The figure shows two triangles on the coordinate grid: What set of transformations is performed on triangle ABC to form triangle A′B′C′?

a.
A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin

b.
A translation 5 units down, followed by a 270-degree counterclockwise rotation about the origin

c.
A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units down

d.
A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units down

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions