Algebra Answers

Determine the complex number z which satisfies the equations |z + 3i| = |z + 5 − 2i|
and |z − 4i| = |z + 2i| simultaneously.

If the roots of the cubic az3 + bz2 + cz + d = 0 form an arithmetic progression α − β,
α, α + β, prove that (2b2 − 9ac)b + 27a2d = 0.

Kari and Samantha have determined that their water-balloon launcher works best when they launch the balloon at an angle within 3 degrees of 45 degrees. Which equation can be used to determine the minimum and maximum optimal angles of launch, and what is the minimum angle that is still optimal?

A. |x – 3| = 45; minimum angle: 42 degrees
B. |x – 3| = 45; minimum angle: 45 degrees
C. |x – 45| = 3; minimum angle: 42 degrees
D. |x – 45| = 3; minimum angle: 45 degrees

Use a standard algorithm to calculate 4 + 2/3 - 3/4

String licorice costs $1.77 for 3 m. How much licorice could Patu buy with $9?

2.5 x 10-3

3.Solve for z if (z−2)^2 + 16=0.
\\(\\pm 4i)
\\(2\\pm 4i)
\\(-1\\pm i)
\\(2\\pm 2i)

The function gleft(xright)=fracx−−35x−7is not defined for x=___________________.
a.7
b.\\(frac{5}{7}\\)
c.5
d.\\(frac{7}{5}\\)

The function g left(xright)=fracx−−3 is not defined for x=___________________.
a.7
b.\\(frac{5}{7}\\)
c.5
d.\\(frac{7}{5}\\)