A high school held an election for class president. Exactly 1,000 votes were cast and they were all for either Gillian or Clive.
2 answers:
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Answer: <em> </em>
Step-by-step explanation:
<h3> <em>The complete exercise is:"A gardener has 27 tulip bulbs, 45 tomato plants, 108 rose bushes, and 126 herb seedlings to plant in the city garden. He wants each row of the garden to have the same number of each kind of plant. What is the greatest number of rows that the gardener can make if he uses all the plants?"</em></h3><h3 />The first step to solve the exercise is to find the Greatest Common Factor (GCF) between 27, 45, 108 and 126.
You can follow these steps in order to find the GCF:
1. You must decompose 27, 45, 108 and 126into their prime factors:
2. You must multiply the commons with the lowest exponents. Then:
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Therefore, the greatest number of rows that the gardener can make if he uses all the plants is:
Let us list out the given information:
Cost per foot = $5
Total fencing cost = $1200
Let L be the length of the barn that will maximize the area of the pasture and W be the width of the rectangular cow pasture.
From the given information, we need to do the fencing for three sides covering 1 L and 2 W's because other L will be the fourth side is part of the side of a barn. We need to write the equation based on the cost information.
If cost/foot is $5, then cost of length ' L ' will be 5L dollars and cost of '2W' width equals 10W dollars. Total cost is $1200. We can set up second equation as
5L + 10W = 1200. This can be simplified by dividing throughout the equation by 5 to get L+ 2W= 240. Solving for L we get L = 240 - 2W
Area of a rectangle is given by A = L ×W.
Substituting 240 - 2W for L we get the area function as..
A=(240 - 2W)×W= 240W-2W²
A = -2W²+240W.
When we have a function of the form f(x) = ax^2 + bx + c, then maximum value of the function can be obtained for x = -b/2a. Using that idea we can find the maximum area.
Here in the area function a = -2 and b = 240
For W = -b/2a = -240/2(-2) = -240/-4 = 60 feet, we get maximum area.
The question is asking us to find Length. We can substitute W = 60 in the equation L = 240 - 2W to find the Length.
L = 240 - 2(60) = 240 - 120 = 120 feet.
Conclusion: The length of the side parallel to the barn that will maximize the area of the pasture is 120 feet.
Note: Here the information 400 feet in the sentence "the fourth side is part of the side of a barn that is 400 feet long" given to distract us, we might not require that information to find the Length.
