System of Equations
Do these two equations intersect?
If so where, and if not why not?
These equations intersect @ x = -9/5 & y = 57/5
f(x, y) = (-9/5, 57/5)
How many zeros can be found in the following equation 2x3 - 3x2 + 4x + 5?
3
Define Algebra
A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulas and equations.
List at least three ways Algebra can be used in real world situations
Determining Distance
Volumes in Containers
Calculating Sale Prices
Etc...
What is a nonlinear system?
Define a system of equations
A set of two or more linear equations with the same variables
Graph the following equation 3x2 +10x + 8
Displayed on white board
Evaluate the expression 2y+7 for y = 4
= 15
When is the Exam
Whenever the exam date is set
Is this a polynomial?
3xy-2
If so why?
If not, why not?
Not, because the y is raised to the negative power making 3x divisible by y which makes the equation a non-polynomial
Locate the point of intersection between these two equations
y = x+5
2x+2 = y
x=3
y=8
(3, 8)
By completing the square, find the coordinates of the turning point of the quadratic graph y = 2x2-2x-8
(1, -9)
Find the Product
8x+5
2x+5
16x2 + 48x + 20
Imagine you own a company that pays out $350,000 in salary per year. A new software investment of 75,000 up front, and a 12,500 license per year, will reduce your yearly salary costs to $300,000. In how many years will you break even, and also begin to actually be money ahead?
Two years
Find ALL the zeros in the following equation
x3 + 3x2 - 4x - 12
x = -3, -2, 2
y = -12
Solve by elimination
3x+4y = 18
-2x+4y = 8
x = 2
y = 3
(2, 3)
Find out where the following equation crosses the y-axis -7x6 + 5x4 + 3x2 + x by graphing
(0, 0)
Factor the following equation and solve for x
3x2 +10x + 8
(x+2) (3x+4)
x = -2, -4/3
You are constructing a frame for a rectangular photo that is 11 inches in height and 17 inches in width. You want the frame to be the same width all the way around and the total area of the frame and photo to be 315 sq. in. What should the outer dimensions of the frame be?
x = -16
x = 2
2x2 + x + 18
Solve for the variables f(x, y, z)
-2x - 3y - 2z = -7
-3x + y - z = 12
-x + 2y + 2z = -3
x = 1
y = 7
z = -8
(1, 7, -8)
Graph 3x3-4x2+6
Displayed on white board or paper
FOIL is an acronym which stands for what?
First
Outer
Inner
Last
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?
35 hot dogs
52 sodas
Which of the following are examples of Non-linear equations
4x2 + y = 5
sqrt(x) = 4
xy + x = 5
s/r + r = 3
All of the Above