Dylan draws a triangle ΔFGH. Alana then takes his triangle and applies a series of translations, rotations, dilations, and reflections to make ΔF’G’H, but does not tell Dylan which transformations she performed. Dylan measures one side of ΔFGH and one side of ΔF’G’H’ and finds that they are the same length. Which of the following must be TRUE about the relationship between ΔFGH and ΔF’G’H’?

A
They are congruent and similar.
B
They are congruent, but not necessarily similar.
C
They are similar, but not necessarily congruent.
D
They are not necessarily similar or congruent.

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step-by-step explanation:

answer: integers are just whole numbers: positive, negative, and zero.

i = {-∞, -2, -1, 0, 1, 2, 3, ∞}

let x = 1st integer

let y = 2nd integer

x = 3y + 17   {equation 1}

xy = -24         {equation 2}

substitute 3y+17 in place of x n equation 2

and solve for y.

(3y+17)y = -24

3y2 + 17y = -24

3y2 + 17y + 24 = 0

from quadratic equation:

y = [-17±√(172-4(3)(24))]/(2(3))

y = (-17 ±√1)/6

y = (-17+1)/6   or     y = (-17-1)/6

y = -16/6           or     y = -18/6

y = -2 2/3         or   y = -3

since we are dealing with

y = -3

x = 3y+17 = -9+17 = 8

the integers are -3, 8

step-by-step explanation: