The figure shows two triangles on a coordinate grid:
a coordinate grid is shown from positive 6 to negative 6 on the x axis and from positive 6 to negative 6 on the y axis. a triangle abc is shown with vertex a on ordered pair 4, negative 2, vertex b on ordered pair 3, negative 2 and vertex c on ordered pair 3, negative 5. another triangle a prime b prime c prime is shown with vertex a prime on ordered pair 1, 2, vertex b prime on ordered pair 2, 2 and vertex c prime on ordered pair 2, 5.
what set of transformations is performed on triangle abc to form triangle a'b'c'?
a 180 degree counterclockwise rotation about the origin followed by a translation 5 units up
a 270 degree counterclockwise rotation about the origin followed by a translation 5 units up
a translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin
a translation 5 units to the left followed by a 270 degree counterclockwise rotation about the origin

Solution:

Vertices of Preimage that is Triangle ABC =A(4,-2), B(3,-2),C(3,-5)

Vertices of image , i.e Δ A'B'C'=A'(1,2),B'(2,2), C'(2,5)

Now, transalation by 5 units left of triangle ABC takes it to

A(4,-2)=(4-5,-2)=(-1,-2)

B(3,-2)=(3-5,-2)=(-2,-2)

C(3,-5)=(3-5,-5)=(-2,-5)

When preimage is rotated through an angle of 180 degree, counterclockwise vertices of triangle (-1,-2),(-2,-2) and (-2,-5) goes to image A'(1,2),B'(2,2), C'(2,5).

Option C: A translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin takes ΔABC to  ΔA'B'C'.

fourth month

step-by-step explanation:

it is the one with the most keychains.

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%