Mauro has 140 ft. of rope. he will cut it into two pieces so that the length of the longer piece is 3 times the length of the shorter piece. what will the length of the longer piece be? what will the length of the shorter piece be? how do you know? describe the process you used to solve. hint: there are many ways to solve this! if you are stuck, use your knowledge of systems of equations to solve. for example, let x be the length of the shorter piece and y be the length of the longer piece.

The length of the shorter piece= 35 ft.

The length of longer piece =105 ft

Step-by-step explanation:

Let x be the length of the shorter piece and y be the length of the longer piece.

Since, the length of the longer piece is 3 times the length of the shorter piece.

Then ...(1)

Also, the total length of the rope = 140 ft.

Thus,

substitute value of y from (1), we get

Hence, the length of the shorter piece= 35 ft.

The length of longer piece = ft

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.