How to solve a quadratic inequality. Visual intuition of what a quadratic inequality means.
Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/polynomial_tutorial/v/terms-coefficients-and-exponents-in-a-polynomial?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_ineq/v/quadratic-inequalities?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=xdiBjypYFRQ
Introduction to basic physics of motion. Introduces the concept of variable velocity/acceleration.
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https://www.youtube.com/watch?v=8wZugqi_uCg
Note: All Khan Academy content is available for free at (www.khanacademy.org)
A deep dive into the Second Amendment, which states that "A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed." In this video, Kim discusses the Second Amendment with scholars Alan Gura and Adam Winkler.
To read more about the Second Amendment, visit the National Constitution Center’s Interactive Constitution. On this site, leading scholars interact and explore the Constitution and its history. For each provision of the Constitution, experts from different political perspectives coauthor interpretive explanations when they agree and write separately when their opinions diverge.
View more lessons or practice this subject at https://www.khanacademy.org/humanities/ap-us-government-and-politics/civil-liberties-and-civil-rights/second-amendment/v/the-second-amendment?utm_source=youtube&utm_medium=desc&utm_campaign=usgovernmentandcivics
Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today!
Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc
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https://www.youtube.com/watch?v=2EjEUoeIccc
Note: All Khan Academy content is available for free at (www.khanacademy.org)
More playing around with trig identities
Watch the next lesson: https://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/trig_iden_tutorial/v/trig-identies-part-3-part-5-if-you-watch-the-proofs?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry
Missed the previous lesson?
https://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/trig_iden_tutorial/v/trigonometry-identity-review-fun?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry
Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=ZWSoyUxAQW0
Determining the projection of a vector on s line
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/expressing-a-projection-on-to-a-line-as-a-matrix-vector-prod?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/unit-vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=27vT-NWuw0M
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Basic overview of capital and human capital. Created by Sal Khan.
Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/return-on-capital?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets
Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/risk-and-reward-introduction?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets
Finance and capital markets on Khan Academy: When are you using capital to create more things (investment) vs. for consumption (we all need to consume a bit to be happy). When you do invest, how do you compare risk to return? Can capital include human abilities? This tutorial hodge-podge covers it all.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=ivy1QmWUtQI
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic/cc-6th-number-opposites/e/number-opposites?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade
Watch the next lesson: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic/cc-6th-number-opposites/v/negative-symbol-as-opposite?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade
Missed the previous lesson? https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic/cc-6th-neg-dec-frac-number-line/v/number-line-3-exercise-example?utm_source=YT&utm_medium=Desc&utm_campaign=6thgrade
Grade 6th on Khan Academy: By the 6th grade, you're becoming a sophisticated mathemagician. You'll be able to add, subtract, multiply, and divide any non-negative numbers (including decimals and fractions) that any grumpy ogre throws at you. Mind-blowing ideas like exponents (you saw these briefly in the 5th grade), ratios, percents, negative numbers, and variable expressions will start being in your comfort zone. Most importantly, the algebraic side of mathematics is a whole new kind of fun! And if that is not enough, we are going to continue with our understanding of ideas like the coordinate plane (from 5th grade) and area while beginning to derive meaning from data! (Content was selected for this grade level based on a typical curriculum in the United States.)
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=2Zk6u7Uk5ow
Note: All Khan Academy content is available for free at (www.khanacademy.org)
An example of simplifying a seemingly complicated resistor circuit. Created by Willy McAllister.
Watch the next lesson: https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-dc-circuit-analysis/v/ee-kirchhoffs-current-law?utm_source=YT&utm_medium=Desc&utm_campaign=electricalengineering
Missed the previous lesson? https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-resistor-circuits/v/ee-voltage-divider?utm_source=YT&utm_medium=Desc&utm_campaign=electricalengineering
Electrical engineering on Khan Academy: A summary of the math and science preparation that will help you have the best experience with electrical engineering taught on Khan Academy. Become familiar with engineering numbers and notation, and learn about the two most important electrical quantities: current and voltage.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=j-iR7puLj6M
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Factor 49x^2-49y^2 as (7x+7y)(7x-7y) or as 49(x+y)(x-y).
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_factoring/e/factoring_difference_of_squares_2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_factoring/v/factoring-to-produce-difference-of-squares?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_factoring/v/factoring-difference-of-squares?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
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https://www.youtube.com/watch?v=YahJQvY396o
Note: All Khan Academy content is available for free at (www.khanacademy.org)