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0

Step-by-step explanation:

given y = (-1/2) (x-3)² - 1

to find the locations of where the graphs intersects the x-axis, we let y = 0 and solve for x (i.e we find the roots)

0 = (-1/2) (x-3)² - 1

1 = (-1/2) (x-3)²

-2 = (x-3)²   (taking square root of both sides)

±√(-2) = x -3

x = 3 ±√(-2)

we note that x is a function of √(-2), which results in an imaginary solutions and no real solutions.

Hence there are no real roots and hence the graph does NOT intersect the x-axis

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2

3100

step-by-step explanation: