Podcast Beta
Questions and Answers
Which of these is a rational number?
If a + b + c = 0, then a² + b² + c² = ?
If (x + 5) is a factor of x² - 20x + 5k, then k = ?
If an angle is 140° more than its complementary angle, then the angle is:
Signup and view all the answers
If x + y = 12 and xy = 32, find the value of x² + y².
Signup and view all the answers
Which of the following represents a rational number?
Signup and view all the answers
What is the value of $25 × 5$?
Signup and view all the answers
If $a + b + c = 0$, what does $a² + b² + c²$ equal?
Signup and view all the answers
What is the remainder when $(x + 5)$ is divided by $(x + 1)$?
Signup and view all the answers
What is the value of $25² - 24²$?
Signup and view all the answers
If $(x + 5)$ is a factor of $x² - 20x + 5k$, what value must $k$ be?
Signup and view all the answers
An angle that is 140° more than its complementary angle must be what?
Signup and view all the answers
If quadrilateral ABCD has ∠A = 90° and sides AB = BC = CA = DA, then it is classified as what type of shape?
Signup and view all the answers
Study Notes
Rational Numbers
- A rational number is a number that can be expressed as a fraction.
- Examples of rational numbers: 1/2, 3, 0.5, 2/7
Simplifying Expressions
- Rationalizing the denominator of √2+1 / √2-1 involves multiplying both numerator and denominator by √2+1 resulting in (√2+1)² / (√2)² - 1² = 3 + 2√2
Exponents and Multiplication
- (25) × (5) = 125
- (25) × (24) = 600
Algebraic Identities
- If a + b + c = 0, then a² + b² + c² = 2(ab + ac + bc)
- If 49x² - b = (7x + √b)(7x - √b), then b = 49
- If (x + 5) is a factor of x² - 20x + 5k, then k = -25
Angles and Geometry
- Complementary angles add up to 90 degrees.
- An angle that is 140° more than its complementary angle is 110 degrees.
- If in quadrilateral ABCD, ∠A = 90° and AB = BC = CA = DA, then ABCD is a square.
Polynomials
- The degree of a polynomial is the highest power of the variable in the polynomial.
- The coefficient of x in the polynomial p(x) = x³ + x² + x + 1 is 1.
Finding Values
- If (x - 1) = 8, x = 9.
- The complement of 30 degrees is 60 degrees.
- (2 - √2)(2 + √2) = 4 - 2 = 2, which is a rational number.
- If (3³/2)³/2 = 81, then x = 4.
Factoring Expressions
- x³ + 27 = (x + 3)(x² - 3x + 9)
- x² + 6√x + 27 = (√x + 3)²
- x² + 7x + 12 = (x + 3)(x + 4)
- 7m²n - 7mn = 7mn(m - 1)
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of rational numbers, exponents, and algebraic identities with this quiz. Explore concepts like simplifying expressions, complementary angles, and the properties of polynomials. Perfect for students in 10th grade looking to reinforce their algebra skills.
