Answer:
Elliot will make 4 hats and 16 scarves
Step-by-step explanation:
Let x be the number of hats and y be the number of scarves Elliot will make.
Elliott wants to make a total of 20 items, then
x + y = 20
Each hat uses 0.2 kilograms of yarn, so x hats use 0.2x kilograms of yarn and each scarf uses 0.1 kilogram of yarn, then y scarves use 0.1y kilograms of yarn. Elliott wants to use twice as much yarn for scarves as for hats, then
0.1y = 2(0.2x)
Thus,
0.1y = 0.4x
y = 4x
Substitute it into the first equation:
x + 4x = 20
5x = 20
x = 4
y = 20 - 4
y = 16
Hence, Elliot will make 4 hats and 16 scarves
Plug x = 0 into the function
f(x) = x^3 + 2x - 1
f(0) = 0^3 + 2(0) - 1
f(0) = -1
Note how the result is negative. The actual number itself doesn't matter. All we care about is the sign of the result.
Repeat for x = 1
f(x) = x^3 + 2x - 1
f(1) = 1^3 + 2(1) - 1
f(1) = 2
This result is positive.
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We found that f(0) = -1 and f(1) = 2. The first output -1 is negative while the second output 2 is positive. Going from negative to positive means that, at some point, we will hit y = 0. We might have multiple instances of this happening, or just one. We don't know for sure. The only thing we do know is that there is at least one root in this interval.
To actually find this root, you'll need to use a graphing calculator because the root is some complicated decimal value. Using a graphing calculator, you should find the root to be approximately 0.4533976515
The answer is definitely 2.4>3x
