First, we know that each corner has now a square of 6 in long, so the heigth of the box will be of this size (as you can see in the picture attached). Then, the length and the width of the box would be the same as the piece, but with 12 in less. Therefore the equations to solve the problem are:

$h=6 in\\w=x-12\\l=x+30-12\\l=x+18\\\\V: volume of the box\\V=6*(x-12)*(x+18)\\2706=6x^{2}+36x-1296\\0=6x^{2}+36x-4002\\\\$

We factorize the 6 and we get:

$0=x^{2}+6x-667\\$

Finally we solve for x, and we get the initial dimensions of the piece of metal:

$x=23$ $l=30+x=30+23=53 in\\w=x= 23 in$

7 0

3 years ago

Trong mặt phẳng tọa độ cho tam giác ABC biết các đỉnh A(-1,2), B(4,7) và trọng tâm tam giác G(3,2). Viết phương trinh đường thẳn

ExtremeBDS [4]

Can you translate so i can help you out .

8 0

3 years ago

Divide to find two equivalent fraction 4/12

SCORPION-xisa [38]

Answer: 2/6 and 1/3

Step-by-step explanation: Equivalent fractions are fractions that have the same value but have different top and bottom numbers.

We can find 1 equivalent fraction by dividing the numerator and the denominator by 2 and we get 2/6. We can also reduce 2/6 by dividing the numerator and the denominator by 2 and we get 1/3.

So two equivalent fractions for 4/12 would be 2/6 and 1/3.

4 0

3 years ago