91影视

Absolute Value Inequalities Solve the absolute value inequality. Express the answer using interval notation and graph the solution set. $$|3 x+2| < 4$$

Simplifying Absolute Value Express the quantity without using absolute value. $$a+b+|a-b|, \text { where } a

Absolute Value Inequalities Solve the absolute value inequality. Express the answer using interval notation and graph the solution set. $$|5 x-2| < 8$$

Recall that the symbol \(\bar{z}\) represents the complex conjugate of \(z .\) If \(z=a+b i\) and \(w=c+d i,\) show that each statement is true. \(z-\bar{z}\) is a pure imaginary number.

Rationalize Put each fractional expression into standard form by rationalizing the denominator. (a) \(\sqrt{\frac{s}{3 t}}\) (b) \(\frac{a}{\sqrt[6]{b^{2}}}\) (c) \(\frac{1}{c^{3 / 5}}\)

Discriminant Use the discriminant to determine the number of real solutions of the equation. Do not solve the equation. $$3 x^{2}=6 x-9$$

Use slopes to determine whether the given points are collinear (lie on a line). (a) \((1,1),(3,9),(6,21)\) (b) \((-1,3),(1,7),(4,15)\)

Simplify the expression. (This type of expression arises in calculus when using the 鈥渜uotient rule.鈥�) $$\frac{\left(1-x^{2}\right)^{1 / 2}+x^{2}\left(1-x^{2}\right)^{-1 / 2}}{1-x^{2}}$$

Use a Special Factoring Formula to factor the expression. $$1+1000 y^{3}$$

Let \(a, b,\) and \(c\) be real numbers such that \(a>0, b<0,\) and \(c<0 .\) Find the sign of each expression. (a) \(-a\) (b) \(b c\) (c) \(a-b\) (d) \(a b+a c\)