Answer:
The first one is -1/2
the second one is x+2y-27=0
Problema Solution
You have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the largest dimensions of this enclosure that you could build?
Answer provided by our tutors
Make a drawing and denote:
x = half of the length of the enclosure
2x = the length of the enclosure
y = the width of the enclosure
P = 800 ft the perimeter
The perimeter of the two enclosures can be expressed P = 4x + 2y thus
4x + 3y = 800
Solving for y:
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y = 800/3 - 4x/3
The area of the two enclosure is A = 2xy.
Substituting y = 800/3 - 4x/3 in A = 2xy we get
A = 2x(800/3 - 4x/3)
A =1600x/3 - 8x^2/3
We need to find the x for which the parabolic function A = (- 8/3)x^2 + (1600/3)x has maximum:
x max = -b/2a, a = (-8/3), b = 1600/3
x max = (-1600/3)/(2*(-8/3))
x max = 100 ft
y = 800/3 - 4*100/3
y = 133.33 ft
2x = 2*100
2x = 200 ft
The answer is D. y = -2x + 20. This is because it has a negative slope (-2x). When a number in a slope-intercept equation has the variable (x), that determines the positive or negative association. If it is a positive slope, it travels up from left to right. If it is a negative slope, it travels down from left to right.
The equation of a line is written as y =Mx + b, where m is the slope and b is the y intercept, which is the y value when x = 0.
You are told the slope is -1/4, so replace m with -1/4. You are also given the point (0,0) which means when x is 0, y is also 0, so replace b with 0.
The equation becomes y= -1/4x + 0
Because y is 0 you aren’t adding anything to the equation so you can remove it from the equation.
Answer is y = -1/4x
