When constructing the centroid of a triangle, you need to find the intersection of all three of which type of line?

Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 15.

Malia is observing the velocity of a cyclist at different times. after two hours, the velocity of the cyclist is 15 km/h. after five hours, the velocity of the cyclist is 12 km/h. part a: write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. show your work and define the variables used. (5 points) part b: how can you graph the equations obtained in part a for the first 12 hours? (5 points) if you can try and make this as little confusing as you can

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)