Solve algebraically (using a sign chart): 2x 2 – 5x + 1 < 0

1. Solve algebraically (using a sign chart): 2x2 – 5x + 1 < 0

3. Hint: if f -1(3) = a, what point is on the inverse? What point must be on the original function f(x)? How does that help us?

5. Given f(x) = 3x3-10x2 + x + 6 = 0List the possible rational zeros.Fully factor, and list the real solutions.

6. Given f(x) = 3x3-10x2 + x + 6 = 0List the possible rational zeros.Fully factor, and list the real solutions.(Problem of the day quiz will be the middle of next week)

7. What is the remainder when f(x) = 2x37-4x21-6x12-5x-1 is divided by (x + 1)?What does that mean?

8. What is the remainder when f(x) = 2x37-4x21-6x12-5x-1 is divided by (x + 1)?What does that mean?Remainder theorem: f(-1) = -2 – (-4) – 6 – (-5) – 1 = 0x + 1 is a factor

9. If Set A is even integers < 10, and Set B is multiples of 3 less than 20, then A U B is:A) {2 ,4, 6 ,8} B) {3 ,6 ,9,12,15,18}C) {6} D) {2,3,4,6,8,9,12,15,18}E) {2,4,6,8,10,12,14,16,18}

10. If Set A is even integers < 10, and Set B is multiples of 3 less than 20, then A U B is:A) {2 ,4, 6 ,8} B) {3 ,6 ,9,12,15,18}C) {6} D) {2,3,4,6,8,9,12,15,18}E) {2,4,6,8,10,12,14,16,18}“U” means union (“or”) those elements of either set  D

11. If the product of x and y is positive and odd, which of the following could not be a value of y?A) -121 B) -1 C) 1 D) 4 E) 25

12. If the product of x and y is positive and odd, which of the following could not be a value of y?A) -121 B) -1 C) 1 D) 4 E) 25(-)(-) = (+), and (+)(+) = (+)Odd * Odd = OddEven * even = evenEven * odd = evenx and y can NOT be even

13. What happened on December 17, 1903?

14. What happened on December 17, 1903? No, it’s NOT my birthday!

15. Simplify:

16. How is an island like the letter t?

17. How is an island like the letter t?You find it in the middle of water.

18. If x2 + y2 = 30 and (x – y)2 = 20, what is the value of xy?A)-5 B) 5 C) 10 D) 50 E) 600

19. If x2 + y2 = 30 and (x – y)2 = 20, what is the value of xy?A)-5B) 5 C) 10 D) 50 E) 600(x – y)2= x2 – 2xy+y2 =(x2 + y2)– 2xysub given info to give:20 = 30 – 2xy  xy = 5

20. Where can you finish reading several books before you finish even one sentence?

21. If x2 + y2 = 15 and xy = 3, then what is the value of (x + y)2?A) 9 B) 12 C) 18 D) 21 E) who cares!

22. If x2 + y2 = 15 and xy = 3, then what is the value of (x + y)2?A) 9 B) 12 C) 18 D) 21E) who cares! (x + y)2 = x2 +2xy + y2 = x2 + y2 +2xy= 15 + 2(3) = 21

23. If x + y = 7 and x – y = 4, then what is the value of x2 - y2 ? A)3 B)11 C)28 D)33 E)65

24. If x + y = 7 and x – y = 4, then what is the value of x2 - y2 ? A)3 B)11 C)28 D)33 E)65Remember: (x + y)(x – y) = x2 - y2

25. Practice random acts of kindness and senseless beauty… If you have a chance to do a kindness to someone, do it… you never know if you’ll have the chance again

26. Given f(x) = ax + b and g(x) = cx + d. If f(x) and g(x) have no points in common, which of the following must be true?A) a ≠ c and b ≠d B) a ≠c and b = dC) a = c and b ≠ d D) a > c and b > dE) a < c and b < d

27. Given f(x) = ax + b and g(x) = cx + d. If f(x) and g(x) have no points in common, which of the following must be true?A) a ≠ c and b ≠d B) a ≠c and b = dC) a = c and b ≠ d D) a > c and b > dE) a < c and b < dWhat does no points in common mean (for these functions)? What does that mean for the slope and y-intercept? Same slope and different y-intercept

28. Why does a deaf woman like the letter A?

29. Why does a deaf woman like the letter A? It can make “her” “hear”!

30. What is the measure of x in terms of y?A) y B) y – 180 C) y – 90 D) 90 – y E) 180 – y y x

31. y x What is the measure of x in terms of y?A) y B) y – 180 C) y – 90D) 90 – y E) 180 – yLet x = 25; 180 – (90 + 25) = 65180 – 65 = 115, so y = 115x = 25 = 115 - 90

32. If you can’t explain it simply, you don’t understand it well enough.--Albert Einstein

33. If xy < 0 and xz > 0, which of the following MUST be true?A) x > 0 B) yz > 0 C) yz < 0D) xyz < 0 E) xyz > 0

34. If xy < 0 and xz > 0, which of the following MUST be true?A) x > 0 B) yz > 0 C) yz < 0D) xyz < 0 E) xyz > 0Technique 1: multiplyx2yz < 0  C (why?)Technique 2:Draw a tree diagram…

35. The next time you get the urge to procrastinate, just put it off!

36. If x equally priced items cost c cents, what is the cost in dollars of y items?A) xc/y B) yc/x C) yc / (100x)D) 100yc / x E) 100xc / y

37. If x equally priced items cost c cents, what is the cost in dollars of y items?A) xc/y B) yc/x C) yc / (100x)D) 100yc / x E) 100xc / y(Note that E = 100A, and D = 100B)

38. If x equally priced items cost c cents, what is the cost in dollars of y items?A) xc/y B) yc/x C) yc / (100x)D) 100yc / x E) 100xc / yLet’s say 10 items (x) cost 100 cents (c), what is the cost of 20 items (y)?The answer must be 2 dollars… so which answer gives us 2 with x = 10, c = 100, and y = 20?Looks like C…

39. Your number is 102Move one number to make this 100

40. Riddle: What is a living creature that has four legs, eats cat food, and sees equally well out of both ends of its body?

41. If k is the smallest of 4 consecutive integers whose sum is s, what is the sum of 8 consecutive integers, the least of which is k?A) s+16 B) s+22 C) 2s D) 2s+16 E) 2s+22

42. If k is the smallest of 4 consecutive integers whose sum is s, what is the sum of 8 consecutive integers, the least of which is k?A) s+16 B) s+22 C) 2s D) 2s+16 E) 2s+22Strategy: pick a number for k (like 1)1+2+3+4 = 10 (s)1+2+3+4+5+6+7+8 = 36which answer gives 36 when s = 10?

43. History question: What happened 50 years ago today, on November 22, 1963?

44. History question: What happened 50 years ago today, on November 22, 1963?(And no, it’s not my birthday – I was 4 when this happened)

45. If Wolfgang runs y yards in 10 minutes, how many feet does he run in 8 minutes?A) 4y / 5 B) 4y / 15 C) 12y / 5 D) 8y E) 24y

46. If Wolfgang runs y yards in 10 minutes, how many feet does he run in 8 minutes?A) 4y / 5 B) 4y / 15 C) 12y / 5 D) 8y E) 24y Hmm, let y be 10, then the answer must be 24… why?Check the answers with y = 10 to see which one gives 24

47. What is it that the more it dries, the wetter it gets?

48. If triangle ABC is isosceles, AB = 3, and BC = 8, what could the perimeter be?I) 11 II) 14 III) 19A) I & II only B) I, II, and III C) II & III only D) II only E) III only

49. If triangle ABC is isosceles, AB = 3, and BC = 8, what could the perimeter be?I) 11 II) 14 III) 19A) I & II only B) I, II, and III C) II & III only D) II only E) III onlyOnly option is AC = 8 (why?)Therefore, 19 is the only option (E)

50. What 3-syllable word contains 26 letters?