The figure shows two triangles on the coordinate grid:

what set of transformations is performed on triangle abc to form triangle a’b’c’

 the correct option is

(D) A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin.

Step-by-step explanation:  We are given two triangles ABC and A'B'C' on the co-ordinate grid.

We are given to select the set of transformations is performed on triangle ABC to form triangle A’B’C’.

From the graph, we note that

the co-ordinate of the vertices of triangle ABC are A(-4, -1), B(-3, -1) and C(-4, -4).

And, the co-ordinates of the vertices of triangle A'B'C' are A'(-1, 1), B'(-2, 1) and C'(-1, 4).

We know that if a point (x, y) is translated 5 units right, followed by a rotation of 180-degrees clockwise about the origin, then its new co-ordinates becomes

(x, y)   ⇒   (-x-5, -y).

So, after these two transformations, the co-ordinates of the vertices of triangle ABC will become

A(-4, -1)   ⇒   (4-5, 1) = (-1, 1),

B(-3, -1)   ⇒   (3-5, 1) = (-2, 1)

and

C(-4, -4)  ⇒  (4-5, 4) = (-1, 4).

The new co-ordinates are the co-ordinates of the vertices of triangle A'B'C'.

Thus, the required set transformations is

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

Thus, option (D) is CORRECT.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.