9 Questions
Which of the following represents the additive inverse of $-5$?
5
In the context of proportionality, if $y$ is directly proportional to $x$, what is the relationship between $y$ and $x$ as $x$ increases?
y increases
When solving an algebraic equation, what is the process of rationalization used for?
To simplify the equation by getting rid of radicals in the denominator
In the context of proportionality, if $y$ is inversely proportional to $x$, what happens to $y$ when $x$ increases?
Decreases
Which of the following represents the multiplicative inverse of $2/3$?
$3/2$
When solving the equation $3x^2 + 5x - 2 = 0$, what are the solutions for $x$?
$x = -2, \frac{1}{3}$
What is the additive inverse of the expression $-7x^3 + 4x^2 - 6x + 9$?
$-7x^3 - 4x^2 + 6x - 9$
In the equation $5x^2 - 3xy + 2y^2 = 0$, what are the solutions for $x$ and $y$?
$x = \frac{3y \pm \sqrt{7y^2 - 40y^2}}{10}$, $y = \frac{3x \pm \sqrt{7x^2 + 40x^2}}{10}$
If $m$ is directly proportional to $n^2$, and $m = 25$ when $n = 5$, what is the value of $m$ when $n = 10$?
$m = 100$
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.
Test your understanding of additive and multiplicative inverses, rationalization, and solving algebraic equations. Explore questions on proportionality constant, direct or inverse proportionality, and interpreting charts and tables to calculate proportionality constants.
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