If g is a simple graph, its line graph l(g) is defined as follows: l(g) has one vertex for each edge in g, and two vertices of l(g) are adjacent if and only if the corresponding edges of g are adjacent. (a) draw l(c3), l(k3,1), l(k4) and l(w5). (b) assume that g is k-regular. show that l(g) is 2k – 2-regular.

The number if marbles of different colors stored in a hat is listed below: 4 red marbles 10 green marbles 7 blue marbles. without looking in the hat, dan takes out a marble at random. he replaces the marble and then takes out another marble from the hat. what is the probability that dan takes out a blue marble in both draws?

Solve each quadratic equation by factoring and using the zero product property. x^2 - 8x + 30 = 3x

He graph of f(x) = |x| is stretched by a factor of 0.3 and translated down 4 units. which statement about the domain and range of each function is correct? the range of the transformed function and the parent function are both all real numbers greater than or equal to 4. the domain of the transformed function is all real numbers and is, therefore, different from that of the parent function. the range of the transformed function is all real numbers greater than or equal to 0 and is, therefore, different from that of the parent function. the domain of the transformed function and the parent function are both all real numbers.