Questions and Answers
Solve the system of equations: -2x - y = -19, x - y = 11
(10, -1)
Zoe has 36 coins (quarters and nickels) that are worth $3.00. How many nickels does she have?
30
Zoe has 36 coins (quarters and nickels) that are worth $3.00. How many quarters does she have?
6
Simplify: (3x³y⁶z)²
Signup and view all the answers
Simplify: (-a²b²c²)³(2ab³c)²
Signup and view all the answers
Simplify: 5x⁰(-10x³)
Signup and view all the answers
Simplify: (x² - x + 1) + (9x² - 9x + 10)
Signup and view all the answers
Simplify: (x² - x + 1) - (9x² - 9x + 10)
Signup and view all the answers
Simplify: (x² - x + 1)(9x² - 9x + 10)
Signup and view all the answers
Factor: x² + 3x - 4
Signup and view all the answers
Solve: x² + 3x - 4 = 0
Signup and view all the answers
Factor: 6x² + 5x - 6
Signup and view all the answers
Solve: 6x² + 5x - 6 = 0
Signup and view all the answers
Factor: 2x² + 7x + 3
Signup and view all the answers
Solve: 2x² + 7x + 3
Signup and view all the answers
Find the vertex of the quadratic equation: y = x² - x - 2
Signup and view all the answers
Simplify: √72
Signup and view all the answers
Simplify: √45
Signup and view all the answers
Simplify: √108
Signup and view all the answers
Simplify: √120
Signup and view all the answers
Simplify: 5√2 + 2√98
Signup and view all the answers
Simplify: 4√20 - √5
Signup and view all the answers
Simplify: 3√20 - √45 + 4√80
Signup and view all the answers
Solve the system of equations: y = 2x + 5, y = 2x - 5
Signup and view all the answers
Solve the system of equations: y = 5x - 7, -3x - 2y = -12
Signup and view all the answers
Solve the system of equations: -4x - 2y = -12, 4x + 8y = -24
Signup and view all the answers
Factor: 4x(8x + 1)
Signup and view all the answers
Factor: (5x + 2)(7x - 2)
Signup and view all the answers
Factor: 3x²(5x³ - 2x + 5)
Signup and view all the answers
Solve: (-2x³ + x - 3x²) - (-7x² - 8x - 8)
Signup and view all the answers
Solve: (-2x³ + x - 3x²) + (-7x² - 8x - 8)
Signup and view all the answers
Solve: x² - 16 = 0
Signup and view all the answers
Find the vertex of the quadratic equation: x² + 16x + 64 = 0
Signup and view all the answers
Find the vertex of the quadratic equation: -x² - 10x - 30 = 0
Signup and view all the answers
Study Notes
Systems of Equations
- Solve the system: -2x - y = -19 and x - y = 11 results in (10, -1).
- Solving y = 5x - 7 and -3x - 2y = -12 gives intersection point (2, 3).
- The system y = 2x + 5 and y = 2x - 5 has no solution as lines are parallel.
- For -4x - 2y = -12 and 4x + 8y = -24, the solution is (6, -6).
Coin Problems
- Zoe has 36 coins worth $3.00 and has 30 nickels.
Quadratic Expressions
- y = x² - x - 2 has vertex at (½, -2¼).
- Find vertices of quadratics: x² + 16x + 64 at (-8, 0) and -x² - 10x - 30 at (-5, -5).
Simplifying Expressions
- Simplifying (3x³y⁶z)² results in 9x⁶y¹²z².
- (-a²b²c²)³(2ab³c)² simplifies to -4a⁸b¹²c⁸.
- 5x⁰(-10x³) results in -50x³.
- (x² - x + 1) + (9x² - 9x + 10) simplifies to 10x² - 10x + 11.
- (x² - x + 1) - (9x² - 9x + 10) simplifies to -8x² + 8x - 9.
- (x² - x + 1)(9x² - 9x + 10) expands to 9x⁴ - 18x³ + 28x² - 19x + 10.
Factoring
- x² + 3x - 4 factors to (x + 4)(x - 1).
- 6x² + 5x - 6 factors to (2x + 3)(3x - 2).
- 2x² + 7x + 3 factors to (2x + 1)(x + 3).
Solving Quadratics
- x² + 3x - 4 = 0 has solutions x = 1 and x = -4.
- 6x² + 5x - 6 = 0 gives solutions x = 2/3 and x = -3/2.
- 2x² + 7x + 3 = 0 solves to x = -½ and x = -3.
Radical Simplification
- √72 simplifies to 6√2.
- √45 simplifies to 3√5.
- √108 simplifies to 6√3.
- √120 simplifies to 2√30.
- 5√2 + 2√98 simplifies to 19√2.
- 4√20 - √5 simplifies to 7√5.
- 3√20 - √45 + 4√80 simplifies to 19√5.
- 3√250 + 5√160 simplifies to 35√10.
Polynomial Factoring
- 4x(8x + 1) represents 32x² + 4x.
- (5x + 2)(7x - 2) expands to 35x² + 4x - 4.
- 3x²(5x³ - 2x + 5) represents 15x⁵ - 6x³ + 15x².
- (-2x³ + x - 3x²) - (-7x² - 8x - 8) simplifies to -2x³ + 4x² + 9x + 8.
- Adding polynomials forms -2x³ - 10x² - 7x - 8.
Roots of Quadratics
- x² - 16 = 0 gives roots x = 4 and x = -4.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge with these flashcards designed for the Algebra 1 Semester 2 Final Exam. Each card contains a problem or equation related to systems of equations, coin problems, and simplification of expressions. Perfect for review and mastering the concepts before the final exam.