Answers:
length of rope = 2 meters
perimeter of meadow = 12.56 square meters
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Explanation:
Assuming there are no structures (buildings, fences, etc) to get in the way of the goat, this means the goat's area that it can roam is a circle with radius r
The area of the circle is pi*r^2 which is equal to 12.56 square meters
pi*r^2 = 12.56
3.14*r^2 = 12.56
r^2 = 4
r = sqrt(4)
r = 2
The radius of the circle is 2 meters. This is the length of the rope. If the goat goes out as far as it can go, and tries to move left/right, then it will trace out a circle of radius 2. This is assuming the rope is kept fully taut the entire time.
The perimeter of the circle is the same as the circumference
circumference = 2*pi*r
circumference = 2*pi*2
circumference = 4*pi
circumference = 4*3.14
circumference = 12.56
The circumference and area are the same because r^2 = 4 and 2*r = 4 when r = 2. For any other positive r value, the area and circumference will be different values.
So in short, if a friend says that the area of a circle is the same as its perimeter, then you can immediately conclude the radius is 2.
Side note: throughout all of this solution, I used the approximation pi = 3.14 though pi has more decimal digits
Always, ALWAYS remeber this format: y = mx + b
In this equation, 'm' is the slope, and 'b' is the y-intercept
When you're trying to find a slope, remember that the equation is 
When finding the rise and run, look at two points that are on the graph AND on the line as well. Essentially, make sure the points you're using are integers.
In this, case, the rise is -3, and the run is 2. This means that the slope is 
Now we have the first part of our equation:
y = - 
+ b
But wait! How do we find b?
Sometimes you have to input x in order to find it, but only when you're not supplied with a graph. In this case, all you have to do is look!
The point of the line that is on the y-axis is called the y-intercept.
In this graph, the y-intercept is -1
Now we have our complete equation!
y = - - 1
Good luck!
Answer:
A is correct
Step-by-step explanation:
A has no solution because since the slopes are the same, setting both equations equal to each other will cancel out the slopes and result in 8=16, meaning no solution will make both sides equal to each other.
B does have a solution because of different slopes
C does have a solution because of different slopes
D does have a solution because of different slopes
