9th Grade Math, Unit 4

How to find where 2 functions intersect

Set the functions to equal eachother. For example if f(x)= 2 and f(x) = x you just set it to x=2 and solve. But this is a simplified example and its already solved.

What can x/5 be written as?

1/5x

How do you find when 2 linear equations have the same value?

• Example. y=3x+8 and y=8x+1. Write as 3x+8=8x+1 and solve to find the x value where the lines have the same value.

What is the difference between linear functions and linear equations?

Linear functions are used to represent relationships between variables
Linear equations are used to find the value two lines are equal.

How many solutions can a linear equation have?

1 solution, infinite solutions, or no solution.

What is a example of a linear equation with infinite solutions?

2x - 10 = 2x - 10. Which when solved is -10=-10

What is a example of a linear equation with no solutions?

2x - 10 = 2x - 9. When solved it gives -10=-9, which is false.

What is a linear equation with 1 solution?

4x + 2 = 16. This solves to x=3.5

What is a identity in math?

A equation that will be true for any values of the variables in it.

How can tables be used in math?

To represent Mathematical situations

There are peanuts and almonds in a bag, combined they are 22 nuts in total. How can you represent this if you dont know either variable value? (p is peanuts, a is almonds)

22 - p = a

Why is it important to convert units?

If you try to multiply 3 miles a hour with 40 minutes, you get 120 per hour miles which is not possible. So you convert 40 into hours with conversion factors, making it 2/3 hours. 2/3 hours times 3 miles a hour is equal to 2 miles per hour.

How do you create work problems?

If one guy works 6 hours on a project to complete it, and another guy works 8 hours on a project to complete it, how fast can they do it together? Well in these problems, these are called work problems. In work problems, the sum is always = 1 or essentially 1 project done. So if a person works 8 hours it can be written as 1/8 and if a person works 6 hours it can be written as 1/6. The equation representing this is 1/8 + 1/6 = 1

What are literal equations?

Equations with more then 1 variable.

What are the goals of literal equations?

C=2pir is a equation to find the circumference, but you can structure this equation to say the radius of a circle when the circumference is known with literal equations. The restructured equation is C/2pi=r. This is achieved by dividing both sides by 2pi to get = r.

What are equilavent forms?

Equations that can be written differently, but have the same solution set when solved. For example 1/2=5/2-2 is the same as 1/2=5/2-4/2.

What is factoring?

Writing a equation like Cx - Gx as (C-G)x

What are absolute value equations?

A equation that states |x|= something

How do you solve absolute value equations?

Absolute value equations have 2 solutions for x, the left side and the positive side of the number line. This needs to be written linearaly with 2 solutions. for example the equation |5-x|=3 on the left side is written as 5-x=-3. When writing to the left side form, the number it is equal to will be turned into negative. In the right side form its written as 5-x=3.

How do you deal with absolute value equations that are negative?

in a equation like -[4-x]=-2, multiply everything by -1 to make the equation positive again.

How do you write the solution set of absolute value equations?

As {value 1, value 2}

What are compound statements?

Mathematical statements that use “and” or the word “or” are compund statements.

What is a compound inequality?

For example. If water can be above 100c or below 1c strictly, it can be written as c > 1 c > 100