Solving Equations and Inequalities
Solve for X:
8(-4x + 9) = 16x
x = 9/6 or 1.5
The _______ of a linear equation is Ax + By = C, where A, B, and C are integers.
Standard Form
Identify the domain of the function:
{(7,1),(13,2),(47,3),(83,4),(0,5)}
Domain = {0, 7, 13, 47, 83}
How can you find the solution of the system of equations?
Get the (x,y) of where the lines cross.
What exponent does a cube root symbol turn into?
1/3 (one third)
Using the quadratic formula (written on the board), find both solutions of the function below:
y = 3x2 + 1/4x - 13
round your answers to the nearest hundredth
2.04 and 2.12
Solve for s:
2.063s + 0.813 = 20.187
(round your answer to three decimal places)
s = 9.391
The slopes of two perpendicular lines are opposite ______.
reciprocals.
What does "constraints on the domain" mean?
It means what the x value cannot equal.
Do you always have to multiply one or both equations in order to use the elimination method?
No, you do not.
Simplify using properties of square roots:
four times the square root of eighty-four
8 times the square root of 21
or 36.661
Solve for x:
21 - 4x = 14x +21
x = 0
Find the slope of the line passing through the points:
(1,7) and (-9,3).
m = 2/5 or 0.4
Using f(x) = x as your parent function, how does the graph of the following function differ from the parent:
g(x) = x + 3
Shifts the graph of f(x) up 3 spaces
What is your preferred method of solving a system of equations: elimination, graphing, or substitution? Why?
Your answer must be a complete sentence with a reason included.
Write the sum in simplest form:
4 times the square root of 38 plus 1 times the square root of 38.
5 times the square root of 38
or 30.822
xy = k.
Solve the equation for x.
x = k divided by y or 1/y times k
Rewrite 12x + 6y = 27 in slope-intercept form.
y = -2x + 4.5
What is the difference between a translation and a transformation of a function?
A translation changes the location.
A transformation changes the shape of the graph.
Is (2,5) a solution to the inequality y > 2x - 3?
Yes, it is.
Is the following equation exponential growth or exponential decay? How do you know?
f(x) = 2.5x
Exponential Growth. Since 2.5 is greater than 1.
Lucy plans to spend between $50 and $65, inclusive, on packages of beads and packages of charms. If she buys 5 packages of beads at $4.95 each, how many packages of charms at $6.55 can Lucy buy while staying within her budget?
Lucy can buy 4, 5, or 6 packages of charms
Are the graphs of the following equations parallel, perpendicular, or neither?
Equation #1: y=1/4x - 8
Equation #2: 2x + y = 5
neither.
What do absolute value bars do to numbers?
They remove the negative or positive sign.
What is the solution to the system of equations?
y = 3x - 1
y = -2x + 3
Solution is (0.8, 1.4) or (4/5, 7/5)
What is a real life example of something that could happen with exponential growth.
Just about anything - we will discuss the answers. COVID-19 and a Zombie Apocalypse are two great examples...