t=t0+(frac{k}{2})w, for w

An inequality with
${\displaystyle x,y,z\ge -1}$ and ${\displaystyle x+y+z=1}$

Consider ${\displaystyle a{z}^2+bz+c=0}$ where a,b,c are all complex numbers. What is the condition (ie the relation between a,b,c) for which the given quadratic has both real roots?

Simplifying a system of linear inequalities
Given two inequalities
$y\ge m_1(x-x_1)+y_1$
and
$y\ge m_2(x-x_2)+y_2$
Is there anyway to solve for the space that they both exist in?

Find a recurrence relation satisfied by this sequence.
${\displaystyle a_n=5^n}$

What is the difference between $(3{)}^{-4}$ and $3^4$?

A 32% trade discount on a camera represents a discount of $147.20 from the suggested retail price.
What is the net price to the buyer?

Determine the convergence or divergence of the sequence.
${\displaystyle \sum _{n=10}^{\mathrm{\infty }}[\frac{1}{4n^2-16n+15}+\frac{1}{2}{\left(\frac{e}{\pi }\right)}^{n-1}]}$