Algebra 2 Day 4 Notes
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This document discusses how to solve and graph absolute value inequalities. It explains that the absolute value of a number represents its distance from 0 on a number line. To solve an absolute value inequality, one treats it like an absolute value equation first to find the critical points, then plots those points on a number line to divide it into intervals. Test points from each interval are plugged back into the original inequality to determine if they satisfy it and belong to the solution set. Examples walk through applying this process to solve and graph two absolute value inequalities.
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Day 31 Ppt A Fish On Two Hooks
The document provides instructions for an activity where students draw force diagrams of a fish suspended from two fishing lines. It gives the known forces and their magnitudes. Students are instructed to draw an initial force diagram, then break the forces down into their x and y components to draw a "clean" force diagram. Using the components and trigonometry, students calculate the angle of one of the fishing lines.
Absolute inequalities
1) The document discusses solving absolute value inequalities by isolating the absolute value, setting up two inequalities with the original inequality and its reverse, and solving each inequality.
2) Examples show setting up the inequalities, solving them individually, and combining the solutions using "and" or "or" depending on whether one or both solutions are possible.
3) One example is always true since absolute values are positive and greater than a negative number, while another is always false since absolute values cannot be less than a negative number.
Kungfu math p4 slide9 (subtraction fraction)pdf
This document discusses subtracting fractions. It provides a 3 step process for subtracting fractions: 1) Make the denominators the same, 2) Subtract the numerators and put the answer over the denominator, and 3) Simplify the fraction if possible. Examples are shown working through subtracting fractions like 29/7 - 2/7 and 1/9 - 2/3. The document emphasizes practicing sample subtraction problems and applying the 3 step process.
Chapter 4.1 and 4.2
The document provides an agenda and lesson plan for a math class. It includes homework assignments, daily scribing, and lessons on divisibility rules, factors, exponents, order of operations, and evaluating expressions.
Nov. 17 Rational Inequalities
The document discusses solving rational inequalities. It explains the steps to solve rational inequalities which are to simplify the expression so zero is on one side, factor any quadratics, place critical numbers on a number line, test points in intervals to determine if the expression is positive or negative, and state the solution intervals. It then works through examples of solving various rational inequalities graphically and algebraically, placing the critical numbers on a number line and determining the intervals where the expressions are positive or negative.
Carmen sanchez
En esta ocasión te presentamos esta información sobre expresiones algebraicas, además de ello ejercicios variados que te pueden ser mucha utilidad
Algebra 2 Lesson 3-9
This document discusses how to solve quadratic inequalities by first solving the inequality as if it were an equality, then plotting the solutions on a number line and testing points in each interval to determine where the inequality is true, and writing the solution using interval notation. Examples are provided of solving quadratic inequalities algebraically.
Solving Absolute Value Equations and Inequalities.ppt
This document provides information and examples for solving absolute value equations and inequalities. It begins with definitions of absolute value and discusses how absolute value equations can have two solutions since the expression inside the absolute value can be positive or negative. Examples are provided for solving absolute value equations by setting the expression equal to both its positive and negative values. The document also discusses how to solve absolute value inequalities by splitting them into "and" or "or" statements and provides examples of solving and graphing various absolute value inequalities.
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TIU Math2 Session: Algebra by Young Einstein Learning Center
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Solving Absolute Value Equations and Inequalities.ppt
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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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Algebra 2 Day 4 Notes
- 1. Day 3 Absolute Value Inequalities We know that the absolute value of a number is the distance that number is from 0 on a number line. Keeping that in mind, how would we find the solution and graph... |x| ≥ 2 |x| < 2 3 2 1 0 1 2 3 3 2 1 0 1 2 3 1
- 2. Solving an absolute value inequality is JUST like solving an absolute value equation, but with one extra step! Ex 1: 2 | x 3 | ≤ 4 1st Solve as if it were an equation and get two answers. These two solutions are called critical points. 2nd Plot the critical points on a number line and pick test points (tp) from each of the three intervals that have been created. 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 **Always plug t.p. into ORIGINAL 2
- 3. Ex 2: | 2x + 3 | > 7 1st Solve as if it were an equation and get two answers. These two solutions are called critical points. 2nd Plot the critical points on a number line and pick test points (tp) from each of the three intervals that have been created. 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 **Always plug t.p. into ORIGINAL 3