Given rectangles lmno and pqrs, which statement explains a way to determine if the two figures are similar?
a. verify corresponding pairs of angles are proportional by translation.
b. verify corresponding pairs of sides are proportional by dilation.
c. verify corresponding pairs of angles are congruent by dilation.
d. verify corresponding pairs of sides are congruent by translation.

B

Step-by-step explanation:

Definition: Two rectangles are similar when they have corresponding sides proportional are proportional by dilation.

For example, rectangles with sides 3 cm, 4cm and 6 cm, 8 cm are similar, but rectangles with sides 3 cm, 4 cm and 6 cm, 10 cm are nor similar.

Since all angles in rectangle are always right angles, then options A and C are false (in terms of your question).

Option D is false too, because translation doesn't change the length, and in this case two rectangles are congruent.

Option B is true according to definition.

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation:

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)