For a craft project, four students each chose three pieces of wire from a box.
don’s wires measure 3 inches, 5 inches, and 12 inches.
margo’s wires measure 6 inches, 8 inches, and 14 inches.
sonji’s wires measure 12 inches, 8 inches, and 17 inches.
liam’s wires measure 16 inches, 8 inches, and 27 inches.
which student chose pieces that can be used to construct a triangle?
don
margo
sonji
liam

Step-by-step explanation:

To find the answer, we need to recur to the triangular inequality, which states that the sum of two sides must be greater than the third side

So, if we apply this triangular inequality to each case, we would find that Sonji's wires can make a triangle, because

Fulfils the theorem.

On the other hand, we have the other measures

Don:

Which is false.

Margo:

Which is also false.

Liam

False again.

Therefore the right answer is Sonji.

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.