The manager of an 110-unit apartment complex knows from experience that at a rent of $300, all the units will be full. on the average, one additional unit will remain vacant for each $20 increase in rent over $300. furthermore, the manager must keep at least 50 units rented due to other financial considerations. currently, the revenue from the complex is $72 comma 000. how many apartments are rented?

The number of rented apartments is 80

Step-by-step explanation:

Hi there!

The revenue is calculated as the number of units rented times the value of the rent. Let y be the revenue, then:

y = 300 · 110

For each $20 increase, one unit will remain vacant. Then, if  the increase is 20x then the number of vacant apartments will be x. In this case, the revenue will be calculated as:

y = (300 + 20x)(110 - x)

Apply distributive property:

y = 33000 - 300x + 2200x - 20x²

y = -20x² + 1900x + 33000

If the revenue is $72000, then:

72000 = -20x² + 1900x + 33000

0 = -20x² + 1900x + 33000 - 72000

0 = -20x² + 1900x - 39000

Solving the quadratic equation using the quadratic formula:

a = -20

b = 1900

c = -39000

x = [-b±√(b² - 4ac)]/2a

x1 = 30 and x2 = 65

Since at least 50 units have to be rented, the numer of apartments rented is 110 - 30 = 80 (because 110 - 65 = 45<50).

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x