y^2 = x isn't a function because there is at least one value of x that produces multiple values of y. In fact, any x value greater than 0 yields two y values. If x = 0, then y = 0 is the only solution. ... Graphically, the equation fails the vertical line test, which is another way to determine that it is not a function.
The answer is (a)..........
I'm not sure if this is the easiest way of doing this, but it surely work.
Let the base of the triangle be AB, and let CH be the height. Just for reference, we have
Moreover, let CH=y and BC=z
Now, AHC, CHB and ABC are all right triangles. If we write the pythagorean theorem for each of them, we have the following system
If we solve the first two equations for y squared, we have
And we can deduce
So that the third equation becomes
(we can't accept the negative root because negative lengths make no sense)
5(n-4)=(4n-12)
First: Distribute 5 into n and -4.
5(n-4)=(5n)+(5*-4)= 5n-20.
Second: Subtract 4n from both sides to eliminate the variable from the right side of the equation.
(5n-20)=(4n-12)
n-20=-12
Next: Add 20 to both sides to eliminate the constant from the left side of the equation.
n-20=-12
n=8
The unknown number is 8.
Approx. 5 miles I would say give or take the 1/2 mile shortcut by taking a straight path back to the house. I don't know if you need an exact distance but I hope this helps.
