3² = 1 + 4 + 9

3rd stage = 14 cubes

With the above idea in mind, we can obtain the number of cubes in the 5th stage as illustrated below:

5th stage = 1² + 2² + 3² + 4² + 5²

5th stage = 1 + 4 + 9 + 16 + 25

5th stage = 55 cubes

Thus, there are 55 cubes in the 5th stage.

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)

answer: h=5.6 i don't really know how to put into words, so i though i would let you do that. i hope i was able to some

step-by-step explanation:

18 = 6(h)+1/2

18 = 6h+1/2

18-1 = 6h/2

17 = 3h

17/3 = h

h = 5.6