We can solve this problem by first solving for the total
volume of the cube. The formula for volume of cube is given as:
V cube = s^3
Where s is the length of one side which is equivalent to
2 inches. Therefore:
V cube = (2 inches)^3
V cube = 8 cubic inch
Assuming that all the pebble fills the cube without any
spaces, then the total weight of the pebbles in the cube would simply be:
Total weight = 0.5 lb per cubic inch * 8 cubic inch
Total weight = 4 lb
Therefore, the total weight of the pebbles in the cube is <u>4
lbs</u>.
Considering the area of the rectangle, we have that the length is of 8 units and the width is of 10 units.
<h3>What is the area of a rectangle?</h3>
The area of a rectangle of length l and width w is given as follows:
A = lw.
In this problem, the area is of 80 square units, while the length and the width are consecutive even integers, hence:
Then:
l(l + 2) = 80
l² + 2l - 80 = 0
(l + 10)(l - 8) = 0.
We need the positive measure, hence:
l - 8= 0 -> l = 8 units.
w = l + 2 = 10 units.
More can be learned about the area of a rectangle at brainly.com/question/10489198
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Area of a rectangle is A = L*W.
Here, A = 56 cm^2 (not 56 cm).
= (56 cm^2)=( L )( W ) = (x+2)*(2x-5) = 2x^2 - 5x + 4x - 10
Simplifying, 2x^2 - 5x + 4x - 10 = 56, or 2x^2 - x - 66 = 0.
Solve this using the quadratic formula:
-(-1) plus or minus sqrt ( (-1)^2 - 4(2)(-66) )
x = -------------------------------------------------------------
2(2)
Finish the work: find x. Most likely you will need to check both of the roots. Keep in mind that x will likely be a positive number.