The questions have been designed to test for deep understanding of math concepts. Detailed explanations and solutions of these questions are also provided.
The questions have been designed to test for deep understanding of math concepts. Detailed explanations and solutions of these questions are also provided.
This will help you in factoring sum and difference of two cubes.
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This will help you in factoring sum and difference of two cubes.
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
For more instructional resources, CLICK me here!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
sdnj asodunvwridknwunvaskodnvojnfvoidoksdoisvslakmdvikmfiovmafkl;asodikvaspdfmvpifmvakfnvjufnvisandfjvfknsoafnvaofjvoasften capitalized, often attributive
1
a
: the 7th letter of the English alphabet
b
: a graphic representation of this letter
c
: a speech counterpart of orthographic g
2
: the fifth tone of a C-major scale
3
: a graphic device for reproducing the letter g
4
: one designated g especially as the seventh in order or class
5
[gravity] : ACCELERATION OF GRAVITY
also : a unit of force that is equal to the force exerted by gravity on a body at rest and is used to indicate the force to which a body is subjected when undergoing acceleration
6
[grand] slang : a sum of $1000
7
: something shaped like the letter G
g
2 of 4
abbreviation (1)
1
acceleration of gravity; gravity
2
game
3
gauge
4
gelding
5
gender
6
generation
7
good
8
gram
G
3 of 4
abbreviation (2)
1
German
2
giga-
3
guanine
4
Gulf
G
4 of 4
certification mark
—used to certify that a motion picture is of such a nature that persons of all ages may be allowed admission
compare NC-17, PG, PG-13, R
Examples of g in a Sentence
Noun
There are two g's in “bigger.”
words that end in g
The song is in the key of G.
Recent Examples on the Webften capitalized, often attributive
1
a
: the 7th letter of the English alphabet
b
: a graphic representation of this letter
c
: a speech counterpart of orthographic g
2
: the fifth tone of a C-major scale
3
: a graphic device for reproducing the letter g
4
: one designated g especially as the seventh in order or class
5
[gravity] : ACCELERATION OF GRAVITY
also : a unit of force that is equal to the force exerted by gravity on a body at rest and is used to indicate the force to which a body is subjected when undergoing acceleration
6
[grand] slang : a sum of $1000
7
: something shaped like the letter G
g
2 of 4
abbreviation (1)
1
acceleration of gravity; gravity
2
game
3
gauge
4
gelding
5
gender
6
generation
7
good
8
gram
G
3 of 4
abbreviation (2)
1
German
2
giga-
3
guanine
4
Gulf
G
4 of 4
certification mark
—used to certify that a motion picture is of such a nature that persons of all ages may be allowed admission
compare NC-17, PG, PG-13, R
Examples of g in a Sentence
Noun
There are two g's in “bigger.”
words that end in g
The song is in the key of G.
Recent Examples on the Webften capitalized, often attributive
1
a
: the 7th letter of the English alphabet
b
: a graphic representation of this letter
c
: a speech counterpart of orthographic g
2
: the fifth tone of a C-major scale
3
: a graphic device for reproducing the letter g
4
: one designated g especially as the seventh in order or class
5
[gravity] : ACCELERATION OF GRAVITY
also : a unit of force that is equal to the force exerted by gravity on a body at rest and is used to indicate the force to which a body is subjected when undergoing acceleration
6
[grand] slang : a sum of $1000
7
: something shaped like the letter G
g
2 of 4
abbreviation (1)
1
acceleration of gravity; gravity
2
gam
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
1. Republic ofthePhilippines
DepartmentofEducation
REGION VII - CENTRAL VISAYAS
DIVISION OF BAIS CITY
LONOY NATIONAL HIGH SCHOOL
ACTIVITY SHEET IN MATHEMATICS 9
Quarter First
Week No Two
Learning
Objectives
*Determineanddescribethenatureof the roots of the quadratic equationsusingthe
discriminant.
*Solve the discriminantofa quadratic equation.
*Developself- reliance
Topic/ Key
Concepts
Content
The roots of any quadratic equation can be found by using any of the four methods (a) extracting
squareroots (b) factoring (c) completing the square (d) quadratic formula. Note that a quadratic equation
mayhave onerealnumbersolution,two realnumbersolution,orno real numbersolution.Thenumberand
kindof solutionof quadratic equationscanbedeterminedfrom apart of the quadratic formula, that is, from
𝑏² – 4𝑎𝑐.
This portion of the quadratic formula that determines the nature of roots of a quadratic equation is
called the discriminant.
DISCRIMINANT OF A QUADRATIC EQUATION
Theexpression 𝑏2 − 4𝑎𝑐 in the quadratic formulaiscalledthediscriminant.
Thediscriminantgivesimportantinformationaboutthecorrespondingsolutionsorroots
𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0of wherea, b, and c are realnumbersand 𝑎 ≠ 0 .
Therootsof anyquadratic equation,𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0, are the pointson the x – axis where the graph
crosses.
Nature and Number of Roots of a Quadratic Equation
Discriminant Nature of Roots
Number of
Solution
Graph
𝑏² – 4𝑎𝑐 = 0 Real and Equal One solution
𝑏² – 4𝑎𝑐 > 0
perfect square
Rational and
Unequal Two distinct
solutions
not perfect
square
Irrational and
Unequal
b² – 4ac < 0 Imaginary No Solution
Procedures EXAMPLE1: Determinethenatureof the roots of eachequation.
A. x2 – 6x + 9 = 0 C. 2x2 – 4x + 5 = 0
B. x2 + 6x + 5 = 0 D. 5x2 – x – 2 =0
SOLUTION:
A. x2 – 6x + 9 = 0 a = 1, b = 6, andc = 9
D = b2 – 4ac
D = 62 – 4(1)(9) Since D= 0, the roots of x2 – 6x + 9 = 0 are real, equal,andrational.
D = 36 – 36
D = 0
B. x2 + 6x + 5 = 0 a = 1, b = 6, andc = 5
D = b2 – 4ac
D = 62 – 4(1)(5) Since D = 16, whichisa perfect square,the roots of x2 + 6x + 5 = 0 are
D = 36 – 20 real,unequal,andrational.
2. D = 16
C. 2x2 – 4x + 5 = 0 a = 2, b = -4, andc = 5
D = b2 – 4ac
D = (-4)2 – (4)(2)(5) Since D = -24, the roots of 2x2 – 4x + 5 = 0 are imaginary andunequal.
D = 16 – 40
D = -24
D. 5x2 – x – 2 =0 a = 5, b = -1, and c = -2
D = b2 – 4ac
D = (-1)2 – 4(5)(-2) Since D = 41, the roots of 5x2 – x – 2 =0 arereal, unequal,and
D = 1 + 40 irrational.
D = 41
Activity 1: Math in A, B, C?
Directions:Write the followingquadratic equationsinstandardform,
ax² + bx + c = 0, then identifythe values of a, b, andc. Answer the questionbelow.
Write your answerona sheet of paper.
ax² + bx + c = 0
1. x² + 5x = 4 _______________a= ____b = ____c = _____
2. -4x2 = 8x – 3 _______________a=____b = ____c = _____
3. 10x – 1 = 4x² _______________a=____b = ____c = _____
4. 15 + 8x – 3x2 = 0 _______________a= ____b = ____c = _____
5. 3x(x – 14)= 12 _______________a= ____b = ____ c = _____
Questions: How did you write quadratic equation in standard form?
Activity 2: Find My Equations and Roots
Directions: Evaluate the expressionb²– 4ac given the followingvalues of a, b, andc then
completethetablebelow.Write your answeron a sheet of paper.
1. a = 1, b = 5, c = 4 4. a = 1, b = - 2, c = -2
2. a = 2, b = 1, c = -21 5. a = 9, b = 0, c = 16
3. a = 4, b = 4, c = 1
Equation b² - 4ac Roots
1.
2.
3.
4.
5.
Activity 3: What is My Nature?
Directions:Determinethenature of the roots of the followingquadratic equationsusingthe
discriminant.Answerthe questionsthat follow.
1. x2 + 6x + 9 = 0 discriminant:______natureof the roots: _________
2. x2 + 9x + 20 = 0 discriminant: ______natureof the roots: _________
3. 2x2 – 10x+ 8 = 0 discriminant: ______ natureof the roots: _________
4. x2 + 5x + 10 = 0 discriminant: ______ natureof the roots: _________
5. x2 + 6x + 3 = 0 discriminant: ______ nature of the roots: _________
6. 2x2 + 6x + 4 = 0 discriminant: ______ nature of the roots: _________
3. Prepared by:
BOBBY B. ONG
Teacher 1
Reminder:
*makeyour ACTIVITY 1 (or even up to 3) as practiceofthe lesson introduced
*your ACTIVITY 2 (or even 4- 5) as abstractionandsynthesis of the lesson
7. 3x2 – 5x = -4 discriminant: ______ natureof the roots: _________
8. 9x2 – 6x = -9 discriminant: ______natureof the roots: _________
9. 10x2 – 4x = 8 discriminant:______natureofthe roots: _________
10. 3x² – 2x – 5 = 0 discriminant:______natureof the roots: _________
Assessment
Pleaseanswerthe WeeklyHomeLearning Plan (theteachermayopt to provide additionalactivities
dependingonthecapabilityof the learnerinvolve)
References Learner’sModule,Lesson 3,page65-76