Refer to the figure shown below.
The feasible region that satisfies all the constraints is the shaded region.
The bounding vertices are
A (0, 3)
B (0, 0)
C (5, 0)
D (1.5, 3.5)
All the functions that define the constraints are either linear or constant.
The maximum value is at vertex D, and equal to 3.5.
Answer:
The function f(x) = 1/5x2 – 5x + 12 is a quadratic function, because the higher exponent is 2.
The correct statements are:
- The value of f(-10) = 82
- The graph of the function is a parabola
- The graph contains the point (20,-8)
Step-by-step explanation:
- The value of f(-10) = 1/5(-10)2 – 5(-10) + 12 = 1/5(100)+50+12 = 82 (<em>True</em> s<em>tatement</em>).
- The graph of the function is a parabola, as all the quadratic functions. (<em>True</em> s<em>tatement).</em>
- The graph of the function opens down: The parabola opens up or down depending on the "a". It is the important part of the function that determines whether it opens up or down, the parabola will open up when "a" is greater than zero.
When "a" is smaller than zero the parabola will open down. In our example a = 1/5 (greater than zero, so the parabola opens up). <em>(False Statement)</em>
- The graph contains the point (20,-8). For f(20) = 1/5(20)2 - 5(20) +12 = 1/5(400) - 100 + 12 = 80 - 100 + 12 = -8 <em>(True Statement).</em>
- The graph contains the point (0,0). For f(0) = 1/5(0)2 - 5(0) + 12 = 12, the correct point is (0,12) <em>(False Statement)</em>.
Answer:
-7
Step-by-step explanation:
Answer:
31..?
Step-by-step explanation:
517 divided by 27 equals 31
The solutions to the inequalities are x >1 and x < 6
<h3>How to solve the inequalities?</h3>
The inequality expression is given as:
-2x + 5 < 3x + 10
Collect the like terms in the above inequality
-2x - 3x < 10 - 5
Evaluate the like terms
-5x < 5
Divide by -5
x >1
Also, we have
5(x - 2) <3x + 2
Open the bracket
5x - 10 < 3x + 2
Evaluate the like terms
2x < 12
Divide by 2
x < 6
Hence, the solutions to the inequalities are x >1 and x < 6
Read more about inequalities at
brainly.com/question/24372553
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