Algebra Know-It-ALL
Part Three 525 Adding the quantity (x^2 + 1) to each side, we get 2 x^2 = 2 Dividing this equation through by 2, we obtain x^2 = ...
526 Review Questions and Answers When we plug either of these into the first original equation, we have to square it. We’ll get ...
Part Three 527 Answer 27-6 The best approach here is to multiply out the right sides of both of the binomial-squared equations, ...
528 Review Questions and Answers When we subtract the quantity (a^2 x^2 +b^2 ) from each side, we get 2 abx=− 2 abx We can add 2 ...
Part Three 529 Now let’s subtract the entire right side of this equation from the left side. When we do that, we obtain x^2 + 2 ...
530 Review Questions and Answers The discriminant of this quadratic is negative, telling us that it has no real roots. The x-val ...
Part Three 531 the second function. Figure 30-3 shows the curves and the solution point. On both axes, each increment represents ...
532 Review Questions and Answers Question 28-4 When we compare the systems stated in Questions 28-2 and 28-3 and graphed in Figs ...
Part Three 533 of the other real solution will become more positive to the same extent. The y-values of both solutions will rema ...
and y= (x− 1)^2 How can we sketch an approximate graph of this system, showing the real solution? Answer 28-6 We can tabulate an ...
Part Three 535 Question 28-7 Let’s modify the system of equations stated in Question 28-6. Suppose we multiply the right side of ...
and y= (x− 1)^2 − 12 How will this affect the graph of the second equation, shown by the dashed curve? How will it affect the re ...
Part Three 537 Answer 28-9 We can tabulate and plot several points in both functions including the real solution, (−1,0). Table ...
538 Review Questions and Answers Question 28-10 Consider the system of equations we evaluated in Answer 27-10, where we found th ...
Part Three 539 The common log is sometimes called the base-10 log, because 10 is the base that we raise to various powers. Quest ...
540 Review Questions and Answers The common log of 1,000 is 3, because 10^3 = 1,000. The common log of 10,000 is 4, because 10^ ...
Part Three 541 Answer 29-5 The natural log is related to a growing number like this: The natural log of e is 1, because e^1 =e. ...
542 Review Questions and Answers Answer 29-8 The common exponential of a number is what we get when we raise 10 to a power equal ...
Part Three 543 Answer 29-10 To find the number x whose natural exponential is 1/e^5 , we must find the power of e that gives us ...
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