8 - solving systems of linear equations by adding or subtractingAnthony_Maiorano

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- 2. Warm- Up Exercises 1. What is the simplified fraction of 35%? 7/20 2. 3. Order the following from greatest to least: 3.45, 3⅗, 54.3%, 3⅓
- 3. Warm- Up Exercises 4. Mike painted 120 houses in 4 months. Jack took two more months to paint the same number of houses. If they worked together to paint an additional 120 houses, how many would each paint? 5. Prom tickets cost $10 for singles and $15 for couples. Fifty more couples tickets were sold than were singles tickets. Total ticket sales were $4000. How many of each ticket type were sold?
- 4. Review of Systems Test 4. Which system of inequality best represents the graph? A. y > -2 and y > x + 1 B. y < -2 and y > x + 1 C. y > -2 and y < x + 1 D. y < -2 and y < x + 1 E. None A. y > -2 and y < x + 1 B. y < -2 and y > x + 1 C. y > -2 and y > x + 1 D. y < -2 and y < x + 1 E. None
- 5. Review of Systems Test 5. 7. What is the solution to the following system of equations? A. ( 2, -2 ) B. ( -2, 2 ) C. No Solution D. Infinite Solutions E. None A. ( 2, -2 ) B. ( -2, 2 ) C. Infinite Solutions D. No Solution E. None
- 6. Review of Systems Test Which of the following graphs represents the solution to the following system of inequalities? 6x – 2y < 6 and x - y < -1 A B C D E. None
- 7. Vocabulary & Formulas Section of Notebook
- 8. Introduction to Monomials: Exponents
- 9. Introduction to Monomials: Exponents
- 10. Introduction to Monomials: Exponents
- 11. Introduction to Monomials: Exponents
- 12. Introduction to Monomials: Exponents
- 13. Introduction to Monomials: Exponents
- 14. Introduction to Monomials: Exponents
- 15. Introduction to Monomials: Exponents Practice Problems 1. 72 2. (-8)2 3. (-9) 3 4. -24 5. -43
- 16. Exponent Laws
- 17. Exponent Laws
- 21. Exponent Laws Simplify to lowest terms:
- 26. Scientific Notation Write 32.500 in Scientific Notation
- 28. Scientific Notation Write the following in Scientific Notation: .00458 = 4.58 • 10 - 3
- 32. Negative and Zero Exponents Take a look at the following problems and see if you can find the pattern. The expression a-n is the reciprocal of an Examples:
- 33. Negative and Zero Exponents *Any number (except 0) to the zero power is equal to 1. Negative Exponents Example 1 Example 2 Since 2/3 is in parenthesis, we must apply the power of a quotient property and raise both the 2 and 3 to the negative 2 power. First take the reciprocal to get rid of the negative exponent. Then raise (3/2) to the second power.
- 34. Negative and Zero Exponents Example 3 Step 1: Step 2: Step 3:
- 35. Negative and Zero Exponents Example 4: Step 1:
- 36. Step 2: Step 3: Step 4:
- 42. Warm- Up Exercises 1. A board 28 feet long is cut into two pieces. The ratio of the lengths of the pieces is 5:2. What are the lengths of the two pieces? 5:7 = X:28; x1 = 20 ft., x2 = 8 feet. 2. The ratio of the length to the width of a rectangle is 5:2. The width is 24 inches long. Find the length. 5:2 = x: 24; Length = 60" 3. What is: 5 6 • 5 - 2 = 5 4 ; 625
- 43. Warm- Up Exercises 4. (12) -5 • (12) 3 Since the bases are the same (12): the exponents are added. -5 + 3 = -2; (12)-2 = 1/12 2 = 1/144 5. 4 2 • 35 • 24 4 3 • 35 • 22 = 22 4 =1 6. Simplify: 5b • 6a4 a c = 30ba4 c
- 52. Monomials Definition: Mono-- The prefix means one. A monomial is an expression with one term. In the equations unit, we said that terms were separated by a plus sign or a minus sign! Therefore: A monomial CANNOT contain a plus sign (+) or a minus (-) sign!
- 54. Multiplying Monomials When you multiply monomials, you will need to perform two steps: •Multiply the coefficients (constants) •Multiply the variables A simple problem would be: (3x2)(4x4) And the answer is: 12x6 Remember, the bases are the same, so you add the exponents
- 60. Multiplying Monomials Now, complete the rest of the problem.
- 63. Multiplying Monomials Answers 1. (3x5y 2 ) (-5x3y 6 ) Multiply the coefficients. Then multiply the variables (add the exponents of like variables). -15x 8 y 8 2.(-2r3s7t4 )2 (-6r2t 6) Raise the 1st monomial to the 2nd power. (4r6s14t8) (-6r2t 6): Multiply the coefficients and add the variables with like bases = -24r 8s14 t14
- 64. Multiplying Monomials Answers, con't. 3. (4a2b2c3)3 (2a3b4c2)2 Raise the 1st monomial to the (64a6b6c9) (4a6b8c4) 3rd power and the 2nd monomial to the 2nd power. Multiply the coefficients and add the variables with like bases = 256a12b14c13
- 65. Dividing Monomials As you've seen in earlier examples, when we work with monomials, we see a lot of exponents. Hopefully you now know the laws of exponents and the properties for multiplying exponents, but what happens when we divide monomials? You probably ask yourself that question everyday.
- 66. Dividing Monomials Expanded Form Examples When you divide powers that have the same base, you subtract the exponents. That's a pretty easy rule to remember. It's the opposite of the multiplication rule. When you multiply powers that have the same base, you add the exponents and when you divide powers that have the same base, you subtract the exponents!
- 67. Dividing Monomials Example 1 Example 2 That's an easy rule to remember. Let's look at one more property. The Power of a Quotient Property. A Quotient is an answer to a division problem. What happens when you raise a fraction (or a division problem) to a power? Remember: A division bar and fraction bar are the same thing.
- 68. Dividing Monomials Power of a Quotient Example 1 Power of a Quotient Example 2
- 69. Dividing Monomials Dividing Monomials Practice Problems
- 70. Dividing Monomials Answer Key
- 71. Simplifying Monomials Properties of Exponents and Using the Order of Operations • If you have a combination of monomial expressions contained with in grouping symbols (parenthesis or brackets), these should be evaluated first. • Power of a Power Property - (This is similar to evaluating Exponents in the Order of Operations). Always evaluate a power of a power before moving on the problem. Example of Power of a Power: • When you multiply monomial expressions, add the exponents of like bases.
- 72. Simplifying Monomials Example of Multiplying Monomials Example of Dividing Monomials
- 73. Simplifying Monomials: Sample Problems
- 74. Simplifying Monomials: Sample Problems Complete the next step:
- 75. Simplifying Monomials: Sample Problems Now the next: Try to complete the problem:
- 76. Simplifying Monomials: Sample Problems
- 77. Simplifying Monomials: Sample Problems Practice Problems
- 80. • x ≤ 4 • 5 -2 If 7 pencils cost $6.65, write the proportion to find the cost for 4 pencils. 7 = 4 6.65 x = 6.65 x 4 / 7 = $3.80