1 / 69

An Explosion of Math!!!!

An Explosion of Math!!!!. By: Matt and Nick. Quick 1 st Power Equation. Example: 4x=12 Answer: x=3. Special Cases of These Equations. A. x 3 -7x 2 =-6x -6x=-6x= (All real #’s) B. 5x/3 + 7/2 = 4 6*5x/3 + 6*7/2 = 6*4 10x+21 = 24 10x = 24-21 10x = 3 x = 3/10 C. 4/x=12 x=3.

leroy
Download Presentation

An Explosion of Math!!!!

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. An Explosion of Math!!!! By: Matt and Nick

  2. Quick 1st Power Equation Example: 4x=12 Answer: x=3

  3. Special Cases of These Equations • A. x3-7x2=-6x -6x=-6x= (All real #’s) • B. 5x/3 + 7/2 = 46*5x/3 + 6*7/2 = 6*410x+21 = 2410x = 24-2110x = 3x = 3/10 • C. 4/x=12 x=3

  4. Example: If x = y, then x + z = y + z. If a+2=7, then a+2+-2=7+-2 Addition Property (of Equality) Multiplication Property (of Equality) Example: If a = b, then a * c = b * c

  5. Example: 3m=3m Reflexive Property (of Equality) Symmetric Property (of Equality) Example: If m=n, then n=m Transitive Property (of Equality) Example: If m=n and n=p, then m=p

  6. Example: (7+1/4)+3/4=7+(1/4+3/4) Associative Property of Addition Associative Property of Multiplication Example: a(bc) = (ab)c

  7. Example: 1/4+7+3/4=1/4+3/4+7  Commutative Property of Addition Commutative Property of Multiplication Example: ab = ba

  8. Distributive Property (of Multiplication over Addition) Example: If -3(x-2)=1, then -3x+6=1 

  9. Example: a+(-a)=0 Prop of Opposites or Inverse Property of Addition Prop of Reciprocals or Inverse Prop. of Multiplication Example: -3/x*-x/3=1

  10. Example: 0 + a = a = a + 0 Identity Property of Addition Identity Property of Multiplication Example: 1 * a = a = a * 1

  11. Example: a × 0 = 0 Multiplicative Property of Zero Closure Property of Addition Example: If x and y are real numbers, then x+y is a real number. Closure Property of Multiplication Example: If x and y are real numbers, then x*y is a real number.

  12. Example: ab × ac = a(b + c) Product of Powers Property Power of a Product Property Example: (ab)m = am · bm Power of a Power Property Example: (ab)c = abc

  13. Example: Quotient of Powers Property Power of a Quotient Property Example:

  14. Example: 170 = 1 Zero Power Property Negative Power Property Example: x-3=1/x3

  15. Zero Product Property Example: If ab = 0, then either a = 0 or b = 0 (or both).

  16. Product of Roots Property Example: Quotient of Roots Property Example:

  17. Example: Root of a Power Property Power of a Root Property Example:

  18. Quiz Time!!! ***You will see an example problem and you will click to see the answer! There are 10 Problems so it should only take a few minutes to complete. Have Fun!

  19. x9*x3=x12 Product of Powers Property

  20. (xy)3= x3y3 Power of Product Property

  21. x3=x3 Reflexive Property of Equality

  22. x3*0=0 Multiplicative Property of Zero

  23. If x-3=9, then x-3+3=9+3 Addition Property of Equality

  24. If x and y are real numbers, then x+y is a real number. Closure Property of Addition

  25. x3*1=x3 Identity Property of Multiplication

  26. (x9)3=x27 Power of a Power Property

  27. 9(x-y)=9x-9y Distributive Property

  28. y3x=xy3 Commutative Property of Multiplication

  29. First Power Inequalities ***In the following slides you will see how to solve first power inequalities.

  30. One Inequality Sign

  31. X+3<6 Answer: X<3 ***To answer this, you would subtract 3 from both sides and end up isolating the variable on the left side and 3 on the other. The inequality sign would stay the same because you are not multiplying/dividing by a negative number.

  32. Conjunction

  33. -2<x and x<3 Answer: -2<X<3 ***To solve a conjunction of two open sentences in a given variable, you find the values of the variable for which both sentences are true.

  34. Disjunction

  35. y-2<-5 or y-2>5 Answer: y<-3 or y>7 ***To solve a disjunction of two open sentences, you find the values of the variable for which at least one of the sentences is true.

  36. All Real #’s

  37. n+5 n+5 Answer: {All real Numbers} ***As you can see, the inequalities cancel out to leave a technically true statement leaving the answer to be “All real numbers”

  38. No Solution

  39. x + 5 > 10 and x -2 < 1 Answer: No Solution ***Two inequalities have no solution when both of them must be true and they result in mutually exclusive conditions. Thus, there is no number that is both greater than 5 and less than 3, therefore there is no solution.

  40. How To Do Linear Equations • Slopes of All Lines: • Rising line-positive slope • Falling line-negative slope • Vertical line- undefined  • Horizontal line- 0 • Equations of All Lines • Horizontal- y=c  • Vertical- x=c  • Diagonal- y=mx+b and Ax+By=C

  41. Linear Equations Cont. • Standard/general form: Ax+By=C • Point-slope form: y-y1=m(x-x1) • Slope intercept form: y=mx+b • How to Graph: Video from Math TV • Click here to Graph y=3x-1

  42. Linear Equations Cont. • How to Find Intercepts • Put the equation into Slope-Intercept form • Y=mx+b • The “b” in the equation is your Y-intercept

  43. Linear Systems

  44. Solve the first equation for y Substitute this expression for y in the other equation, and solve for x. Substitute the value of x in the equation in Step 1, and solve for y. ***P.417 in your book has great examples! Substitution Method

  45. Add similar terms of the two equations Solve the resulting equation Substitute what you got for x and plug it into either of the equations and solve for y ***P.426 in your book has great examples! Elimination Method

  46. Systems of Equations • Independent- two distinct non-parallel lines that cross at exactly one point (solution is always some x,y-point) • Dependant- two lines that intersect at every point (solution is the whole line) • Inconsistent- shows two distinct lines that are parallel (never intersect), has no solution • ***Graphs of these terms are on following slide!

  47. Graphs from www.purplemath.com

  48. Factoring • Grouping (2x2 and 3x1)- You use this when you have 4 or more terms • GCF- You use this when you have any number of terms • Difference of Squares- Use this with Binomials • Sum and Difference of Cubes- Use with Binomials • PST- Trinomials • Reverse FOIL-Trinomials

  49. Rational Expressions Factor and Cancel *Factor first! *Common factor in both the numerator and the denominator and so we can cancel the x-4 from both Answer

  50. Rational Expressions Addition and Subtraction of Rational Expressions *Common denominator is: 6x5 *Multiply each term by an appropriate quantity to get this in the denominator and then do the addition and subtraction Answer

More Related