Algebra 2 Notes 1-3
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The document provides an overview of solving absolute value equations in multiple steps. It explains that absolute value equations are first isolated, then split into separate equations, solved individually, and solutions are checked. Examples of six absolute value equations are worked through to demonstrate the process. The key steps are to isolate the absolute value expression, split it into separate equations, solve each equation, and check the solutions.
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3. Change the sign on the other side of the equation only after isolating the absolute value term.
4. Solve each equation individually.
5. Check the solutions by substituting them back into the original equation.
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Here are the steps to solve each absolute value inequality:
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3 < x < 9
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p + 2 < 6 and p + 2 > -6
p < 4 and p > -4
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More from Kate Nowak
Notes Day 6: Bernoulli Trials
This document defines Bernoulli trials and the binomial distribution. A Bernoulli trial is a random experiment with two possible outcomes: success or failure. A sequence of Bernoulli trials involves performing the experiment multiple independent times, keeping the probability of success the same. The binomial distribution calculates the probability of getting a certain number of successes in n Bernoulli trials. It satisfies properties where the experiment is conducted n times independently with a constant success probability p and failure probability of 1-p.
Notes Day 6: Prove that sides are in proportion
This document appears to be an attachment of classwork on corresponding sides of similar triangles. The attachment is a PDF file that likely contains exercises, examples, or instructions related to teaching students about corresponding sides of similar triangles in geometry. In fewer than 3 sentences, the document provides homework or class material on similar triangles and their corresponding sides.
Notes Day 4&5: Prove that Triangles are Similar
The document discusses three theorems for determining similarity of triangles:
1) The Angle-Angle Similarity (AA) Postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
2) The Side-Angle-Side Similarity (SAS) Theorem states that if an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar.
3) The Side-Side-Side Similarity (SSS) Theorem states that if the corresponding sides of two triangles are proportional, then the triangles are similar.
Day 13-3: Similar Polygons
Similar figures have the same shape but not necessarily the same size. Two polygons are similar if their corresponding angles are congruent and their corresponding sides are proportional. The symbol for similarity is ~. This document provides examples of determining if shapes are similar by checking if corresponding angles are congruent and sides are proportional.
Day 14-4: Probability with Permutations & Combinations
This document provides examples of using permutations and combinations to calculate probabilities of events occurring. It discusses:
- Calculating the probability of selecting two white and two red balls from an urn containing six white and five red balls by finding the number of ways to choose two white and two red balls, and dividing by the total number of possible outcomes.
- Calculating probabilities for other events involving selecting balls from urns with different ball combinations.
- Calculating probabilities for events involving selecting students for a team from groups with different numbers of boys and girls.
- Calculating the probability of choosing a specific letter from a word by counting the number of ways to choose that letter and dividing by the total letters.
Probability Day 3 - Permutations and Combinations
The document discusses factorial notation and its definition as the product of all positive integers less than or equal to n. It also covers the fundamental counting principle for combining outcomes, permutations which care about order, combinations which do not care about order, and examples of counting problems involving balls in an urn.
Probability day 1
The homework assignment includes problems from two pages in the textbook, with problems 1, 2, 10-14, and 24-27 from pages 42-43, and problems 1-17 odd and 36-40 from pages 534-536.
Lsn 12 6
This document contains a graph with labeled x and y axes ranging from -6 to 6. Within this range are curved lines forming a circle centered at the point (4, 1).
Day 2 And 3 Midpoint And Slope
The document provides formulas and examples for calculating slope and midpoints of lines and determining properties of triangles. It includes the slope formula, definitions for lines with the same or opposite reciprocal slopes, the midpoint formula, an example of finding the other endpoint given one endpoint and the midpoint, and an example of proving a triangle is isosceles and right using its vertex coordinates.
Lsn 12-1: The Distance Formula
To find the distance between points G(-5, -8) and H(3,7) use the distance formula. Also use the distance formula to find the distance between points L(15, 37) and M(42, 73). The distance formula is used to calculate the distance between the points (-19, -16) and (-3, 14).
Lsn 13-1: Function Translations
The passage discusses the importance of summarization in efficiently conveying key information from lengthy documents. It notes that effective summaries distill the most critical details and events into a brief yet informative recap of the overall topic and narrative. The ability to produce high-quality summaries is a useful skill for professionals across many fields in order to save time and focus on the most pertinent details.
Lsn 11 12 Kites
This document contains numerical values for variables a, b, c, and d in two sections about arithmetic and midsegments. In the arithmetic section, the values are 42, 63, 117, and 14 for the first line, and 30, 28.5, 87, and 12 for the second line. In the algebra section, x is given as 6 for the first two lines, but no values are provided for the third line.
Lsn 11-12: Kites
This document contains numerical values for variables a, b, c, and d in two sections about arithmetic and midsegments. In the arithmetic section, the values are 42, 63, 117, and 14 for the first line, and 30, 28.5, 87, and 12 for the second line. In the algebra section, x is given as 6 for the first two lines, but no values are provided for the third line.
Lsn 11-10: Applications & Regents Problems
This document contains 3 trigonometry word problems: 1) Find the length of a segment labeled x in a diagram with a 12 foot side. 2) Given a 46 foot sign on a building, find the height of the building using angles of elevation. 3) Given angles of elevation to a lighthouse from a ship and its distance traveled, find how close the ship is to dangerous rocks near the lighthouse.
Lsn 11-6: Law of Cosines
The document provides examples of using the Law of Sines and Law of Cosines to solve for missing sides and angles of triangles. It includes 5 multi-step triangle problems worked out using the two trigonometric laws, with the key points being that Law of Sines is used when an angle is given alone, Law of Cosines is used when a side is given alone or one triangle has a right angle, and letter assignments in the Law of Cosines formula can be changed.
Lsn 11-7: Law of Cosines to find an Angle
The document provides 3 examples of using the Law of Cosines to find the measure of an angle given the lengths of 3 sides of a triangle. The first example finds the measure of an acute angle C in a triangle with sides of lengths 5, 12, and 9. The second finds the right angle C in a triangle with sides of lengths 5, 12, and 13. The third finds the measure of an obtuse angle C in a triangle with sides of lengths 5, 12, and 15.
Lsn 11-5: Law of Sines
Here are the steps to solve these Law of Sines problems:
1. Given: a = 13, b = 20, A = 75°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(75°)/13 = sin(B)/20
sin(75°)*20/13 = sin(B)
B = sin-1(0.8) = 67°
2. Given: a = 25, B = 38°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(38°)/25 = sin(m°)/20
sin(38°)*20/25 = sin
Lsn 11-8: Proving a Rhombus/Rectangle
To prove that a quadrilateral is a rectangle or rhombus, you must first prove that it is a parallelogram by showing that both pairs of opposite sides are parallel and congruent. Then, you need only one additional condition - either that the diagonals are congruent (rectangle) or that one angle is a right angle (rectangle), or that the diagonals are the same length (rhombus) or that one pair of consecutive sides are congruent (rhombus). The document provides an example proof of showing a quadrilateral is a rectangle.
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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Algebra 2 Notes 1-3
- 1. Day 3 Absolute Value Absolute Value: | 3 | = ______ | 3 | = _______ Now, in reverse... | x | = 3 5 4 3 2 1 0 1 2 3 4 5 1
- 2. Ex 1: 2| x | 4 = 10 1st Isolate Absolute Value Expression 2nd Split into two different equations 3rd Solve each equation separately 4th Check both solutions ** 2
- 3. Ex 2: ½| x + 4 | = x 1st Isolate Absolute Value Expression 2nd Split into two different equations 3rd Solve each equation separately 4th Check both solutions ** 3
- 4. Ex 3: | x + 8 | + 4 = 3x 1st Isolate Absolute Value Expression 2nd Split into two different equations 3rd Solve each equation separately 4th Check both solutions ** 4
- 5. 1. |3x| = 27 9, 9 2. 5 |x + 1| + 6 = 21 4, 2 3. |x | + 3 = 2x 3 4. |6x + 7| 2 = 5x no solution 5. |3 x + 5| 2x = 3x + 4 ½ 6. 2 |x + 3| 4x = 12 3 5