Which of the following would make the period longer? a) Increase the amplitude Decrease the mass b) Decrease the amplitude Increase the mass c) Decrease the spring constant Increase the spring constant

b) Decrease the amplitude Increase the mass.

Step-by-step explanation:

The period does not depend on the amplitude. The period depends on the spring constant, k and the mass, m.

Mathematically,

T = 2pi × sqrt(m/k)

The more amplitude the more distance to cover but the faster it will cover the distance. The distance and speed will cancel each other out, so the period will remain the same. Increasing the mass increases the period of oscillation.

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".