Suppose g is a planar graph that is not necessarily connected, as required in euler's formula (theorem 2). recall that a component his a connected subgraph of g with the property that there is no path between any vertex in h and any vertex of g not in h. (a) find the appropriate modification of euler's formula for a planar graph with c components. (b) show that the corollary is valid for unconnected planar graphs.

Solve for x -2.3(r - 1.2 ) = -9.66 enter you answer as decimal.

Tim's phone service charges $23.06 plus an additional $0.22 for each text message sent per month. if tim's phone bill was $28.56, which equation could be used to find how many text messages, x, tim sent last month?

Questions 7-8. use the following table to answer. year 2006 2007 2008 2009 2010 2011 2012 2013 cpi 201.6 207.342 215.303 214.537 218.056 224.939 229.594 232.957 7. suppose you bought a house in 2006 for $120,000. use the table above to calculate the 2013 value adjusted for inflation. (round to the nearest whole number) 8. suppose you bought a house in 2013 for $90,000. use the table above to calculate the 2006 value adjusted for inflation. (round to the nearest whole number)