PreCalculus I → 1.1 – Homework - DZEYMOV MATH BOOKS

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PreCalculus I

PreCalculus I

1.1 – Homework

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1. Select all elements below that are natural numbers

2

$\sqrt{3}$

$\frac{2}{3}$

5

Question 1 of 45

2. Select all elements below that are integers

2

$\sqrt{3}$

$\frac{2}{3}$

5

Question 2 of 45

3. Select all elements below that are rational numbers

$\sqrt{3}$

5

2

$\frac{2}{3}$

Question 3 of 45

4. Select all elements below that are irrational numbers

$\frac{2}{3}$

5

2

$\sqrt{3}$

Question 4 of 45

5. The set of numbers between and including 5 and 16 can be written as follows:

$\{x|5>x>16\}$

$\{x|5\le x\le16\}$

$\{x|5<x>16\}$

$\{x|5<x<16\}$

Question 5 of 45

6. The set of numbers between but not including -6 and 6 can be written as follows:

$\{x|-6<x>6\}$

$\{x|-6>x>6\}$

$\{x|-6\le x\le 6\}$

$\{x|-6<x<6\}$

Question 6 of 45

7. The set of numbers between 8 and 24, including 8, but not including 24 can be written as follows:

$\{x|8<x>24\}$

$\{x|8>x>24\}$

$\{x|8\le x<24\}$

$\{x|8<x\le 24\}$

Question 7 of 45

8. The set of numbers between but not including 3 and 7 can be written as follows:

$[3,7)$

$[3,7]$

$(3,7)$

$(3,7]$

Question 8 of 45

9. The set of numbers between and including -3 and 12 can be written as follows:

$(-3,12]$

$[-3,12)$

$(-3,12)$

$[-3,12]$

Question 9 of 45

10. The set of numbers between and including 3 and 7 can be written as follows:

$[3,7]$

$(3,7]$

$(3,7)$

$[3,7)$

Question 10 of 45

11. Use properties of real numbers to write the expression without parentheses. Do not use any spaces in your answer.

$2(x-4)$

Question 11 of 45

12. Use properties of real numbers to write the expression without parentheses. Do not use any spaces in your answer.

$(3c)(c+2d-5f)$

$3c^2+6cd+15c+15f$

$3c^2+6cd-15cf$

$4c+5d-2cf$

$4c+2d-5f$

Question 12 of 45

13. Use properties of real numbers to write the expression without parentheses. Simplify your result

$\frac{2}{3}(6x+5)$

$2x+10$

$\frac{12}{3}x+\frac{10}{3}$

$4x+5$

$4x+\frac{10}{3}$

$3x+5$

Question 13 of 45

14. Perform the indicated operation:

$4\left(\frac{3}{8}+\frac{1}{2}\right)$

$\frac{8}{5}$

$\frac{2}{7}$

$-\frac{1}{2}$

$\frac{7}{2}$

$\frac{16}{10}$

Question 14 of 45

15. Perform the indicated operations:

$\dfrac{\frac{2}{5}+\frac{1}{2}}{\frac{1}{10}+\frac{3}{15}}$

Question 15 of 45

16. Perform the indicated operations:

$\left(\frac{1}{2}+\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{4}\right)$

$-\frac{3}{16}$

$\frac{1}{16}$

$\frac{1}{4}$

$\frac{3}{16}$

0

Question 16 of 45

17. Perform the indicated operations:

$\left(\frac{2}{3}+\frac{1}{9}\right)\left(2-\frac{1}{5}\right)$

0

$\frac{7}{5}$

$\frac{7}{45}$

$-\frac{5}{27}$

1

Question 17 of 45

18. Select the correct symbol from the dropdown menu to make a true statement

$\frac{3}{5}$ 0.5

Question 18 of 45

19. Place the correct symbol in the space to make a true statement

$\frac{2}{3}$ 0.67

Question 19 of 45

20. Place the correct symbol in the space to make a true statement

$-\frac{3}{4}$ $-\frac{1}{2}$

Question 20 of 45

21. Place the correct symbol in the space to make a true statement

$-2$ $-5$

Question 21 of 45

22. State whether the inequality is true or false.

$\frac{4}{5}<\frac{2}{3}$

True

False

Question 22 of 45

23. State whether the inequality is true or false.

$\sqrt{3}>1.6$

True

False

Question 23 of 45

24. State whether the inequality is true or false.

$\sqrt{5}>\frac{5}{2}$

True

False

Question 24 of 45

25. State whether the inequality is true or false.

$7\le7$

True

False

Question 25 of 45

26. State whether the inequality is true or false.

$-\pi>-3.2$

True

False

Question 26 of 45

27. State whether the inequality is true or false.

$3.\overline{35}>3.3\overline{5}$

True

False

Question 27 of 45

28. For the indicated sets, find $A\cap B$ :

$A=\{5,10,15,20,25\}, \ \ \ \ \ B=\{4,8,10,12,20\}$

$A\cap B=\{4,5,8,15\}$

$A\cap B=\{4,5,8,10,12,15,20,25\}$

$A\cap B=\{10,20\}$

$A\cap B=\{5,10,15,20,25\}$

Question 28 of 45

29. For the indicated sets, find $A\cup B$ :

$A=\{5,10,15,20,25\}, \ \ \ \ \ B=\{4,8,10,12,20\}$

$A\cup B=\{10,20\}$

$A\cup B=\{4,5,8,15\}$

$A\cup B=\{5,10,15,20,25\}$

$A\cup B=\{4,5,8,10,12,15,20,25\}$

Question 29 of 45

30. For the indicated sets, find $A\cup B$ :

$A=\{2,3,4,8,9,12,15\}, \ \ \ \ \ B=\{2,3,5,8,12,20\}$

$A\cup B=\{2,3,8,12\}$

$A\cup B=\{2,3,4,6,9,12,15,20\}$

$A\cup B=\{5,9,15,20\}$

$A\cup B=\{2,3,4,5,8,9,12,15,20\}$

Question 30 of 45

31. For the indicated sets, find $A\cap B$ :

$A=\{2,3,4,8,9,12,15\}, \ \ \ \ \ B=\{2,3,5,8,12,20\}$

$A\cap B=\{2,3,8,12\}$

$A\cap B=\{2,3,4,5,8,9,12,15,20\}$

$A\cap B=\{5,9,15,20\}$

$A\cap B=\{2,3,4,6,9,12,15,20\}$

Question 31 of 45

32. For the indicated sets, find $A\cup B \cup C$ :

$A=\{1,2,3,4\},\ \ \ \ \ B=\{4,5,6,8\},\ \ \ \ \ C=\{2,3,4,10\}$

$A\cup B \cup C=\{4\}$

$A\cup B \cup C=\{3,4\}$

$A\cup B \cup C=\{1,5,6,8,10\}$

$A\cup B \cup C=\{1,2,3,4,5,6,8,10\}$

Question 32 of 45

33. For the indicated sets, find $A\cap B \cap C$ :

$A=\{1,2,3,4\},\ \ \ \ \ B=\{4,5,6,8\},\ \ \ \ \ C=\{2,3,4,10\}$

$A\cap B \cap C=\{1,5,6,8,10\}$

$A\cap B \cap C=\{4\}$

$A\cap B \cap C=\{3,4\}$

$A\cap B \cap C=\{1,2,3,4,5,6,8,10\}$

Question 33 of 45

34. Find $A\cup B$ if:

$A=\{x|x\ge5\}, \ \ \ \ B=\{x|x<20\}$

$\mathbb{R}$

$(20,\infty)$

$[5,20)$

$(-\infty,5)\cup(20,\infty)$

Question 34 of 45

35. Find $A\cap B$ if:

$A=\{x|x\ge5\}, \ \ \ \ B=\{x|x<20\}$

$(20,\infty)$

$\mathbb{R}$

$(-\infty,5)\cup(20,\infty)$

$[5,20)$

Question 35 of 45

36. Find $A\cup B$ if:

$A=\{x|x>12\}, \ \ \ \ B=\{x|x<-18\}$

$(-18,12)$

$\mathbb{R}$

$\emptyset$

$(-\infty,-18)\cup(12,\infty)$

Question 36 of 45

37. Find $A\cap B$ if:

$A=\{x|x>12\}, \ \ \ B=\{x|x<-18\}$

$(-18,12)$

$(-\infty,-18)\cup(12,\infty)$

$\mathbb{R}$

$\emptyset$

Question 37 of 45

38. Express the set in interval notation

$[-2,2)$

$(2,-2]$

$(-2,2]$

$(-2,2)$

Question 38 of 45

39. Express the set in interval notation

$(-8,5)$

$[-8,5)$

$(8,-5]$

$(-8,5]$

Question 39 of 45

40. Express the set in interval notation

$(-10,-3]$

$(-10,-3)$

$[-10,-3]$

$[-10,-3)$

Question 40 of 45

41. Express the set in interval notation

$(-\infty,-8)\cup[1.5,\infty)$

$[-\infty,-8)\cup[1.5,\infty]$

$(-\infty,-8)\cup(1.5,\infty)$

$(-\infty,-8]\cup(1.5,\infty)$

Question 41 of 45

42. Evaluate:

$\left|-\sqrt{25} \right|$

5

25

-25

-5

Question 42 of 45

43. Evaluate:

$\left| 8-\left|-8\right|\right|$

16

4

-16

0

Question 43 of 45

44. Evaluate:

$\left|3-\left|-10\right|\right|$

7

30

13

-7

Question 44 of 45

45. Evaluate:

$5-\left|2-10\right|$

17

13

-3

-7

Question 45 of 45

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1.1 – The Real Numbers – Real Numbers

1.1 – Quiz

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