What do you notice about each solution? :
Picture 1 - They never intersect/touch.
Picture 2 - They are intersecting.
Picture 3 - They are on top of each other.
What do you notice about the graphs for each set of equations? :
Picture 1 - The lines are parallel.
Picture 2 - They are intersecting.
Picture 3 - They are on top of each other. (otherwise known as coincident lines).
What do you notice about each set of equations? :
Picture 1 - They have the same slope but different y-intercepts.
Picture 2 - Both the slopes and y-intercepts are different for each equation.
Picture 3 - They have the same slope and same y-intercept.
What generalization can you make? :
Picture 1 - When equations have the same slope but different y-intercepts they will be parallel when graphed.
Picture 2 - When the equations have different slopes and different y-intercepts they will be intersecting.
Picture 3 - When the equations are the same they will be coincident lines when graphed.
Answer:
-3 is a solution.
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
Step-by-step explanation:
<u>Step 1: Define</u>
3 - 4r ≥ 15
<u>Step 2: Solve for </u><em><u>r</u></em>
- [Subtraction Property of Equality] Subtract 3 on both sides: -4r ≥ 12
- [Division Property of Equality] Divide -4 on both sides: r ≤ -3
<u>Step 3: Compare</u>
- Substitute in <em>r</em>: -3 ≤ -3
This is true. -3 is less than <em>or equal to</em> -3.
Think of the greater than sign as an equals sign. Then, you solve for m
Answer:
a³-b³=(a-b)³+3ab(a-b)
or
(a-b)(a²+b²+ab
Step-by-step explanation:
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