Provide a recursive definition of the function f(n) = (n+

See definition below

Step-by-step explanation:

Since we have to give a recursive definition, we must give a initial value f(0). Additionally, the value of f(n) must depend on the value of f(n-1) for all n≥1.

The required value of f(0) is (0+1)!=1!=1.

Now, the factorial itself is a recursive function, because (n+1)!=(n+1)n!. In terms of f, this means that f(n)=(n+1)f(n-1) for all n≥1.

Then, our definition is: f:N→N is defined by

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".