The top and bottom margins of a poster are 2 cm and the side margins are each 8 cm. if the area of printed material on the poster is fixed at 386 square centimeters, find the dimensions of the poster with the smallest area.

Answer :

39.294 cm × 9.823 cm

Explanation :

Let x be the length ( in cm ) of the printed material and y be the width ( in cm ) of the printed material,

So, the area of the printed material,

According to the question,

A = 386 cm²,

Since, the printed area is obtained in the margin of 2 cm from both top and bottom and margin of 8 cm in sides,

Thus, length of the poster = (x + 16) cm and width = (y + 4)

So, the area of the poster,

Differentiating with respect to x,

Again differentiating with respect to x,

For maxima or minima,

Sides can not be negative,

Also, at x = 39.294,

i.e. is minimum at x = 39.294,

∵ y = = 9.823

Hence, the dimensions of the poster with the smallest area,

39.294 cm × 9.823 cm

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".