The problem statement gives a relation between the amount removed from one bag and the amount removed from the other. It asks for the amount remaining in each bag. Thus, there are several choices for variables in this problem, some choices resulting in more complicated equations than others.
Let's do it this way: let x represent the amount remaining in bag 1. Then the amount removed from bag 1 is (100-x). The amount remaining in bag 2 is 2x, so the amount removed from that bag is (100-2x). The problem statement tells us the relationship between amounts removed:
... (100 -x) = 3(100 -2x)
... 100 -x -3(100 -2x) = 0 . . . . . . subtract the right side
... 5x -200 = 0 . . . . . . . . . . . . . . eliminate parentheses and collect terms
... x -40 = 0 . . . . . . . . . . . . . . . . .divide by 5
... x = 40 . . . . . . . . . . . . . . . . . . . add 40
- 40 kg is left in the first bag
- 80 kg is left in the second bag
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<u>Check</u>
The amount removed from the first bag is 60 kg. The amount removed from the second is 20 kg. The amount removed from the first bag is 3 times the amount removed from the second bag, as described.
Answer:
3n^2 - 5n - 28
Step-by-step explanation:
(n - 4)(3n + 7)
3n^2 + 7n - 12n - 28
3n^2 - 5n - 28
hope this hepls!!!
Answer:
18.84 is the answer
Step-by-step explanation:
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9514 1404 393
Answer:
D: all real numbers
R: f(x) > 0
A: f(x) = 0
(-∞, 0), (+∞, +∞)
vertical stretch by a factor of 2; left shift 2 units
Step-by-step explanation:
The transformation ...
g(x) = a·f(b(x -c)) +d
does the following:
- vertical stretch by a factor of 'a'
- horizontal compression by a factor of 'b'
- translation right by 'c' units
- translation up by 'd' units
For many functions, horizontal coordinate changes are indistinguishable from vertical coordinate changes. Exponential functions tend to be one of those.
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Using the above notation, you seem to have f(x) = 3^x, and g(x) = 2f(x+2). The transformation is a vertical stretch by a factor of 2, and a translation left 2 units.
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As with all exponential functions, ...
- the domain is "all real numbers"
- the range is all numbers above the asymptote: f(x) > 0
- the horizontal asymptote is f(x) = 0
The function is a growth function, so ...
- x → -∞, f(x) → 0
- x → ∞, f(x) → ∞
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<em>Additional comment</em>
The left shift is equivalent to an additional vertical stretch. The function could be rewritten as ...
f(x) = 18(3^x)
with no left shift and a vertical stretch by a factor of 18 instead of 2.
