Suppose the interval ​[5​,7​] is partitioned into n=4 subintervals. What is the subinterval length Upper Delta x​? List the grid points x0​, x1​, x2​, x3​, x4. Which points are used for the​ left, right, and midpoint Riemann​ sums?

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (-4, 0) and (6,0). the y-intercept of thefirst parabola is (0, –12). the y-intercept of the second parabola is (0-24). what is the positive difference between the avalues for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth.

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)

Are the corresponding angles congruent? explain why or why not.