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What else can I help you with?
Which equation could represent the area of a square as a function of a side?
A=S2... Where A = area, and S = length of one side.
What is true about the solutions of a quadratic equation when the radicand of the quadratic formula is a perfect square?
The two solutions are coincident.
In general when solving a radical equation should you first isolate the radical and then both sides?
It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.
When solving a radical equation you should first isolate the radical and then?
It often helps to square both sides of the equation (or raise to some other power, such as to the power 3, if it's a cubic root).Please note that doing this may introduce additional solutions, which are not part of the original equation. When you square an equation (or raise it to some other power), you need to check whether any solutions you eventually get are also solutions of the original equation.
Why is it necessary to check for extraneous solutions in radical equations?
1) When solving radical equations, it is often convenient to square both sides of the equation. 2) When doing this, extraneous solutions may be introduced - the new equation may have solutions that are not solutions of the original equation. Here is a simple example (without radicals): The equation x = 5 has exactly one solution (if you replace x with 5, the equation is true, for other values, it isn't). If you square both sides, you get: x2 = 25 which also has the solution x = 5. However, it also has the extraneous solution x = -5, which is not a solution to the original equation.
What equation could represent the area of a square as a function of a side?
The area ( A ) of a square can be represented as a function of its side length ( s ) using the equation ( A(s) = s^2 ). In this equation, ( A ) is the area, and ( s ) is the length of one side of the square. As the side length increases, the area increases quadratically.
Which equation could represent the area of a square as a function of a side?
A=S2... Where A = area, and S = length of one side.
How do you solve a square root equation?
To solve a square root equation, first isolate the square root term on one side of the equation. Then, square both sides to eliminate the square root. After squaring, solve the resulting equation for the variable. Finally, check your solutions to ensure they are valid, as squaring can introduce extraneous solutions.
How is a radical equation similar to a linear equation?
Technically,no. A radical equation has a radical (Square root) in it, and has two solutions because the square root can be positive or negative.
Explain how to identify whether an equation has no solution or infinitely many solutions?
An equation can be determine to have no solution or infinitely many solutions by using the square rule.
What is true about the solutions of a quadratic equation when the radicand of the quadratic formula is a perfect square?
The two solutions are coincident.
What is the perimeter equation for a square?
P_square=4L where L is the length of the side of the square.
Do you need to put a plus or minus sign in front of a square root answer you get from finding the inverse of a quadratic equation?
Yes. Quite often, if you don't, you'll lose solutions. That is, the transformed equation - after taking square roots - will have less solutions than the original equation.
This ellipse is centered at the origin and has a horizontal axis of length 14 and a vertical axis of length 16 What is its equation?
The equation is based on formula (x - h)square / A square + (y-k)square / B square = 1. To apply to the above ellipse the equation would be similar to (x- 0) square/ 14 square + (2014 - 0) square / 16 square.
When does a equation have two solutions?
Two cases in which this can typically happen (there are others as well) are: 1. The equation includes a square. Example: x2 = 25; the solutions are 5 and -5. 2. The equation includes an absolute value. Example: |x| = 10; the solutions are 10 and -10.
Which equation has the solutions x equals 1 plus and minus the square root of 5?
The equation that has the solutions ( x = 1 \pm \sqrt{5} ) can be derived from the quadratic formula. Specifically, these solutions can be expressed as roots of the equation ( x^2 - 2x - 4 = 0 ). When simplified, this equation matches the given solutions, as substituting ( x = 1 \pm \sqrt{5} ) satisfies the equation.
Check all solutions to the equation If there are no solutions check None x2 equals 25?
To solve the equation (x^2 = 25), we can take the square root of both sides. This gives us two solutions: (x = 5) and (x = -5). Thus, the solutions to the equation are (x = 5) and (x = -5).
