Algebra 1 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?

105

Work Shown:

x = length of shorter piece, 3x = length of longer piece

x+3x = 140

4x = 140

4x/4 = 140/4

x = 35

3*x = 3*35 = 105

So the longer piece is 105 feet long (shorter piece is 35 ft).

Note how 35+105 = 140 which helps confirm the answer.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2