Suppose we are given two graphs g1 = (v, e1 ) and g2 = (v, e2 ) with the same set of vertices v = {1, 2, . . , n}. prove that is it np-hard to find the smallest subset s ⊆ v of vertices whose deletion leaves identical subgraphs g1 \ s = g2 \ s. for example, given the graphs below, the smallest subset has size 4

Two vertices of a polygon are (7, −18) and (7, 18) . what is the length of this side of the polygon? enter your answer in the box. units

Simonne used the following steps to simplify the given expression. 12 - 3(-2x + 4) step 1: 12 + (–3)·(–2x) + (–3)·(4) step 2: 12 + 6x + (–12) step 3: 12 + (–12) + 6x step 4: 0 + 6x step 5: 6x what property of real numbers was used to transition from step 3 to step 4? a. identity property of addition b. inverse property of addition c. associative property of addition d. commutative property of addition

One integer is 8 times another. if the product is 72, then find the integers