6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c

answer: the correct option is d.

explanation:

it is given that the triangle j'k'l' shown on the grid below is a dilation of triangle jkl using the origin as the center of dilation.

from the given graph it is noticed that k(4,8) and k'(2,4). let origin is defined by o and scale factor is defined by k, then

[tex]k=\frac{ok'}{ok}[/tex]     (1)

distance formula,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]ok'=\sqrt{(2-0)^2+(4-0)^2}= \sqrt{4+16}= \sqrt{20}=2\sqrt{5}[/tex]

[tex]ok=\sqrt{(4-0)^2+(8-0)^2}= \sqrt{16+64}= \sqrt{80}=4\sqrt{5}[/tex]

put these values in equation (1).

[tex]k=\frac{2\sqrt{5}}{4\sqrt{5}}= \frac{1}{2}[/tex]

therefore scale factor is   [tex]\frac{1}{2}[/tex]   and option d is correct.

the five is the numerator