check the picture below.
now, if we split that triangle like so with that red line, we can use the right-triangle there, to get θ.

Answer:
B: 1/64
Step-by-step explanation:
2^3 = 8
8^(-2)=1/(8^2)=1/64
When both increase, the slope is positive (+)/(+)=(+)
We have a line passing through 3 points. We can use the first
two points to find the equation of the line.
(6,3), (8,4)
slope m = (4-3)/(8-6) = 1/2
We can use the point slope form y-y1 = m(x-x1) or
the slope intercept form y = mx + b
to find the equation of the line.
Let's take the point (6,3) and use y = mx + b to find b
y = 3, x = 6, m = 1/2
3 = (1/2)(6) + b
3 = 3 + b
0 = b
The equation of our line is y = (1/2)x
We have a line of equation y = (1/2)x going through point (n,-2)
Plugging in we have: -2 = (1/2)n
2(-2) = n
-4 = n
Your answer is n = -4
NOTE: looking at the 3 points as given initially: (6,3), (8,4), (n,-2)
We can see that 3 = (1/2)6 and 4 = (1/2)8 so -2 = (1/2)n makes sense
Hope this helps you :)
1) A quadratic will have no real roots when its discriminant is negative


Dividing by 4,

We have a positive coefficient on k^2 so this parabola is a CUP (concave up positive) so has a minimum at the vertex. If the vertex y value is less than zero, the inequality will be true in the range between the zeros.

That's true for

2) We look for the meet of the line and the parabola:


For two intersections we need a positive discriminant:



That's means two negative or two positive, so
or 