91Ó°ÊÓ

Expressing solutions to the nearest one-thousandth. $$3 x^{2}-12 x-10=0$$

Give a step-by-step description of how to solve \(3 x^{2}+9 x-\) \(4=0\) by completing the square.

Set up an equation and solve each problem. A group of students agreed that each would contribute the same amount to buy their favorite teacher an \(\$ 80\) birthday gift. At the last minute, 2 of the students decided not to chip in. This increased the amount that the remaining students had to pay by \(\$ 2\) per student. How many students actually contributed to the gift?

Find each of the products and express the answers in the standard form of a complex number. $$(-5 i)(-12 i)$$

Use the discriminant to help solve each problem. Determine \(k\) so that the solutions of \(x^{2}-2 x+k=0\) are complex but nonreal.

Set up an equation and solve each problem. A retailer bought a number of special mugs for \(\$ 48\). She decided to keep two of the mugs for herself but then had to change the price to \(\$ 3\) a mug above the original cost per mug. If she sells the remaining mugs for \(\$ 70\), how many mugs did she buy and at what price per mug did she sell them?

For the indicated variable. Assume that all letters represent positive numbers. \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) for \(y\)

Find each of the products and express the answers in the standard form of a complex number. $$(3 i)(2-5 i)$$

Use the discriminant to help solve each problem. Determine \(k\) so that \(4 x^{2}-k x+1=0\) has two equal real solutions.

For the indicated variable. Assume that all letters represent positive numbers. \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) for \(x\)