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Answer:
Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters high and have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer than its width.
The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height.
Complete the equation that models the volume of the tray in terms of its width, x, in centimeters.
3x2 + 15x = 252
Is it possible for the width of the tray to be 7.5 centimeters?
no it is too large
Step-by-step explanation:
An equation is formed when two equal expressions. The equation that models the volume of the tray in terms of its width, x, in centimeters is 3x² + 15x - 252 = 0.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the width of the rectangular prism die be represented by x.
Given that the length of the tray should be five centimeters longer than its width. Therefore, the length and the width of the prism can be written as,
Width = x
Length = x + 5
Further, it is given that the volume of die is 252 cubic centimeters in order for the dice to roll properly. Also, the height of the prism is 3 centimeters. Therefore, the Volume can be written as,
Volume = Length × Width × Height
252 = (x + 5) × x × 3
252 = 3x(x+5)
252 = 3x² + 15x
3x² + 15x - 252 = 0
Hence, the equation that models the volume of the tray in terms of its width, x, in centimeters is 3x² + 15x - 252 = 0.
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