# 25 Problems : Solve for Real or Imaginary Roots, Word Problems (Sum of two numbers) , Lowest Terms, Inequalities and Quadratic Equations

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1. Perform the indicated operation: (x3 - 2x2 - 4x + 3)  (x - 3)

2. Find the product: (x - 2)(x + 3)(x - 4)

3. Simplify without having negative exponents: (- 3s-3t2)-2

4. Convert to scientific notation and then solve. Give answer in scientific notation: (0.0000003)4

5. Factor completely: 3a3b - 3ab3

6. Factor completely: ax - 2a - 5x + 10

7. Solve: (2x - 1)(3x + 5) = 5

8. The sum of two numbers is 4, and their product is -32. Write the complete solution (no guessing or trial by error) and find the numbers.

9. Perform the indicated operation and write the answer in lowest terms:

10. Perform the indicated operation and write the answer in lowest terms:

11. Simplify:

12. Solve:

13. For a certain time period the ratio of the dollar value of exports to the dollar value of imports for the United States were 2 to 3. If the value of exports during that time period was 48 billion dollars, then what was the value of imports?

14. Simplify:

15. Simplify:

16. Simplify:

17. Find all real or imaginary solutions:

18. Find all real or imaginary solutions:

19. Two positive numbers differ by 11, and their square roots differ by 1. Write the complete solution (no guessing or trial by error) and find the numbers.

20. Solve by using the quadratic formula: 2x2 + 5x - 3 = 0

21. Solve by completing the square: 2x2 + x - 6 = 0

22. Solve by any method:

23. Graph the quadratic equation and state the domain and range: y = 16 - x2

24. Solve the inequality: w2 + 3w < 18. Also state (in proper interval notation) and graph the solution set.

25. Solve the inequality: . Also state (in proper interval notation) and graph the solution set.

On the attachment are 25 problems that need to be Solved completely in detail for me.

- Some may involve graphing.

- Also, they must be solved in Word using Equation Editor or similar. No hand written solving please, because I can not read scanned documents on my computer.

- Also, must be solved using Algebra concepts only, not Calculus or other methods.

Please see attachment more details to see if you can help.

THANKS!

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##### Solution Summary

Twenty-five Problems involving Solve for Real or Imaginary Roots, Word Problems (Sum of two numbers) , Lowest Terms, Inequalities and Quadratic Equations are solved. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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