What percent is 72 of 120???
2 answers:
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Answer:
No, Chancee mixed up the variables, the correct solution is that x must be between 20 and 40 and y must be between 0 and 10.
Step-by-step explanation:
Here, x and y are positive integers,
Such that, their sum is not more than 40,
i.e. x + y ≤ 40 where x, y ≥ 0,
⇒ y ≤ 40 - x ...............(1),
Their difference is at least 20,
i.e. x - y ≥ 20
-y ≥ 20 - x
⇒ y ≤ x - 20 ............(2),
Graphing y ≤ 40 - x :
Related equation of inequality (1),
y = 40 - x
if x = 0, y = 40,
if y = 0, 0 = 40 - x ⇒ x = 40,
'≤' represents a solid line,
Join the points (0, 40) and (40, 0) by solid line.
Graphing y ≤ x - 20:
Related equation of inequality (1),
y = x - 20,
if x = 0, y = -20,
if y = 0, 0 = x - 20 ⇒ x = 20,
'≤' represents a solid line,
Join the points (0, -20) and (20, 0) by solid line.
By graphing we obtained a feasible region that is the solution of the system of inequalities (1) and (2) ( shown below ),
In which,
20 ≤ x ≤ 40 and 0 ≤ y ≤ 30
Hence, Chancee did not find the correct solution.
The given functions are:
The domain is the set of all possible values that the independent variable (x) can take.
The range is the set of values that the function will take.
For these functions, the domain is all real numbers since they both will work with any positive or negative number (-∞,∞). Thus, the range is the same, all real numbers (-∞,∞).
But, for the purpose of the question let's analyze the interval you took for the table of values:
For f(x) function, you take x-values from -3 to 3, then the domain in this interval is [-3,3] and the range is the output values (f(x)), then the range is [-7,11].
For g(x) function, you take x-values from -7 to 11, then the domain in the interval is [-7,11] and the range (the g(x) values obtained) is [-3,3].
As can be noticed, in the interval the domain of the f(x) functions is the same as the range of the g(x) function, and the domain of the g(x) function is the same as the range of f(x) function. This happens because g(x) is the inverse function of f(x).