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Solve algebraically (using a sign chart): 2x 2 – 5x + 1 < 0. 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?.
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Solve algebraically (using a sign chart): 2x2 – 5x + 1 < 0
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?
Given f(x) = 3x3-10x2 + x + 6 = 0List the possible rational zeros.Fully factor, and list the real solutions.
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)
What is the remainder when f(x) = 2x37-4x21-6x12-5x-1 is divided by (x + 1)?What does that mean?
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
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}
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
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
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
What happened on December 17, 1903? No, it’s NOT my birthday!
How is an island like the letter t?You find it in the middle of water.
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
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
Where can you finish reading several books before you finish even one sentence?
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!
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
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
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
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
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
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
Why does a deaf woman like the letter A? It can make “her” “hear”!
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
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
If you can’t explain it simply, you don’t understand it well enough.--Albert Einstein
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
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…
The next time you get the urge to procrastinate, just put it off!
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
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)
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…
Riddle: What is a living creature that has four legs, eats cat food, and sees equally well out of both ends of its body?
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
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?
History question: What happened 50 years ago today, on November 22, 1963?
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)
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
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
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
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)