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Chapter 1: Problem 11
Find each product and write the result in standard form. $$ (-5+4 i)(3+i) $$
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Find all values of \(x\) satisfying the given conditions. $$ \begin{aligned} &y_{1}=2 x^{2}+5 x-4, y_{2}=-x^{2}+15 x-10, \text { and } &y_{1}-y_{2}=0 \end{aligned} $$
In Exercises 122鈥�133, use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. You are choosing between two texting plans. Plan A has a monthly fee of 15 dollar with a charge of 0.08 dollar per text. Plan \(B\) has a monthly fee of 3 dollar with a charge of 0.12 dollar per text. How many text messages in a month make plan A the better deal?
In Exercises 122鈥�133, use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and 88. There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90. a. What must you get on the final to earn an \(A\) in the course? b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than \(80,\) you will lose your \(\mathrm{B}\) in the course. Describe the grades on the final that will cause this to happen.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The quadratic formula is developed by applying factoring and the zero-product principle to the quadratic equation \(a x^{2}+b x+c=0\)
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'll win the contest if I can complete the crossword puzzle in 20 minutes plus or minus 5 minutes, so my winning time, \(x\), is modeled by \(|x-20| \leq 5\)
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