Math Problem Statement
Solution
The image you've provided appears to be a textbook or instructional guide related to polynomials and involves calculating the area of a lawn with rectangular sections. Here’s a breakdown of the steps involved in the problem shown in the image:
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Total Area Calculation:
- The total area of the lawn is calculated using the formula for the area of a rectangle:
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Subtraction of Non-Grass Regions:
- There are smaller rectangular sections that do not require grass seed, which need to be subtracted from the total area.
- The area of the square regions is units.
- The other rectangular region with dimensions has an area of units.
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Grass Area Calculation:
- The area that requires grass seed is found by subtracting the areas of the non-grass regions from the total area:
- Simplification confirms that this is an equivalent expression.
If you need further clarification or a more detailed explanation of any specific part, feel free to ask!
Here are five related questions you might find helpful:
- How do you factorize the polynomial ?
- What is the significance of finding the area that requires grass seed?
- Can this method be used for lawns with different shapes, such as circular sections?
- How would you adjust the calculation if the length and width of the lawn were in different units?
- What is the importance of simplifying expressions like ?
Tip: When dealing with area calculations, always make sure all the units are consistent to avoid errors in your final answer.
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Area Calculation
Simplification
Formulas
Area of a rectangle: A = l × w
Total area: 60x^2 units^2
Subtraction of non-grass areas: 60x^2 - (16 + 40x - 32) units^2
Theorems
Simplification of polynomials
Suitable Grade Level
Grades 8-10
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