Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 9 sin 7θ

The given function symmetric about the y-axis.

Step-by-step explanation:

The given function is

               .... (1)

1. Symmetry about the x-axis: If the point (r, θ ) lies on the graph, then the point  (r,-θ ) or (-r, π - θ ) also lies on the graph.

2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r,π - θ ) or (-r, -θ ) also lies on the graph.

3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.

Put (r, -θ ) in the given function.

Therefore it is not symmetric about x-axis.

Put (-r, -θ ) in the given function.

Therefore it is symmetric about y-axis.

Put (-r,θ ) in the given function.

Therefore it is not symmetric about the origin.

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".