If de = 37 cm and ef = 16 cm, then what are the possible lengths for df so that de, ef, and df can form a triangle? explain your reasoning.

21 < DF < 53 ; Triangle Inequality Theorem

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any two sides is greater than the sum of the third side.

DE + EF > DF          EF + DF > DE                 DE + DF > EF

37 + 16 > DF           16 + DF > 37                  37 + DF > 16

       53 > DF                   DF > 21                           DF > -21

Now let's put together the answers.  Note that DF > -21 is irrelevant since all lengths must be greater than 0.

53 > DF  and DF > 21  means that DF is between 53 and 21

>    21 < DF < 53

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".

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation: