Damon is designing a new dorm for a university. they are trying to create more of an extended family feel so it is to be a 5200 square foot house with several rooms in it. the city has an ordinance that says that every resident must have 350 square feet of living space. the university has decided that unless 15 students can reside in the house it is not cost effective. in order to calculate the number of students that can live there, damon divides 5200 by 15. is he correct?

Step-by-step explanation:

Area of the new dorm = 5200 square foot

As per ordinance every resident should have the living space for every resident = 350 square feet

As per rule number of residents who can live in this area = = 14.85

As per rule only 14 students can reside in this space.

Damon is not correct.

He should divide the total space 5200 feet² by space required for every resident 350 feet².

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is