Pentagon abcde and pentagon a'b'c'd'e' are shown on the coordinate plane below: pentagon abcde and pentagon a prime b prime c prime d prime e prime on the coordinate plane with ordered pairs at a negative 4, 5, at b negative 6, 4, at c negative 5, 1, at d negative 2, 2, at e negative 2, 4, at a prime 4, negative 7, at b prime 2, negative 6, at c prime 3, negative 3, at d prime 6, negative 4, at e prime 6, negative 6. which two transformations are applied to pentagon abcde to create a'b'c'd'e'?

Reflection across x- axis and then translation (x+8,y-2).

Step-by-step explanation:

We are given that a pentagon ABCDE with vertices A at (-4,5), B at (-6,4),C at (-5,1) , D at (-2,2) , E at (-2,4).

The pentagon A'B'C'D'E' is the image of pentagon ABCDE  create after transformation.

The vertices A' at (4,-7),B' at (2,-6), C' at (3,-3), D' at (6,-4) and E' at (6,-6).

We have to find the transformation applied on pentagon ABCDE to create A'B'C'D'E'.

The rule of transformation of reflection across x- axis is given by

Therefore, the coordinates of ABCDE after reflection across x- axis is given by

Now, apply the translation

Therefore, after applying translation then, we get

Hence, A'B'C'D'E' is created .

Reflection across x- axis and then translation (x+8,y-2).

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: