The equation y^2 - 4y - 4x^2 + 13 = 0 will produce a hyperbola. - how can we tell by simply observing the equation?
in what direction do the branches of this hyperbola open?
- How do you know? Explain.
- Sketch a graph of this hyperbola clearly indicating how you have determined the key characteristics (centre, vertices, eccentricity, foci).
Give the domain and range of this hyperbola.

19.

step-by-step explanation:

you add the 9 in the tens column since it is a single digit and 9 plus zero is 9 so it is 19

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

the answer for this is 0.25 km. : )