Im just trying to graduate a hotel 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 8 meters by 8 meters, and the seating area is 4 meters by 4 meters. b. the lobby is 6 meters by 6 meters, and the seating area is 4 meters by 4 meters. c. the lobby is 10 meters by 10 meters, and the seating area is 6 meters by 6 meters. d. the lobby is 12 meters by 12 meters, and the seating area is 8 meters by 8 meters.

If the length of lobby is l and length of seating area is s

First equation is l =s+4 and second is 2s∧2= l∧2 - 16

If we replace l in second equation we get 2s∧2=(s+4)∧2 -16

l=12 and s=8

Correct answer is D

Good luck!!!

answer: 1,380

step-by-step explanation:

1: you turn %15 into a decimal by moving the decimal point two places to the left.

2: and then you multiply .15 by 1,200 , which will get you 180.00

3: from there you will add 180 to 1,200

4: which will get you 1,380

hope it *im kind of slow so idk if my answer is right*

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.