To simplify the expression:
-(6 x^3 - 2 x + 3) - 3 x^3 + 5 x^2 + 4 x - 7
Start with - (6 x^3 - 2 x + 3) = -6 x^3 + 2 x - 3:
-6 x^3 + 2 x - 3 - 3 x^3 + 5 x^2 + 4 x - 7
Next, combine similar terms: -3 x^3 - 6 x^3 + 5 x^2 + 4 x + 2 x - 7 - 3 = (-3 x^3 - 6 x^3) + 5 x^2 + (4 x + 2 x) + (-7 - 3):
(-3 x^3 - 6 x^3) + 5 x^2 + (4 x + 2 x) + (-7 - 3)
-3 x^3 - 6 x^3 results in -9 x^3:
-9 x^3 + 5 x^2 + (4 x + 2 x) + (-7 - 3)
Combine 4 x and 2 x to get 6 x:
-9 x^3 + 5 x^2 + 6 x + (-7 - 3)
The operation -7 - 3 yields -10:
-9 x^3 + 5 x^2 + 6 x - 10
Factoring out -1 from -9 x^3 + 5 x^2 + 6 x - 10 leads to:
Final Answer: - (9 x^3 - 5 x^2 - 6 x + 10)
Let
denote the length of the pond and <span> signify its width. It's recognized that the pond's volume equals the area of its base multiplied by its depth. In this case, the base area can be computed as volume divided by depth, equating to 72000 in³ divided by 24 in, resulting in an area of 3000 in². Given that the area is expressed as x multiplied by y, we come to equation 1, 3000 = x * y. If we have x = 2y, we substitute this into equation 1, leading to 3000 = (2y) * y, simplifying to 2y² = 3000 and consequently y² = 1500, giving y = 38.7 in. Thus, x = 2y yields x = 2 * 38.7 = 77.4 in. The conclusion is that the pond's length is 77.4 in while its width is 38.7 in.
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Step-by-step explanation:
I included the work done
The expression evaluates to 54.
