Claire went into a movie theater and bought 9 bags of popcorn and 2 pretzels, costing a total of $80. Melanie went into the same movie theater and bought 7 bags of popcorn and 4 pretzels, costing a total of $72. Write a system of equations that could be used to determine the price of each bag of popcorn and the price of each pretzel. Define the variables that you use to write the system.

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

The lines shown below are parallel. if the green line has a slope of -1, what is the slope of the red line?

Write an algebraic expression to match each statement a. four less than 8 times a number b. twice the difference of a number and six c. nine from a number squared