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Questions and Answers
What property was used to manipulate the expression $a(bc) + 4 = (ab)c + 4$?
What property was used to manipulate the expression $a(bc) + 4 = (ab)c + 4$?
Associative
In which quadrant does the point (5, -3) lie?
In which quadrant does the point (5, -3) lie?
IV
What kind of interval does the following graph illustrate? Open dot at -2 with a straight line to an open dot at 5.
What kind of interval does the following graph illustrate? Open dot at -2 with a straight line to an open dot at 5.
open
How many solutions does an inconsistent system have?
How many solutions does an inconsistent system have?
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If the following polynomial is reordered by a descending degree of x, what is this polynomial? $x^3 + z^3 - x^3z + x^4z^4$?
If the following polynomial is reordered by a descending degree of x, what is this polynomial? $x^3 + z^3 - x^3z + x^4z^4$?
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Which of the following correctly translates 'three times a number increases four'?
Which of the following correctly translates 'three times a number increases four'?
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What is $3.25 × 10^{-6}$?
What is $3.25 × 10^{-6}$?
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What is $1.104 × 10^5$?
What is $1.104 × 10^5$?
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What is $(15x - 3y) - (3x + 8y)$?
What is $(15x - 3y) - (3x + 8y)$?
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What is $(2x + 6)(3x + 2)$?
What is $(2x + 6)(3x + 2)$?
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What is $(3a^3)^2$ outside the parentheses?
What is $(3a^3)^2$ outside the parentheses?
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What is $(2b - 5c)(2b + 5c)$?
What is $(2b - 5c)(2b + 5c)$?
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What is $(x - 2)(-4x^2 - 7x + 10)$?
What is $(x - 2)(-4x^2 - 7x + 10)$?
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What is $ rac{3q^3r^2 - 2qr}{3qr}$?
What is $ rac{3q^3r^2 - 2qr}{3qr}$?
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What is $ rac{a^2 - a - 20}{a + 4}$?
What is $ rac{a^2 - a - 20}{a + 4}$?
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What is $(2.5 × 10^{-2})(5.0 × 10^{7})$?
What is $(2.5 × 10^{-2})(5.0 × 10^{7})$?
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What is $ rac{8.0 × 10^{-4}}{2.0 × 10^{5}}$?
What is $ rac{8.0 × 10^{-4}}{2.0 × 10^{5}}$?
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What is the solution to the equation $16x + 2 = x + 17$?
What is the solution to the equation $16x + 2 = x + 17$?
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What is the solution to $(x - 3)(x + 4) = (x + 2)^2 - 1$?
What is the solution to $(x - 3)(x + 4) = (x + 2)^2 - 1$?
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What are the solutions to $|x + 2| - 4 = 12$?
What are the solutions to $|x + 2| - 4 = 12$?
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Given the points (3, -2) and (5, 4), what is the equation of the line?
Given the points (3, -2) and (5, 4), what is the equation of the line?
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Given the point (9, -1) parallel to $y = 5x - 4$, what is the equation of the line?
Given the point (9, -1) parallel to $y = 5x - 4$, what is the equation of the line?
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What does the expression $2x + 7 < 3$ represent?
What does the expression $2x + 7 < 3$ represent?
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Solve the system graphically: $2x + y = -4$ and $x + 3y = 3$.
Solve the system graphically: $2x + y = -4$ and $x + 3y = 3$.
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The cost for 2 adults and 5 children to eat at the local buffet restaurant is $46.50. The cost for 1 adult and 1 child is $15. What is the cost of a child's meal?
The cost for 2 adults and 5 children to eat at the local buffet restaurant is $46.50. The cost for 1 adult and 1 child is $15. What is the cost of a child's meal?
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Study Notes
Algebra Concepts
- The Associative Property is used in rearranging expressions, demonstrated by ( a(bc) + 4 = (ab)c + 4 ).
- The point (5, -3) is located in the IV quadrant of the Cartesian plane.
- An interval illustrated by an open dot at -2 to an open dot at 5 indicates an open interval.
- An inconsistent system of equations will have no solutions, denoted as 0.
Polynomial Manipulation
- The polynomial ( x^3 + z^3 - x^3z + x^4z^4 ) can be reordered to ( x^4z^4 + x^3 - x^3z + z^3 ) by descending degree of ( x ).
Translating Expressions
- The phrase "three times a number increases four" translates to the algebraic expression ( 3x + 4 ).
Scientific Notation
- The expression ( 3.25 \times 10^{-6} ) equals ( 0.00000325 ).
- The number ( 1.104 \times 10^{5} ) converts to ( 110,400 ).
Simplifying Expressions
- The expression ( (15x - 3y) - (3x + 8y) ) simplifies to ( 12x - 11y ).
- The binomial product ( (2x + 6)(3x + 2) ) results in ( 6x^2 + 22x + 12 ).
- Raising the term ( (3a^3) ) to the exponent of 2 results in ( 9a^6 ).
- Factoring ( (2b - 5c)(2b + 5c) ) yields ( 4b^2 - 25c^2 ).
- The product ( (x - 2)(-4x^2 - 7x + 10) ) simplifies to ( -4x^3 + x^2 + 24x - 20 ).
- The expression ( \frac{3q^3r^2 - 2qr}{3qr} ) is simplified to ( q^2r - \frac{2}{3} ).
Rational Expressions
- The rational expression ( \frac{a^2 - a - 20}{a + 4} ) simplifies to ( a - 5 ).
Calculating with Scientific Notation
- Multiplying ( (2.5 \times 10^{-2})(5.0 \times 10^{7}) ) results in ( 1.25 \times 10^{4} ).
- Dividing ( 8.0 \times 10^{-4} ) by ( 2.0 \times 10^{5} ) simplifies to ( 4 \times 10^{-9} ).
Solving Equations
- The linear equation ( 16x + 2 = x + 17 ) has the solution ( x = 1 ).
- The equation ( (x - 3)(x + 4) = (x + 2)^2 - 1 ) results in ( x = -5 ).
- The equation ( |x + 2| - 4 = 12 ) yields solutions ( x = -18 ) and ( x = 14 ).
Line Equations and Systems
- The line passing through points (3, -2) and (5, 4) has the equation ( y = 3x - 11 ).
- A line parallel to ( y = 5x - 4 ) through point (9, -1) is described by the equation ( 5x - 46 ).
Interval Notation
- The expression ( 2x + 7 \geq 3 ) corresponds to a graph with a closed dot on 4 extending to the left and a closed dot on 2 extending to the right.
Graphical Solutions
- The graphical solution to the system of equations ( 2x + y = -4 ) and ( x + 3y = 3 ) is found at the point ( (-3, 2) ).
Word Problems
- In a situation with costs for meals at a buffet, the cost of a child's meal was calculated as $5.50 using the equations derived from given costs for adults and children.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge with these flashcards from Algebra 1, focusing on key concepts and properties of algebraic expressions. This quiz covers topics such as the associative property, quadrants, and types of intervals in graphs. Challenge yourself to review and reinforce your understanding of essential algebra principles.
