The expression that represents the volume of a rectangular-shaped box is: A. x³ + x² - 12x.
<h3>What is the Volume of a
Rectangular Prism?</h3>
A rectangular-shaped box is a rectangular prism. To find the volume of a rectangular-shaped box, we would apply the formula of the volume of a rectangular prism, which is expressed as: V = (length)(width)(height).
We are given the following dimensions of the rectangular-shaped box:
Let the height be represented as x
Height of the rectangular-shaped box = x in.
Length of the rectangular-shaped box = (x - 3) in.
Width of the rectangular-shaped box = (x + 4) in.
Plug in the values into the volume formula:
Volume of the rectangular-shaped box = (x - 3)(x)(x + 4)
Expand (x - 3)(x)(x + 4)
Volume of the rectangular-shaped box = x³ + x² - 12x.
Therefore, the expression that represents the volume of a rectangular-shaped box with the given dimensions is: A. x³ + x² - 12x.
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This is easy once you look at it you just have to move the decimal 7 places and you'll get 24,000,000
Heya !
Using a theoram about triangles ,
Given a triangle ∆ABC, the sum of the lengths of any two sides of the triangle is greater than the length of the third side ,
Also , the length of third side always greater than absolute difference of the other two sides ,
Let the third side be x ,
So , x < 9 + 8 and x > 9 - 8
x < 17 and x > 1
Hence , x ∈ [ 2 , 17 ] inch.
Above case is true for any triangle , be it scalene , Isosceles , Right-angled ...
As , for Isosceles , the third side can be 8 or 9 inches ,
For scalene , all values in the above range satusfies ,
For right angled triangle , we have 2 cases ,
Case 1 : Third side is the hypotenuse
Then , x = √(9²+8²) = √145 = 12.0415 inch.
Case 2 : Third side is not the hypotenuse
Then , x = √(9²-8²) = √17 = 4.1231 inch.
Hope it helps you ! :)
I'm assuming that you are talking about sequences <3
In the context of a recursive formula where we have "n-1" in sub-index of "a", you can think of "a" as the previous term in the sequence. In the context of an explicit formula like "-5+2(n-1)" "n-1" represents how many times we need to add 2 to the first term to get the nth term.
Dw if you don't understand, sequences and functions isn't an easy topic
Foils stands for first, outer, inner, last.
For example:
(3x + 5)(2x + 3)
Multiply the firsts together.
3x * 2x = 5x²
Now multiply the outer together.
3x * 3 = 9x
Now multiply the inners.
5 * 2x = 10x
Now multiply the lasts.
5 * 3 = 15
so the answer would be:
5x² + 9x + 10x + 15
5x² + 19x + 15
Hope this helps :)
