Triangle abc is similar to triangle ade, which is formed with angle a and side ad, as shown. what could be the coordinates of point e? (2,–1) (–1,2) (–3,–1) (–1,–3)

Only option B is correct, i.e. (-1, 2).

Step-by-step explanation:

Two triangles are similar when their corresponding angles are congruent.

Triangle ABC would be similar to triangle ADE when ∠A = ∠A, ∠B = ∠D, and ∠C = ∠E.

Since A is common vertex and D is on side AB, then it is sure that E would be on side AC.

The information ∠B = ∠D, and ∠C = ∠E makes sure that DE║BC.

It means slope of DE = slope of BC.

⇒ (y-3)/(x-2) = (-4+1)/(-5-4)

⇒ (y-3)/(x-2) = (-3)/(-9)

⇒ (y-3)/(x-2) = 1/3

We can try and plug all four options in the proportion and check which one satisfy the equation.

option A: (-1-3)/(2-2) ≠ 1/3

option B: (2-3)/(-1-2) = 1/3

option C: (-1-3)/(-3-2) ≠ 1/3

option D: (-3-3)/(-1-2) ≠ 1/3

Hence, only option B is correct, i.e. (-1, 2).

answer: the correct one is a

step-by-step explanation:

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560