The weight of a piece of wire is directly proportional to its length. a piece of wire is 25cm long and has a weight of 6 grams. another piece of the same wire is 30cm long. calculate the weight of the 30cm piece of wire p is inversely proportional to m. p=48 when m=9 calculate the value of p when m =12.

Part A

Weight of a piece of wire is directly proportional to its length

⇒ Weight of wire piece (W) α Length of wire (L)

⇒ W = k × L

When L = 25 cm, then W = 6 gms

⇒ = k

⇒ k =

To calculate weight of 30 cm wire, put value of k and W in the expression W = k × L

⇒ W = × 30

⇒ W = 7.2 gms

Part B

p α m

⇒ p = k × m

If p=48 and m=9

k =

⇒ k =  

Now to calculate p when m = 12, substitute the value of m and k in p = k × m

p = × 12

⇒ p = 64

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".