I paid $2480 for the facility and also need to pay $14 for each person who participates. I am charging each participant $54, how many people must compete to break even

62 people must compete to break even.

Step-by-step explanation:

The money paid for the facility is $2480. $14 is paid for each participant and each person that participate in the competition is charged $54.

In order to break even(profit is same as cost), the amount of money spent(cost) must be equal to the money gotten(revenue).

Let us assume that x number of people participated, therefore $14x would be spent for x number of people. The total cost would the be $(14x + 2480)

Also the money to be charged for x people would be $54x.

At break even, total cost = total money gained(revenue)

⇒ 2480 + 14x = 54x

2480 + 14x - 14x = 54x - 14x

∴ 30x = 2480

40x/40 = 2480/40

x = 62

Therefore 62 people must compete to break even.

{3 + i, 3 - i, 3, -1}

step-by-step explanation:

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.