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Chapter 1: Problem 15
Find each product and write the result in standard form. $$ (3+5 i)(3-5 i) $$
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A machine produces open boxes using square sheets of metal. The machine cuts equal-sized squares measuring 3 inches on a side from the corners and then shapes the metal into an open box by turning up the sides. If each box must have a volume of 75 cubic inches, find the length and width of the open box.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can check inequalities by substituting 0 for the variable: When 0 belongs to the solution set, I should obtain a true statement, and when 0 does not belong to the solution set, I should obtain a false statement.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \((2 x-3)^{2}=25\) is equivalent to \(2 x-3=5\).
A bank offers two checking account plans. Plan A has a base service charge of 4.00 dollar per month plus 10垄 per check. Plan B charges a base service charge of $2.00 per month plus 15垄 per check. a. Write models for the total monthly costs for each plan if x checks are written. b. Use a graphing utility to graph the models in the same [0, 50, 10] by [0, 10, 1] viewing rectangle. c. Use the graphs (and the intersection feature) to determine for what number of checks per month plan A will be better than plan B. d. Verify the result of part (c) algebraically by solving an inequality.
Explain how to solve \(x^{2}+6 x+8=0\) using factoring and the zero-product principle.
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