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What can be said of an ellipse when the two denominator values in its standard equation are the same?
When the two denominator values in the eclipse standard equation are the same, it can be said to be in foci.
When an equation includes a term with a variable denominator?
When an equation includes a term with a variable denominator, it can lead to complications such as undefined values, particularly when the denominator is equal to zero. To solve such equations, it's important to identify and exclude any values that make the denominator zero, as these will not be valid solutions. Additionally, when manipulating the equation, one should be cautious to avoid introducing extraneous solutions that do not satisfy the original equation. Ultimately, the presence of a variable denominator requires careful analysis to ensure all potential solutions are valid.
What statement best describes the excluded values of a rational expression?
The excluded values of a rational expression are the values of the variable that make the denominator equal to zero. These values are not in the domain of the expression, as division by zero is undefined. To identify excluded values, set the denominator equal to zero and solve for the variable. Any solution to this equation represents an excluded value.
How do you plot the graph of a quadratic equation?
Just like any other equation, you can set up a table of x values, and calculate the corresponding y values. Then plot the points on the graph. In this case, it helps to have some familiarity with quadratic equations (you can find a discussion in algebra books), and recognize (from the form of the equation) whether your quadratic equation represents a parabola, a circle, an ellipse, or a hyperbola.
How do you find an oblique asymptotes?
An oblique asymptote is another way of saying "slant asymptote."When the degree of the numerator is one greater than the denominator, an equation has a slant asymptote. You divide the numerator by the denominator, and get a value. Sometimes, the division pops out a remainder, but ignore that, and take the answer minus the remainder. Make your "adapted answer" equal to yand that is your asymptote equation. To graph the equation, plug values.
Does every equation of the form x2 mx y2 nyp represent a circle?
No, not every equation of the form (x^2 + mx + y^2 + ny = p) represents a circle. For an equation to represent a circle, it must be in the standard form ((x - h)^2 + (y - k)^2 = r^2), where (r) is the radius. The presence of linear terms (mx) and (ny) means that the equation could represent a different conic section, such as an ellipse or hyperbola, depending on the values of (m), (n), and (p).
What values of x gives a denominator equal to 0?
The denominator cannot be 0. A number with denominator 0 is not defined.
Why the Y values are in the numerator and the X-Values are in the denominator?
That is not necessarily so. You can have the X-Values in the numerator and the Y-values in the denominator. The only half-way decent explanation is in the X-values represent an independent variable and the Ys are dependent.
What is the standard equation for finding range?
What sort of range-distance of an object, range of a plane, range of possible values, are all possible.
What is an equation that's true for all values?
an equation that's true for all values is an identity.
What is called when the denominator is zero in a rational function?
The function is not defined at any values at which the denominator is zero.
What does solve the equation mean?
Find values for the variable that satisfy the equation, that is if you replace those values for the variable into the original equation, the equation becomes a true statement.
