Basic Algebra (45 Problems)
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1. Express the following product powers of t as a single power of t
2. Write without parenthesis
3.
4. Simplify without negative exponents
5. Simplify without negative exponents
6. Multiply and simplify
(4z - 2u - 2)(6z - 5u + 6)
7. Write in simplest form without parentheses
(z - 5)(z + 7)
8. Factor Completely
9. Factor
10. Factor
tu - 5w - 5u + wt
11. Find the roots of quadratic equation
12. Solve for w
13. Solve for u (Simplify)
14. Multiply and write in lowest terms
15. Express in lowest terms
16. Subtract and write in lowest terms
17. Write as a single rational expression
18. Reduce to lowest terms
19. Solve for x (Simplify)
20. Find all values of u.
21. Solve proportion for x.
22. Simplify
23. Rewrite in simplified radical form and assume all variables represent positive numbers
24. Write in simplified radical form
25. Simplify in lowest terms
26. Simplify and assume variables represent positive real numbers
27. Write in simplified radical form by rationalizing denominator
28. Solve for u, where u is a real number
29. Solve for x (Simplify)
30. Solve where x is a real number (Simplify)
31. Simplify
32.
33. Write answer in standard form
34. Find value of k such that of a perfect square
35. Solve x by using quadratic formula
36. Find all real or imaginary roots of
37. Factor
38. When a ball is thrown, its height in meters h after t seconds is given by the equation
where v is the initial upwards velocity in meters per second. If v=10 meters per second, find all values of t for which h=3 meters.
39. Need the vertex and 4 additional points of
40. Find x-intercepts and coordinates of the vertex for the parabola
41. Factor Completely
42. Graph the set
43. Find the slope
(-21,5)(9,-10)
44. Greatest Common Factor
45.
46. Factor Completely
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Forty-five basic algebra problems are solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
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1. Express the following product powers of t as a single power of t
=
2. Write without parenthesis
3.
Solution.
4. Simplify without negative exponents
=
5. Simplify without negative exponents
6. Multiply and simplify
(4z - 2u - 2)(6z - 5u + 6)
7. Write in simplest form without parentheses
(z - 5)(z + 7)
8. Factor Completely
9. Factor
10. Factor
tu - 5w - 5u + wt
11. Find the roots of quadratic equation
Solution. As , from we know that
So,
w=-7 or w=3
12. Solve for w
Solution. As , we have
i.e.,
(w-5)(w+1)=0
So, w=5 or w=-1
13. Solve for u (Simplify)
Solution. As , we have
2=-4u
So,
u= -2/4
=-1/2
14. Multiply and write in lowest terms
15. Express in lowest terms
16. Subtract and write in lowest terms
17. Write as a single rational expression
18. Reduce to lowest terms
19. Solve for x (Simplify)
Solution. We have
So,
...
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
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- "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."
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