Mang Jose plans to fence his rectangular lot before he will plant mushrooms for his mushrooms production business. The perimeter of the lot is 40 meters and the area is 96 square meters.Using the concept of the sum and product of roots of a quadratic equation, how would you determine the length and the width of the rectangular lot? Provide a quadratic equation representing this scenario.
Someone help me
Answers
Answer: The rectangular lot is 12x8 meters
Step-by-step explanation:Perimeter of a geometric figure is the sum of all its sides.
A rectangle is a quadrilateral that has opposite sides parallel and equal, which means, and suppose l is length and w is width:
P = 2l + 2w
The perimeter of the lot is 40m, thus:
2l + 2w = 40
Area of a rectangle is calculated as:
A = length x width
The lot has area of 96, thus:
lw = 96
Solving the system of equations:
2l + 2w = 40 (1)
lw = 96 (2)
Isolate l from (1):
2l = 40 - 2w
l = 20 - w (3)
Substitute (3) in (2):
w(20-w) = 96
There are many methods to determine the roots of a quadratic equation. One of them is using the sum and product of those roots.
- Sum of the roots is given by:
sum = 20
- Product of the roots is:
prod = 96
The roots of the quadratic equation are numbers which the sum results in 20 and product is 96:
w₁ = 12
w₂ = 8
If we substitute w to find l, the numbers will be l₁ = 8 and l₂ = 12.
Since length is bigger than width, the rectangular lot Mang Jose has to plant mushrooms measures 12m in length and 8m in width
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Mike won 46.67% of all of his matches.
What is a percentage?
A ratio or value that may be stated as a fraction of 100 is called a percentage. Moreover, it is indicated by the symbol "%."
The total number of matches that Mike wrestled is:
Total matches = number of matches won + number of matches lost + number of matches tied
Total matches = 7 + 6 + 2
Total matches = 15
To find the percentage of matches that Mike won, we can use the formula:
Percentage = (Number of matches won / Total number of matches) x 100%
Plugging in the values we know, we get:
Percentage = (7 / 15) x 100%
Percentage = 0.4667 x 100%
Percentage = 46.67%
Therefore, the Percentage = 46.67%.
To learn more about the percentage;
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Answer:
Mike won 46.67% of his matches
Step-by-step explanation:
Mike participated in a total of 7 + 6 + 2 = 15 matches.
The percentage of matches that Mike won can be found by diving the matches he won by the total number of matches and multiplying it by 100 to convert the decimal to a percentage.
(7/15) x 100% ≈ 46.67%
Therefore, Mike won approximately 46.67% of his matches.
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