If a runner who runs at a constant speed of p miles per hour runs a mile in exactly p minutes what is the integer closest to the value p

The value of p is 7.746. The nearest integer is 8.

Step-by-step explanation:

The speed of the runner is p miles per hour.

The speed formula is

It is given that he runs a mile in exactly p minutes. We know that

So, we get

Since the speed is p.

Taking square both sides.

Therefore the value of p is 7.746. The nearest integer is 8.

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".