Given the values of the linear functions f (x) and g(x) in the tables, where is (f – g)(x) positive?
1 answer:
Comparing the functions, from the tables, it is found that (f - g)(x) is positive in the interval (–∞, 9) .
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- For the subtraction function, we simply subtract both functions, thus:
- It is positive if f is greater than g, that is: f(x) > g(x).
- It is a linear function, so one function is greater before the equality, one after.
- They are equal at x = 9.
- If x < 9, f(x) > g(x), and thus, (f - g)(x) is positive, which means that the desired interval is:
(–∞, 9)
A similar problem is given at brainly.com/question/24610273
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Answer:
Width of the uniform path that surrounds the piece of land = 3 m
Step-by-step explanation:
Let the width of the path that surrounds the piece of land be x.
The situation described is sketched in the attached image to this solution.
The dimension of the Length of the piece of land including the uniform path that surrounds it = (40 + 2x) m
The Breadth of the piece of land including the uniform path that surrounds it = (25 + 2x) m
The area of the piece of land including the uniform path that surrounds it
= (Area of the piece of land) + (Area of the uniform path that surrounds it)
Area of the piece of land = Length × Breadth = 40 × 25 = 1000 m²
Area of the uniform path that surrounds it = 426 m² (Given in the question)
The area of the piece of land including the uniform path that surrounds it = 1000 + 426 = 1426 m²
But the area of the piece of land including the uniform path that surrounds it is also
= (Length of the piece of land including the uniform path that surrounds it) × (Breadth of the piece of land including the uniform path that surrounds it
= (40 + 2x) + (25 + 2x)
= 1000 + 80x + 50x + 4x²
= (4x² + 130x + 1000) m²
Equation these 2 areas
4x² + 130x + 1000 = 1426
4x² + 130x - 426 = 0
Solving the quadratic equation
x = 3 or -35.5
Since the width cannot be negative,
x = 3 m
Hope this Helps!!!
