Maria Louisa looks at a sequence of shapes and records the number of vertices in each of the shapes in the sequence. The first shape has 9 vertices, the second shape has 13 vertices, and the third shape has 17 vertices.
If Maria Louisa assumes that the number of vertices in the sequence of shapes follows the same pattern, how many
vertices would she
expect the 24 shape to have?

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb