The vertices of ABC are A 1,5 B 3, 9 and C 5,3 The vertices of DEF are D -3,3 E -2,5 and F -1,2 which conclusion is true about the triangles? The ratio of their corresponding sides is 1:3

They are congruent by the definition of congruence in terms of rigid motions

The ratio of their corresponding angles is 1:3

They are similar by the definition of similarity in terms of a dilation

The correct option is;

They are similar by the definition of similarity in terms of a dilation

Step-by-step explanation:

Vertices ABC are A (1, 5) B (3, 9) and C (5, 3)

Vertices DEF are D(-3, 3) E (-2, 5) F(-1, 2)

The length of the segments of ΔABC are;

AB = √((1 - 3)² + (5 - 9)²) = 2·√5

BC = √((3 - 5)² + (9 - 3)²) = 2·√(10)

AC =√((1 - 5)² + (5 - 3)²) = 2·√5

The length of the segments of ΔDEF are;

DE = √((-3 - (-2))² + (3 - 5)²) = √5

DF = √((-3 - (-1))² + (3 - 2)²) = √5

EF =√((-2 - (-1))² + (5 - 2)²) = √10

Therefore, the ratio of the sides DE:AB, DF:AC and EF:BC are 1:2

Therefore, the triangles ΔABC and ΔDEF are similar by the definition of similarity in terms of a dilation of 2.

d

step-by-step explanation:

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.