Nicola gets her electricity and gas from the same supplier. she receives a notification from her supplier that prices for electricity and gas have increased. how much more will nicola now have to pay for her electricity and gas, based on her average monthly consumption? (round your answer at the end of the calculation)

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).

What are the values of each variable in the diagram below?