Use your grapher to determine which of the graphs matches the polar equation r = 1 + 2 cos θ.

Given:

r = 3 sin 2θ
Find:   Graph that matches the polar equation   Solution:

Use the polar graph type in the graphing calculator and enter the following values: 3sin (2 theta).   Please see the attached image for the answer. The graph would look like butterfly wings.

11 + x

Step-by-step explanation:

Let's write out each of the answer choices:

A) 11x

B) 11 + x

C) 11 minus x  ⇒  11 - x

D) Negative x + 11  ⇒  -x + 11

Examine each of them. Clearly, A and D aren't the same (A is multiplication, not addition, and D has a negative x instead of a positive x). C is actually the same as D, if you switch the places of 11 and -x: 11 - x = -x = 11.

Finally, answer choice B is correct because by the Commutative Property of Addition, 11 + x = x + 11.

Hope this helps!