Pregunta
Workers at a wildlife center plan a new habitat for meerkat
The habitat must include at least
meerkat. The area of the habitat is
meerkats can the habitat hold? Write, solve, and graph an
inequality to find the’possible numbers.of.meerkats.
Show your work.
The habitat must include at least
meerkat. The area of the habitat is
meerkats can the habitat hold? Write, solve, and graph an
inequality to find the’possible numbers.of.meerkats.
Show your work.
Ask by Blake May. in the United States
Jan 24,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The habitat can hold up to 12 meerkats.
Solución
To determine how many meerkats the habitat can accommodate, we’ll set up and solve an inequality based on the given information.
Given:
- Total Habitat Area:
- Space Requirement per Meerkat:
Let:
-
= number of meerkats
Step 1: Set Up the Inequality
Each meerkat requires at least
Since the habitat must accommodate at least
Step 2: Solve the Inequality
To find the maximum number of meerkats the habitat can hold, solve for
Divide both sides by 6.5:
Conclusion:
The habitat can accommodate up to 12 meerkats.
Step 3: Graph the Inequality
We’ll graph the inequality
Since I can’t create images directly, here’s a description of the graph:
- Draw a horizontal line and mark points from 0 to 15 (for clarity).
- Highlight the region from 0 up to and including 12.
- Use a closed circle at
to indicate that 12 meerkats are allowed.
Number of Meerkats (n)
0 ———————•——————————•———————>
6 12 15
- The closed dot at
signifies that 12 is included in the solution. - The arrow points to the left of 12, indicating all numbers less than or equal to 12 are valid.
Final Answer:
The habitat can hold up to 12 meerkats.
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Simplifique esta solución Bonus Knowledge
To determine how many meerkats can be accommodated in the habitat, we can set up an inequality based on the given area requirements.
Let
Given that the total area of the habitat is
Now, to solve for
Thus, the habitat can hold a maximum of 12 meerkats.
To graph this inequality, you would draw a number line and mark the point 12. Since the inequality is “less than or equal to,” you would shade everything to the left of 12, including the point 12 itself (often represented with a closed circle).
So, the solution is
Now, let’s summarize the key points:
- Number of meerkats that can fit: 12.
- Graph: A number line showing all integer values from 0 to 12, closed at 12.
Problem-Solving Tips & Common Mistakes:
When working with inequalities, a common mistake is to incorrectly change the direction of the inequality sign while solving. Remember that you only reverse the inequality when you multiply or divide by a negative number! Also, always pay attention to units; make sure that your measurements are consistent.
Real-World Application:
Understanding how to efficiently calculate space requirements has real-world implications in wildlife conservation and habitat management. By ensuring adequate living space for animals, wildlife centers can promote healthier, happier animals that thrive in their environments. Whether designing new habitats or optimizing existing ones for animal care, these calculations help ensure the well-being of precious wildlife!
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