At the Howelton Hot Dog Happiness competition, Olaf eats five fewer than triple the hot dogs Alfred eats. Olaf eats 67 hot dogs. Alfred eats "a" hot dogs. How many does Alfred eat? Have to do PEMDAS backwards, just need help setting up the equation.

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 8 y is greater than or equal to negative 5 over 2 times x plus 5 part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points) part b: is the point (5, −8) included in the solution area for the system? justify your answer mathematically. (4 points)

What is the value of the discriminant of the quadratic equation -2x = -8x + 8 and what does its value mean about thenumber of real number solutions the equation has?

Which of the following would be a reasonable estimate for the weight of a pencil? a. 1 × 10^-20 lb b. 1 × 10^20 lb c. 1 × 10^2 lb d. 1 × 10^-2 lb