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zlopas [31]
3 years ago
15

A box without a top is made from a rectangular piece of cardboard, with dimensions 4 m by 2 m, by cutting out square corners wit

h side length x.
Which expression can be used to determine the greatest possible volume of the cardboard box?
(x−4)(x−2)x

(x−4)(x−2)x

(4−2x)(2−2x)x

(4x−2)(2x−4)

Mathematics
1 answer:
Ede4ka [16]3 years ago
6 0

Answer:

The expression that can be used to find the volume of the cardboard box is:

(4−2x)(2−2x)x

Step-by-step explanation:

A box without a top is made from a rectangular piece of cardboard, with dimensions 4 m by 2 m, by cutting out square corners with side length x.

i.e. the box is in the shape of a cuboid.

Now the volume of a box is same as the volume of a cuboid.

We know that the volume of a cuboid is given as:

Volume of cuboid=Length×Breadth×Height.

So, the length of the cuboid box is: 4-2x

and the width of the box is: 2-2x

Also, the height of box is: x

Hence, the volume of cuboid is:

Volume=(4-2x)\times (2-2x)\times x\\\\Volume=(4-2x)(2-2x)x

Hence, the expression for the volume of cuboid box is:

             (4−2x)(2−2x)x

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A total of 815 tickets were sold for the school play. They were either adult tickets or student tickets. There were 65 more stud
kvv77 [185]

Answer:

<u>375 Adult Tickets.</u>

Step-by-step explanation:

Here, we can simply set up an equation using variable <em>x </em>in place of the unknown student/adult tickets.

x = # of <u>adult</u> tickets sold

x + 65 = # of <u>student</u> tickets sold.

1) x + x + 65 = 815 (set both ticket amounts equal to the total)

2) 2x + 65 = 815 (added common variables together)

3) 2x = 750 (negated the +65, subtracted it from both sides)

4) x = 375 (divided both sides by 2)

5) 815 - 375 = 440 (subtracted the x from the total number of <u>adult</u> tickets, to recieve the amount of <u>childrens</u>' tickets.

Therefore,

Since there were fewer adult tickets sold (-65), 375 is the number of adult tickets, and 440 is the number of student tickets.

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