Rewrite the function by completing the square. f(x)=x^2+16x-46
1 answer:
Answer:
Step-by-step explanation:
Completing the square is a multi-step process that involved rewriting an equation such that it has a factored term, a coefficient, and a constant. First, group the equation, then add a term such that the grouped part of the equation can be simplified, then balance the equation, finally simplify and factor the equation.
Group;
Add in a term that makes the grouped part of the equation a perfect square, this can be done by dividing the linear term by 2, then balancing the equation;
Simplify, factor;
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Let x ft be the lenght of the fence and y ft be the width of the fence.
1. The length of the habitat should be at least 80 feet, then
2. The perimeter of the habitat should be no more than 300 feet. The perimeter of the fenceis 2x+2y ft, then
3. The system of inequalities that represent the model is
The graph of these inequalities is attached.
Two possible solutions are
- x=100 ft, y=20 ft (100≥80 and 2·100+2·20=240≤300);
- x=110 ft, y=30 ft (110≥80 and 2·110+2·30=280≤300).
