91Ó°ÊÓ

Set up an equation and solve each problem. Suppose that \(\$ 500\) is invested at a certain rate of interest compounded annually for 2 years. If the accumulated value at the end of 2 years is \(\$ 594.05\), find the rate of interest.

Find each of the products and express the answers in the standard form of a complex number. $$(3+2 i)(5+4 i)$$

Find each of the products and express the answers in the standard form of a complex number. $$(4+3 i)(6+i)$$

Solve each of the following equations for \(x\). $$10 x^{2}-31 a x-14 a^{2}=0$$

Set up an equation and solve each problem. Suppose that \(\$ 10,000\) is invested at a certain rate of interest compounded annually for 2 years. If the accumulated value at the end of 2 years is \(\$ 12,544\), find the rate of interest.

How would you solve the equation \(x^{2}-4 x=252 ?\) Explain your choice of the method that you would use.

Find each of the products and express the answers in the standard form of a complex number. $$(6-2 i)(7-i)$$

\(a\) and \(b\) represent the lengths of the legs of a right triangle, and \(c\) represents the length of the hypotenuse. Express answers in simplest radical form. Find \(c\) if \(a=4\) centimeters and \(b=6\) centimeters.

Solve each of the following equations for \(x\). $$4 x^{2}+4 b x+b^{2}=0$$

\(a\) and \(b\) represent the lengths of the legs of a right triangle, and \(c\) represents the length of the hypotenuse. Express answers in simplest radical form. Find \(c\) if \(a=3\) meters and \(b=7\) meters.