Questions and Answers
What is the value of b?
-332
What is the expression for y in the equation: 6x - 3y = 36?
y = 2x - 12
If you purchase 6 bottles of juice, how many bottles of water can you buy when the equation is 3w + 4j = 39?
3
What are the coordinates of the point given?
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What does the y-intercept represent in Dylan's quarter spending scenario?
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What is the equation given in the absolute value function?
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What are the coordinates of the point given?
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What is the length of the third side if the perimeter of a triangle is 9x + 7y, and two sides are 2x + 3y and 4x - y?
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What is the expression of b² - b + 4?
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What is the factored form of x² + 12x - 64?
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What is the factored form of 25b² - 60b + 36?
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What is the factored form of 6x² + 28x + 16?
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Study Notes
Algebra Concepts and Definitions
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b = -332 defines a specific value for the variable b in an algebraic context.
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y = 2x - 12 represents a linear equation. To solve for y, manipulate the equation 6x - 3y = 36 to express y in terms of x.
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Water and juice problem: The equation 3w + 4j = 39 relates the number of water bottles (w) and juice bottles (j) purchasable for $39. Purchasing 6 juice bottles allows you to calculate how many water bottles can be bought.
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Coordinate point (-2, 1) indicates a specific location in the Cartesian plane representing the x and y values.
Graph Features and Characteristics
- The y-intercept is crucial for understanding linear graphs. For Dylan in the arcade, the y-intercept represents his initial amount of quarters before spending begins.
Function Forms
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The expression y = |x - 3| defines an absolute value function that reflects distance from the line x = 3.
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Coordinate point (-1, -2) indicates another specific point in a 2D plane with negative values for both x and y.
Algebraic Expressions
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3x + 5y relates to the perimeter of a triangle given by 9x + 7y. To find the third side, consider subtracting the known sides (2x + 3y and 4x - y) from the total perimeter.
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b² - b + 4 is a quadratic expression that may require factoring or solving techniques.
Factoring and Expanding
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(x - 4)(x + 16) is the factored form of x² + 12x - 64, showcasing the relationship between roots and factorization.
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(5b - 6)² represents the squared binomial form of 25b² - 60b + 36, illustrating simplification in algebraic expressions.
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2(3x + 2)(x + 4) demonstrates factoring of the quadratic 6x² + 28x + 16 into a product of linear factors.
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