Suppose that a graph with e edges connected planar simple and vertices contains no simple circuits of length 4 or less. Show that e <=(5 / 3) -(10 / 3) if v >=4

(a) Let S = {1, 2, 3} and R = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} be a binary relation on S. Then (i) Decide whether the given relation R is reflexive, irreflexive, symmetric, and/or Transitive.

Solve by factoring and using the principle of zero products. 2x^2 - 20x = 0

radium 221has a half-life of 30 seconds. how long will it take for 95% of it to decompose?

i have principal payment of 4082.16 and interest of 15.99. what is the interest daily.

a ladder 20 feet long rests 12 feet from the base of a sloping wall and reaches 14 feet up the face of the wall what is the angle of inclination of the ladder ?of the wall?

I need help solving this problem y = -2/3x -12

A nut wholesaler sells a mix of peanuts and cashews. The wholesaler charges $2.50 per pound for peanuts and $5.30 per pound for cashews. The mix is to sell for $3.30 per pound. How many pounds of peanuts and how many pounds of cashews should be used to make 100 pounds of the mix?

Rewrite as an equivalent exponential equation logwQ=4

what is 25^1/2