zero solutions. If you plot these two lines, you will see that they are parallel and do not intersect.
The answer follows:
The roots of an equation means the solutions of an equation. Different methods have been developed for different kinds of equation. It is not possible to give an overview in one or two paragraphs, but in simpler cases, the same operation is done on both sides of the equation, with the aim of "isolating" the variable you are solving for, that is, having it alone on one side. In some complicated cases, no "explicit" solutions exist, and "numerical" solutions have to be used; this basically means using trial-and-error.
No, an equation with integer coefficients does not always have an integer solution. For example, the equation (x + 1 = 2) has an integer solution, (x = 1), but the equation (2x + 3 = 1) has no integer solution since (x = -1) is not an integer. Solutions depend on the specific equation and its constraints, and rational or real solutions may exist instead.
The equation ( x - y = 3 ) represents a straight line in the coordinate plane. Since it is a linear equation with two variables, it has infinitely many solutions, as any point (x, y) on the line satisfies the equation. Specifically, for any value of ( y ), you can find a corresponding value of ( x ) such that the equation holds true.
She did not figure out a particular equation but found the set of conditions under which solutions to a class of partial differential equations would exist. This is now known as the Cauchy-Kovalevskaya Theorem.
1.1x2 + 3.3x + 4 = 6 First rearrange the equation to equal zero so that we can use the quadratic formula. 1.1x2 + 3.3x - 2 = 0 Using the quadratic formula, the solutions are x = -3.52 and x = 0.52 Both of these solutions are real, so the original equation has two real solutions.
A quadratic equation always has TWO (2) solutions. They may be different, the same, or non-existant as real numbers (ie they only exist as complex numbers).
The answer follows:
The roots of an equation means the solutions of an equation. Different methods have been developed for different kinds of equation. It is not possible to give an overview in one or two paragraphs, but in simpler cases, the same operation is done on both sides of the equation, with the aim of "isolating" the variable you are solving for, that is, having it alone on one side. In some complicated cases, no "explicit" solutions exist, and "numerical" solutions have to be used; this basically means using trial-and-error.
No, an equation with integer coefficients does not always have an integer solution. For example, the equation (x + 1 = 2) has an integer solution, (x = 1), but the equation (2x + 3 = 1) has no integer solution since (x = -1) is not an integer. Solutions depend on the specific equation and its constraints, and rational or real solutions may exist instead.
Assuming x(2-10x)=21 to be solved for x, distribute to -10x2+2x=21, or 10x2-2x+21=0. By the quadratic equation, we can determine there are no real solutions because the square root of -836 does not exist. In imaginary solutions, we can reduce to 1/10*(1 + sqrt(-209)) and 1/10*(1-sqrt(-209)) as solutions.
She did not figure out a particular equation but found the set of conditions under which solutions to a class of partial differential equations would exist. This is now known as the Cauchy-Kovalevskaya Theorem.
No, solid solutions also exist.
One option is "cannot exist". The equation is linear and linear equations do not have vertices.
No, solutions can exist in different states of matter, not just in the liquid state. Solutions can exist in the solid, liquid, or gas state depending on the solvent and solute involved in the mixture.
An equation for production doesn't exist.
No, this is not a function. The graph would have a vertical line at x=-14. Since there are more than one y value for every given x value, the equation does not represent a function. The slope of the equation also does not exist.