Luke notices that by taking any three consecutive integers, multiplying them together, and adding the middle number to the result, the answer always seems to be the middle number cubed.
For example:
3.4.5+ 4 = 64 = 43
4.5.6 +5 = 125 = 53
9. 10. 11 + 10 = 1000 = 103
a. To prove his observation, Luke writes (n + 1)(n+2)(n+3) + (n + 2). What answer is he hoping
to show this expression equals?

Part a what is the area of triangle i? show your calculation. part b triangles i and ii are congruent (of the same size and shape). what is the total area of triangles i and ii? show your calculation. part c what is the area of rectangle i? show your calculation. part d what is the area of rectangle ii? show your calculation. part e rectangles i and iii have the same size and shape. what is the total area of rectangles i and iii? show your calculation. part f what is the total area of all the rectangles? show your calculation. part g what areas do you need to know to find the surface area of the prism? part h what is the surface area of the prism? show your calculation. part i read this statement: “if you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” is this statement true or false? why? part j read this statement: “if you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” is this statement true or false? why?

Find the midpoint m of z1=(8+5i) and z2=(12+3i)

45% of the trees in a park are apple trees. there are 27 apple trees in the park. how many trees are in the park in all?