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What is a value or values that make an equation true?
A value or values that make an equation true are known as the solutions or roots of the equation. For example, in the equation (x + 3 = 7), the value (x = 4) is a solution because substituting it into the equation balances both sides. In general, solutions satisfy the equality expressed in the equation.
What equation using absolute values would have a solution of either 7 o 15?
An equation using absolute values that has solutions of either 7 or 15 is ( |x - 11| = 4 ). This equation works because when you solve it, you set up two cases: ( x - 11 = 4 ) (which gives ( x = 15 )) and ( x - 11 = -4 ) (which gives ( x = 7 )). Thus, both values are solutions to the equation.
What are you finding when you solve a quadratic equation?
You are finding the roots or solutions. These are the values of the variable such that the quadratic equation is true. In graphical form, they are the values of the x-coordinates where the graph intersects the x-axis.
When solving a quadratic equation what do the X-values stand for as it relates to plotting the graph of the equation?
In a quadratic equation, the X-values represent the points where the graph of the equation intersects the X-axis, known as the roots or zeroes of the equation. These points indicate the values of X for which the quadratic expression equals zero. When plotted, these X-values help define the shape of the parabola, which can open upwards or downwards depending on the leading coefficient. The X-values also reflect the solutions to the equation when set equal to zero.
How do you identify 2 solutions to a linear equation?
A linear equation is that of a straight line. Any one of the infinitely many points on the line will be solutions. If the equation is in terms of the variables x and y, just pick any two values of x, solve for y and the results will be the coordinates of two solutions.
What are 3 other names for solutions of a quadratic equation?
Roots, zeroes, and x values are 3 other names for solutions of a quadratic equation.
What is a value or values that make an equation true?
A value or values that make an equation true are known as the solutions or roots of the equation. For example, in the equation (x + 3 = 7), the value (x = 4) is a solution because substituting it into the equation balances both sides. In general, solutions satisfy the equality expressed in the equation.
What are you finding when you solve a quadratic equation?
You are finding the roots or solutions. These are the values of the variable such that the quadratic equation is true. In graphical form, they are the values of the x-coordinates where the graph intersects the x-axis.
When solving a quadratic equation what do the X-values stand for as it relates to plotting the graph of the equation?
In a quadratic equation, the X-values represent the points where the graph of the equation intersects the X-axis, known as the roots or zeroes of the equation. These points indicate the values of X for which the quadratic expression equals zero. When plotted, these X-values help define the shape of the parabola, which can open upwards or downwards depending on the leading coefficient. The X-values also reflect the solutions to the equation when set equal to zero.
How do you identify 2 solutions to a linear equation?
A linear equation is that of a straight line. Any one of the infinitely many points on the line will be solutions. If the equation is in terms of the variables x and y, just pick any two values of x, solve for y and the results will be the coordinates of two solutions.
How many number of solutions are there for equation square of mod x minus 3times mod xplus 2 equal zero?
The equation is |x|2-3|x|+2=0 If x>0 then the equation becomes x2-3x+2=0 (x-2)(x-1)=0 x=1,2 We get two values for x. If x<0, then the equation is again x2-3x+2=0 We again get two values. Therefore, the total number of solutions=4.
How do you use a graph to determine 3 solutions of an equation?
To determine three solutions of an equation using a graph, first plot the equation on a coordinate plane. Identify the points where the graph intersects the x-axis; these x-values represent the solutions of the equation. Each intersection point corresponds to a solution, so you can read the x-coordinates of these points to find the three solutions. Ensure that the graph is drawn accurately for precise identification of the solutions.
How many solutions should you have when solving absolute value equation when possible?
When solving an absolute value equation, you can typically have two solutions, one for each case where the expression inside the absolute value can be either positive or negative. For example, the equation |x| = a has the solutions x = a and x = -a, assuming a is non-negative. However, if the equation results in a negative value inside the absolute value, there will be no solutions, as absolute values cannot be negative.
An equation that has infinite solutions is called?
An equation that has infinite solutions is called an identity. This occurs when the equation is true for all values of the variable involved, often resulting from equivalent expressions on both sides of the equation. Examples include equations like (0 = 0) or (x + 2 = x + 2).
When you square each side of an equation is the resulting equation equivalent to the original?
No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2No. The resulting equation has more solutions. For example, x = 2 has only one solution and that is x = 2.butx2= 4, the squared equation, has two solutions: x = +2 and x = -2
Which best explains why the equation 3x plus 8 3x - 5 has no solutions?
The equation (3x + 8 = 3x - 5) has no solutions because when we attempt to isolate (x), we end up with a contradiction. Subtracting (3x) from both sides results in (8 = -5), which is not true. Since there are no values of (x) that can satisfy this equation, it has no solutions.
Why is only the x value of the intersection point the solution to an equation in a quadratic function?
In a quadratic function, the intersection points with the x-axis represent the values of x where the function equals zero, which are the solutions to the equation. Since a quadratic is typically expressed in the form ( ax^2 + bx + c = 0 ), the y-value at these intersection points is always zero, indicating that the solutions are solely defined by the x-values. Therefore, only the x-values of these intersection points are relevant as they represent the roots of the equation.
