Solve the inequality 52 - 3x < -14
1 answer:
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Answer:
The general formula that can be used to find the required combinations for n flavor ice-cream.
For 10 ice-cream flavors
Step-by-step explanation:
Let V = Vanila, C = Chocolate, S = Strawberry, P = Pineapple, B = Berry
2 ice-cream flavor:
V, C
{V/V, V/C, C/C}
3 possible combinations
3 ice-cream flavor:
V, C, S
{V/V, V/C, V/S, C/S, C/C, S/S}
6 possible combinations
4 ice-cream flavor:
V, C, S, P
{V/V, V/C, V/S, V/P, C/S, C/P, S/P, C/C, S/S, P/P}
10 possible combinations
5 ice-cream flavor:
V, C, S, P, B
{V/V, V/C, V/S, V/P, V/B, C/S, C/P, C/B, S/P, S/B, P/B, C/C, S/S, P/P, B/B }
15 possible combinations
So we have a series of
3, 6, 10, 15...
This series is known as Triangular number series
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15
The general formula for this series is
Using the above formula we can predict the number of 2-scoop combinations with 10 flavors.
Therefore, there are 55 different combinations of 2-scoop with 10 flavors.
Well for f(x) = 2x²+2
1)
the domain is all possible values "x" can safely take, safely meaning, it has no foreseeable constraints, hmm , in this case, there aren't any, so "x" values can be ℝ, and thus the domain is ℝ
2)
the range, is all values f(x) gets, from all those mutations "x" takes, notice, you have 2x², if you make "x" some negative value like say, -1,000,000, then you'll end up with 2(-1,000,000)², which simply can be rewritten as 2(-1,000,000)(-1,000,000), now, negative times negative, is positive
that means, no matter which negative value "x" takes, the value coming out of 2x², will always be positive, and "x" is positive, the same, 2x² will spit out a positive value
so, f(x) will never be negative, since 2x²+2 will never give a negative value
the lowest f(x) can get is when x = 0, then you get 2(0)²+2, which is just 2
so, f(x) goes as low as 2, then goes back up, so the range is y ≥ 2
3)
to get the inverse of any expression, you start off by switching the variables
so, let's do so
4)
the domain of the inverse, well, if two expressions are inverse of each other, say f(x) and g(x), are inverse of each other, the "domain of f(x), is the range of g(x)" and "the range of f(x) is the domain of g(x)"
so, what's the domain of the inverse? well, what's the "range" of f(x), is anything BUT below 2, well, that's also the domain for the inverse
5)
surely you know by now, what's the range of the inverse? well, what's the domain of f(x)? is ℝ, so, that's the range of the inverse then
1)
the domain is all possible values "x" can safely take, safely meaning, it has no foreseeable constraints, hmm , in this case, there aren't any, so "x" values can be ℝ, and thus the domain is ℝ
2)
the range, is all values f(x) gets, from all those mutations "x" takes, notice, you have 2x², if you make "x" some negative value like say, -1,000,000, then you'll end up with 2(-1,000,000)², which simply can be rewritten as 2(-1,000,000)(-1,000,000), now, negative times negative, is positive
that means, no matter which negative value "x" takes, the value coming out of 2x², will always be positive, and "x" is positive, the same, 2x² will spit out a positive value
so, f(x) will never be negative, since 2x²+2 will never give a negative value
the lowest f(x) can get is when x = 0, then you get 2(0)²+2, which is just 2
so, f(x) goes as low as 2, then goes back up, so the range is y ≥ 2
3)
to get the inverse of any expression, you start off by switching the variables
so, let's do so
4)
the domain of the inverse, well, if two expressions are inverse of each other, say f(x) and g(x), are inverse of each other, the "domain of f(x), is the range of g(x)" and "the range of f(x) is the domain of g(x)"
so, what's the domain of the inverse? well, what's the "range" of f(x), is anything BUT below 2, well, that's also the domain for the inverse
5)
surely you know by now, what's the range of the inverse? well, what's the domain of f(x)? is ℝ, so, that's the range of the inverse then