Determine the number of real solutions for each of the given equations. y = -3x2 + x + 12
y = 2x2 - 6x + 5
y = x2 + 7x - 11
y = -x2 - 8x - 16

1 real solution
2 real solution
no real solution

The width of a rectangle is 20 units. can the perimeter p of the rectangle be 64 units when its length x is 11 units? no, because p = 2x + 2(20) no, because p ≠ 2x + 2(20) yes, because p ≠ 2x + 2(20) yes, because p = 2x + 2(20)

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

Which expression is equivalent to -5(3x - 6/7)