there are 40 entries in the science fair. How many ways can they finish in first, second, and third place?
1 answer:
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Answer:
Part A)
Part B) The solution in the attached figure
Step-by-step explanation:
<u><em>The complete question is</em></u>
Suppose Rick has 40 ft of fencing with which he can build a rectangular garden. Let X represent the length of the garden and let Y represent the width.
A. Please write an inequality representing the fact that the total perimeter of the garden is at most 40 ft.
B. Please sketch part of the solution set for this inequality that represents all possible values for the length and width of the garden.
Part A)
Let
x ----> the length of the rectangular garden
y ----> the width of the rectangular garden
we know that
The perimeter of the rectangular garden is equal to
In this problem the word "at most" means "less than or equal to"
so
The inequality that represent this situation is
Simplify
Part B) we have
Isolate the variable y
subtract x both sides
The solution of the inequality is the shaded area below the solid line
The slope of the solid line is negative (m=-1)
The y-intercept of the solid line is (0,20)
The x-intercept of the solid line is (20,0)
therefore
The solution is the triangular shaded area
see the attached figure
Remember that
Both the length and the width must be positive
we are given
The angle is at right angled
It means that it's angle will be 90 degree
Since, these angles are part of right angle
so, their sum must be 90 degree
so, we get
now, we can solve for a
divide both sides by 7
and we get
.............Answer