Aparticle moves along the x–axis so that at time t its position is given by x(t) = (t+1)(t–3)3. for what values of t is the velocity of the particle increasing?

I'll assume that's an exponent at the end there:

The first derivative gives the velocity.  The second derivative gives the acceleration; increasing velocity is the same as positive acceleration.  So we want to find when the second derivative is positive.

Let's see if we can use to avoid multiplying this out.

That worked; let's do it again:

That's a nice parabola.  It's zero or negative for so positive everywhere else:

Increasing velocity when t < 1 or t > 3

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".

40% off the regular price is the correct answer.

step-by-step explanation: