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Questions and Answers
Which of the following represents the additive inverse of $-5$?
Which of the following represents the additive inverse of $-5$?
- 0
- -(-5)
- -5
- 5 (correct)
In the context of proportionality, if $y$ is directly proportional to $x$, what is the relationship between $y$ and $x$ as $x$ increases?
In the context of proportionality, if $y$ is directly proportional to $x$, what is the relationship between $y$ and $x$ as $x$ increases?
- y decreases
- y increases (correct)
- y remains constant
- y becomes negative
When solving an algebraic equation, what is the process of rationalization used for?
When solving an algebraic equation, what is the process of rationalization used for?
- To solve for the unknown variable
- To convert a decimal number to a fraction
- To simplify the equation by getting rid of radicals in the denominator (correct)
- To eliminate irrational numbers from the equation
In the context of proportionality, if $y$ is inversely proportional to $x$, what happens to $y$ when $x$ increases?
In the context of proportionality, if $y$ is inversely proportional to $x$, what happens to $y$ when $x$ increases?
Which of the following represents the multiplicative inverse of $2/3$?
Which of the following represents the multiplicative inverse of $2/3$?
When solving the equation $3x^2 + 5x - 2 = 0$, what are the solutions for $x$?
When solving the equation $3x^2 + 5x - 2 = 0$, what are the solutions for $x$?
What is the additive inverse of the expression $-7x^3 + 4x^2 - 6x + 9$?
What is the additive inverse of the expression $-7x^3 + 4x^2 - 6x + 9$?
In the equation $5x^2 - 3xy + 2y^2 = 0$, what are the solutions for $x$ and $y$?
In the equation $5x^2 - 3xy + 2y^2 = 0$, what are the solutions for $x$ and $y$?
If $m$ is directly proportional to $n^2$, and $m = 25$ when $n = 5$, what is the value of $m$ when $n = 10$?
If $m$ is directly proportional to $n^2$, and $m = 25$ when $n = 5$, what is the value of $m$ when $n = 10$?
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Study Notes
Proportionality and Algebraic Equations
- The additive inverse of -5 is 5.
- If y is directly proportional to x, then y increases as x increases, and the relationship between y and x can be represented by the equation y = kx, where k is a constant.
- Rationalization is the process of removing radical expressions from the denominator of a fraction, often used when solving algebraic equations.
- If y is inversely proportional to x, then y decreases as x increases, and the relationship between y and x can be represented by the equation y = k/x, where k is a constant.
- The multiplicative inverse of 2/3 is 3/2.
Solving Algebraic Equations
- The solutions for x in the equation 3x^2 + 5x - 2 = 0 can be found by factoring or using the quadratic formula.
- The additive inverse of the expression -7x^3 + 4x^2 - 6x + 9 is 7x^3 - 4x^2 + 6x - 9.
- The solutions for x and y in the equation 5x^2 - 3xy + 2y^2 = 0 can be found by factoring or using substitution or elimination methods.
Direct Proportionality
- If m is directly proportional to n^2, then m = kn^2, where k is a constant.
- If m = 25 when n = 5, then the value of m when n = 10 can be found by substituting n = 10 into the equation m = kn^2, given the initial condition.
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