Algebra problems

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Questions and Answers

Which of the following statements correctly describes the relationship between variables and constants in algebraic expressions?

  • Variables and constants both represent fixed values, but constants are always integers.
  • Variables represent unknown or changing quantities, while constants represent fixed values. (correct)
  • Variables represent fixed values, while constants represent unknown or changing quantities.
  • Variables and constants both represent unknown or changing quantities, but variables are always letters.

Simplify the following expression: $5x + 3y - 2x + y - x$.

  • $2x + 4y$ (correct)
  • $2x + 3y$
  • $3x + 3y$
  • $4x + 4y$

Solve the following linear equation for $x$: $3(x + 2) = 5x - 4$.

  • $x = 3$
  • $x = 1$
  • $x = 2$
  • $x = 5$ (correct)

What is the solution set for the quadratic equation $x^2 - 5x + 6 = 0$?

<p>{2, 3} (B)</p> Signup and view all the answers

Consider the system of equations:

$y = 3x - 2$

$x + 2y = 8$

What is the solution for $x$ and $y$?

<p>$x = 2, y = 4$ (A)</p> Signup and view all the answers

Solve the inequality: $4x - 3 < 9$.

<p>$x &lt; 3$ (B)</p> Signup and view all the answers

Given the function $f(x) = 2x^2 - 3x + 1$, what is the value of $f(2)$?

<p>$f(2) = 3$ (C)</p> Signup and view all the answers

What is the slope of the linear function $f(x) = -3x + 5$?

<p>-3 (A)</p> Signup and view all the answers

Simplify the expression: $(x^3 * y^2)^4$

<p>$x^{12} * y^8$ (B)</p> Signup and view all the answers

Simplify the radical expression: $\sqrt{72}$

<p>$6\sqrt{2}$ (A)</p> Signup and view all the answers

Flashcards

Algebra

A branch of mathematics using statements to describe relationships between quantities.

Variables

Symbols representing unknown or changeable values in expressions or equations.

Constants

Fixed numbers that do not change their value in an expression or equation.

Expressions

A combination of variables, constants, and math operations without an equals sign.

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Equations

A statement showing the equality between two expressions, using an equals sign.

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Terms

Individual parts of an expression or equation, separated by + or - signs.

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Coefficients

The numerical factor of a term that contains a variable.

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Operators

Symbols indicating math operations, like +, -, ×, ÷, or ^.

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Like Terms

Terms with the same variable(s) raised to the same power(s).

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Inverse Operations

Operations that reverse the effect of another operation.

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Study Notes

The provided text is identical to the existing notes, so no changes are necessary.

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