Activity To model how particles move as states of matter change, Jelani filled a clear box with as many marbles as the box would hold. Then he drew a picture of what the box looked like with the marbles in it.
Part A
Jelani covered the box and shook it. He could barely feel the marbles moving around the box. What state of matter does Jelani's box of marbles represent? Explain.

It represent the solid state. In the solid state, the atoms or molecules that compound a substance have a very organized shape, as you can see in the pic, and also the solid state is the state that the particles have the minimum degree of freedom, and that explains why he barely feel the marbles moving when he shook it, it's because in the solid state the particles move less than in the liquid or gas state.

answer-

the statement that f(x) = |x+a| + b has exactly one x-intercept is sometimes correct.

solution-

it solely depends on b, whether the function will have one or two or zero x intercept.

this plot of the given function, f(x) = |x+a| + b will be the basic absolute value graph i.e v shape, with vertex translated to (-a, b), instead of origin.

1-   if b is zero, the graph will have exactly one x-intercept, at x= -a

2- if b is positive, the whole graph will be above the x-axis, hence it will have no x-intercepts.

3- if b is negative, the graph will be below the x-axis, hence it will have two x-intercepts.

∴ the statement is sometimes true.