Ahotel has a square lobby. management wants to reserve a smaller square area in stone to serve as the base of a new seating area. the side length of the seating area will be four meters less than the side length of the lobby, as shown below.

after purchasing materials, the manager noticed that two times the area of the seating area was equal to 16 square meters less than the area of the entire lobby.

write and solve a system of equations to determine the dimensions of the whole lobby and the smaller seating area cutout.

a.
the lobby is 10 meters by 10 meters, and the seating area is 6 meters by 6 meters.
b.
the lobby is 8 meters by 8 meters, and the seating area is 4 meters by 4 meters.
c.
the lobby is 12 meters by 12 meters, and the seating area is 8 meters by 8 meters.
d.
the lobby is 6 meters by 6 meters, and the seating area is 4 meters by 4 meters.

Liam's parents are driving three times as fast as liam is biking, but they left later than he did. if his parents caught up with him two hours after he left, how much later than liam did they leave?

You and three friends will be going out to eat at your favorite restaurant! each of you will order three items of your choice. you will also need to leave a tip. if you split the bill evenly among all four of you, how much will each person need to contribute? locate a menu for your favorite restaurant and pick three items for yourself and each friend. list the restaurant name, items, and prices in a table like the one below. in the column labeled subtotal, determine the cost of each person’s order. the customary tip is 20% of the total bill. in the column labeled tip, calculate the amount of tip each person should leave. in the column labeled total bill, determine the total of each person’s order, including the tip. restaurant name: names item 1 price item 2 price item 3 price subtotal tip total bill your name friend #1 friend #2 friend #3 part 2: questions answer the following questions, showing all work: what is the total cost of the entire bill (all four meals), including tip? write an expression using fractions to show how to determine the amount that each person will pay. then calculate each person's contributions showing all steps in long division. if each person paid an equal amount, who would save the most money? explain your reasoning using at least two complete sentences.

Secant be and cf intersect at point d inside a what is the measure of cde