Week 4 (Graphing & Linear Equations)
Which quadrant is (4, -sqrt(8)) located in?
Quadrant IV
What is the slope and y-intercept of the following equation:
-2y = -3x + 1
y = mx + b
y = 3/2x -1/2
m (slope) = 3/2b (y-intercept) = (0, -1/2)
Correct Approach:
1. Get all terms to 1 side, 0 on the other.
2. Factor quadratic using guess and check method.
3. Use ZPP to split into many smaller equations.
4. Find all answers.
5. Check your work!
Try factoring when b does not equal to 0 (Recall: ax^2 + bx + c = 0 is the general form of a quadratic).
Solve for y:
40 = 20*sqrt(y)
2 = sqrt(y)
Square both sides:
y = 2^2 = 4
What is the distance formula?
d = sqrt((x2-x1)^2+(y2-y1)^2)
Find the slope of the line connecting the following two points:
(2/3, -3) and (i^2, 2)
m = (y2 - y1) / (x2-x1)
-1 = i^2!
m = -3-2/(2/3+1)
m = -3
Find the solutions to the following equation:
27x^2 = 12
x = +/- 2/3
Solve for all possible values of x:
abs(3x-6) = 12
Note: "abs" indicates that absolute value bars are placed around (3x-6)
3x - 6 = 12 OR 3x - 6 = -12
x = -2 or x = 6
Find the x and y-intercepts of the following equation algebraically: 1.2 + 0.6x - 0.3y = 0
x-intercept: (-2, 0)
y-intercept: (0, 0.4)
What does the WISE acronym stand for?
W: Words
I: In
S: Symbols
E: Expression/Equation
Remember: it is also WISE to check your answers!
Find the discriminant of 20x^2 + 5x + 3 = 0.
D = b^2 - 4ac
D = (25) - 4*20*3
D = 25 - 240
D = -215
Are the following inequalities T/F?
1. 0 > -5
2. -10 < -8
3. -5 > -4
1. T
2. T
3. F
Solve the following linear equation (ax + b = 0):
(5x + 1)(x + 3) = (10x + 2)(0.5x + 1.5)
True for all real numbers
Simplify the following expression: i^18
(i^2)^9
= (-1)^9
= -1
What does it indicate if I have the following:
D = 0
D = Negative Number
D = Positive Number
D = 0: One Solution
D = Negative Number: You have a negative under the square root --> Your answers will be complex! (Two complex answers)
D = Positive Number: Two real answers
You want to rent a car for the day, but you want to spend less than $75. There is a base fee of $50, and you are charged $0.20 per additional mile. What is the maximum number of miles you can drive?
50 + 0.20x < 75
x < 125
Set up the following word problem (use WISE):
You and your friend both want to meet at the movie theatre at the same time and you propose to run rather than drive. You live 5 miles from the movies, and your friend lives 7 miles from the movies. Your friend wants to get there at the same time, so they propose that they will run 2mph faster than you. How fast do you need to drive?
Let s = your speed
Let s + 2 = your friend's speed
s = d/t, or t = d/s
5/s = 7(s+2)
Use cross multiplication to solve for s
Simplify the following: (4+i)(3+2i)(8i)
What are the real and complex parts of the solution?
40i - 112
Complex: 40i
Real: -112
Use the quadratic formula to find the roots of the following equation:
4x^2 - 4x + 10 = 0
Also: Was the discriminant, positive, negative, or zero?
What are the actions that keep the inequality direction, and what are actions that flip the inequality direction?
Keep Inequality Direction:
-Add/subtract a positive constant from either side
-Add/subtract a negative constant from either side.
-Multiply/divide by positive constant
Switch Inequality Direction
-Multiply/divide by a negative number