Astudent needs 3 pieces of wire for a science project. the second piece must be 3 times as long as the first. the third piece must be twice as long as the second. the student has 350 inches of wire to make the three pieces. let x be the length of the first wire. a.) write an inequality that models the situation. b.) what are the possible lengths of the shortest piece of wire?

Part a) The inequality that represent the situation is

Part b) The possible lengths of the shortest piece of wire are all positive real numbers less than or equal to

Step-by-step explanation:

Let

x------> the length of the first wire

3x---> the length of the second wire

2(3x)=6x -----> the length of the third wire

Part a) WRITE AN *INEQUALITY* THAT MODELS THE SITUATION

we know that

The inequality that represent the situation is

Part b) WHAT ARE THE POSSIBLE LENGTHS OF THE SHORTEST PIECE OF WIRE?

we know that

The shortest piece of wire is the first wire

so

Solve the inequality

The possible lengths of the shortest piece of wire are all positive real numbers less than or equal to

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step-by-step explanation:

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for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c