Atheater manager is planning an upcoming concert. regular tickets will cost $12 and student tickets will cost $8. the theater can seat at most 200 people. the manager wants to collect at least $1000 from ticket sales. let x represent the number of regular tickets sold. let y represent the number of student tickets sold. which inequalities are among the constraints for this situation? select each correct answer. 1. x+y≥200 2. 12x+8y≤1000 3. 12x+8y≥1000 4. x+y≥1000 5.x+y≤200 6.12x+8y≤200

The answers are 12x+8y≥1000, 12x+8y≤1000, x+y≤200, and x+y≥200,

The explanation behind the first equation is 12x signifies the regular tickets, being at $12 each. And 8y signifies the student tickets being $8 each. The symbol is "≥", because the manager wants $1000 or more from the ticket sale. While the second equation, just the same with the first but the symbols differ since the sale could be lesser than 1000.

The explanation behind the third equation is 200 is the number of seats at most. In the fourth equation, if many people came, they would lack seats so that’s why the greater sign is used.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.