Alg1 lesson 3 2
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This document appears to be an introduction to an interactive chalkboard tutorial on solving basic equations and checking solutions. It includes examples of writing, solving, and checking equations such as: h - 12 = -27; k + 63 - 63 = 92 - 63; a - 24 + 24 = 16 + 24; and t + 22 - 22 = -39 - 22. The document emphasizes the importance of writing an equation for a word problem, solving the equation, and checking the solution. It provides two word problems as additional examples: finding a number that is 14 more than 27, and finding a number that is 12 less than -25.
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x2 – 4 = 0
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5.Example 2. Solve: 5x² - 11 = 49
Solution:
5x² - 11 = 49
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5x² = 60
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Factor the left member.
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11.By Quadratic Formula
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5. 2x² - 3 + 12x
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an equation of the form
ax2 + bx + c = 0
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Complete Quadratic
3x2 + 5x + 6 = 0
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Place all terms in the left member of the equation, so that the right member is zero.
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Set each factor that contains the unknown equal to zero.
Solve each of the simple equations thus formed.
Check the answers by substituting them in the original equation.
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x² = 6x – 8
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Write the equation with the variable terms in the left member and the constant term in the right member.
If the coefficient of x² is not 1, divide every term by this coefficient so as to make the coefficient of x² equal to 1.
Take one-half the coefficient of x, square this quantity, and add the result to both members.
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LIKE and FOLLOW me here!
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https://tinyurl.com/ybo27k2u
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You will learn how to factor the difference of two squares.
For more instructional resources, CLICK me here! 👇👇👇
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! 👍👍👍
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
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This document provides an overview of the Math 110 Algebra - Fall 2018 course. It covers exponents, radicals, factoring, rational expressions, solving quadratic equations, solving rational equations, and solving radical equations. The course aims to teach students various rules and techniques for simplifying expressions and solving equations involving these algebraic concepts. Examples are provided to demonstrate each technique, along with practice problems for students to test their understanding.
Quadratic equations / Alge
The document discusses quadratic equations. It begins by defining quadratic equations as polynomials of degree two that are set equal to zero. It then provides examples of identifying quadratic equations from collections of equations. Methods covered for solving quadratic equations include factoring, using the quadratic formula, and determining the nature of roots based on the discriminant. It also discusses writing quadratic equations in standard form and translating word problems into quadratic equations.
U1 02 operaciones expresiones algebraicas
The document discusses calculating the numerical value of algebraic expressions by substituting values for variables and performing the indicated operations. It provides examples of substituting values into single-variable expressions like P(x) and multi-variable expressions like Q(y,z) to find the numerical value. It also covers adding, subtracting, and multiplying polynomials, demonstrating how to combine like terms and distribute coefficients.
January 23
Steps are shown for solving systems of equations by the elimination method, including multiplying one equation by a constant to eliminate a variable before adding the equations. Examples are provided of solving systems by substitution, where one variable is solved for in one equation and substituted into the other equation. Practice problems are given for students to apply
First Quarter - Chapter 2 - Quadratic Equation
Okay, let's think through this with the new information:
* The equation modeling the height is: h = -16t^2 + vt + c
* The initial height (c) is still 2 feet
* The initial velocity (v) is now 20 feet/second
* The target height (h) is still 20 feet
So the equation is:
20 = -16t^2 + 20t + 2
0 = -16t^2 + 20t + 18 (subtract 20 from both sides)
Evaluating the discriminant:
(20)^2 - 4(-16)(-18) = 400 - 288 = 112
Since the discriminant is positive
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1150 day 11
Ratios, proportions, and percents can be used to compare quantities and solve problems. A ratio compares two quantities, like the number of squares to circles. Equal ratios form a proportion, which can be used to solve for unknown values. Percents represent a number out of 100. Common percent calculations include finding a percent of a number and converting between fractions, decimals, and percents. The percent proportion states that the percent equals the part divided by the whole quantity.
1150 day 10
This document covers topics related to repeating decimals, irrational numbers, and square roots. It includes examples of writing repeating decimals as fractions, ordering decimals, finding square roots, and using the Pythagorean theorem. Various math problems are presented along with step-by-step solutions to illustrate these concepts.
1150 day 9
1) Decimals represent numbers using place value with decimal points. To write decimals in expanded form, they are broken into place value terms using positive and negative exponents.
2) Fractions can be converted to decimals using division or by writing the fraction as a ratio of two numbers and setting up a proportion to solve for the decimal.
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1150 day 8
This document provides an overview of rational numbers including:
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1150 day 7
This document discusses prime and composite numbers, greatest common divisors (GCD), and least common multiples (LCM). It provides examples of finding the GCD and LCM of various numbers using different methods like the intersection of sets method, prime factorization method, and Euclidean algorithm. Key definitions include: a prime number has exactly two distinct positive divisors, a composite number has factors other than itself and 1, the GCD is the largest integer that divides numbers, and the LCM is the smallest number that is a multiple of the given numbers.
1150 day 6
Integers include positive and negative whole numbers. Absolute value is the distance from zero. Addition and subtraction on a number line involve moving left or right. Multiplication follows patterns based on sign. Division is the inverse of multiplication regarding sign. A number is divisible by another if it can be written as a product of an integer multiple. Divisibility tests identify patterns in a number's digits.
1150 day 5
Algebraic thinking involves recognizing patterns, modeling situations with symbols, and analyzing change. It relies on understanding variables to represent unknown quantities. The document traces the evolution of algebraic thinking from simple equations to more complex concepts like functions, composite functions, and properties of equations. It provides examples of how algebraic reasoning and symbols can be used to represent and solve real-world problems.
1150 day 4
The document discusses various aspects of whole number operations including:
1) Place value systems and how numbers are represented in bases other than 10 such as base 5 and base 12.
2) Algorithms for addition, subtraction, multiplication, and division using various models and representations.
3) Properties of operations like the commutative, associative, identity, and zero properties of multiplication.
1150 day 3
The document discusses different number systems used throughout history including Hindu-Arabic, Egyptian, Babylonian, Mayan, and Roman systems. It also covers basic concepts of whole numbers such as addition, subtraction, and their properties. Different models are presented to demonstrate whole number operations including set, number line, take-away, comparison, and missing addend models.
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The document discusses sets and set operations including defining sets, elements, cardinal and ordinal numbers, equal and equivalent sets, subsets, Venn diagrams, and set operations like union, intersection, and complement. Examples are provided to illustrate concepts like finite and infinite sets, subsets, Venn diagrams representing multiple sets and operations, and using Venn diagrams to solve problems involving sets and their relationships.
1150 day 1
The number of terms in each sequence can be determined by finding a one-to-one correspondence with the counting numbers.
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This document discusses solving an ambiguous triangle where it is not a right triangle and the measures of angles and sides are not fully known. It determines that trigonometric functions and the Law of Sines cannot be used. It identifies that the Law of Cosines is the appropriate theorem to use to begin solving since it requires only knowing the measures of three sides.
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The document discusses solving for unknown sides and angles of triangles using trigonometric functions like the law of sines. Several multi-step example problems are worked through that involve determining if a triangle is possible based on given information, finding missing side lengths, and calculating angles. Diagrams are included to illustrate each step of the example problems.
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The document contains instructions for finding trigonometric function values given specific angle measurements or terminal side locations. It includes:
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2) Finding the six trig functions of an angle with a terminal side at (-3, 4)
3) Finding the reference angle of 330°
4) Finding the reference angle of an angle in Quadrant III
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Alg2 lesson 13-3
The document contains instructions for finding trigonometric function values given specific angle measurements or terminal side locations. It includes:
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The document describes how to draw angles in standard position on a unit circle and convert between degrees and radians. It provides examples of drawing angles such as 210°, -45°, and 540° in standard position and rewriting angles such as 30°, 45°, and an unspecified angle in radians and degrees. It also gives examples of finding coterminal angles for 210° with one positive and one negative measure.
Alg2 lesson 13-1
This document discusses trigonometric functions and their ratios, including sine, cosine, tangent, cosecant, secant, and cotangent. It provides examples of using trigonometric functions to solve values in right triangles, including finding missing side lengths and angle measures. Special right triangles with ratios of 1/2, 1/√3, and 1/√2 are also covered.
Alg2 lesson 11-2 and 11-4
The document provides information about arithmetic and geometric series. It defines arithmetic and geometric series, provides examples of finding sums of arithmetic series using formulas, and defines the key terms (first term, common ratio, number of terms, last term) used in the formula to calculate the sum of a geometric series.
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Alg1 lesson 3 2
- 1. Welcome to Interactive Chalkboard
- 2. Welcome to Interactive Chalkboard
- 3. Welcome to Interactive Chalkboard
- 4. Welcome to Interactive Chalkboard
- 6. Solve . Then check your solution. Check: h – 12 = -27 -15 – 12 = -27 -27 = -27 Example 2-1a
- 7. Solve . Then check your solution. k + 63 – 63 = 92 - 63 Check k + 63 = 92 29 + 63 = 92 92 = 92 Example 2-2a
- 8. Solve . Then check your solution. a – 24 + 24 = 16 + 24 a = 40 Check: a – 24 = 16 40 – 24 = 16 16 = 16
- 9. Solve . Then check your solution. t + 22 – 22 = -39 – 22 t = -61 Check: t + 22 = -39 -61 + 22 = -39 -39 = -39 Example 2-2b
- 10. Solve ·3 ·3 ·5 ·5 y = Example 2-4a
- 11. Solve . ·2 ·2 Example 2-4c
- 12. Solve . ·2 ·2 Example 2-4c
- 13. Solve . ·2 ·2 Example 2-4c
- 14. Answer: Write an equation for the problem. Then solve the equation and check your solution. Fourteen more than a number is equal to twenty-seven. 14 27 n Example 2-5a
- 15. Write an equation for the problem. Then solve the equation and check your solution. Twelve less than a number is equal to -25 12 - n -25 n – 12 = -25 n – 12 + 12 = -25 + 12 n = -13 Example 2-5a