Carolina is mowing lawns for a summer job. for every mowing job, she charges an initial fee plus \$6$6dollar sign, 6 for each hour of work. her total fee for a 444-hour job, for instance, is \$32$32dollar sign, 32. let f(t)f(t)f, left parenthesis, t, right parenthesis denote carolina's fee for a single job fff (measured in dollars) as a function of the number of hours ttt it took her to complete it. write the function's formula. f(t)=f(t)=f, left parenthesis, t, right parenthesis, equals

For this case, the first thing we must do is define variables.

We have then:

t: number of hours

F (t): total charge

We write the function that models the problem:

Where,

b: represents an initial fee.

We must find the value of b.

For this, we use the following data:

Her total fee for a 4-hour job, for instance, is $ 32.

We have then:

From here, we clear the value of b:

Then, the function that models the problem is:

the function's formula is:

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.