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What is the solution set of the equation x squared minus 3x minus 4 equals 0?
X2 - 3X - 4 = 0factored(X + 1)(X - 4)----------------X = - 1X = 4-------------------(- 1, 0) and (4, 0)================solution set of X interception points
Is it possible for a sixth-degree polynomial to have only one solution?
Yes. y = x6 has only one solution, at (0, 0).In fact, if you think about it, the family of equations y = a(x+b)6 (where a and b can be any real constant; including x6, 2(x-4)6, 42(x+1)6, and so on) all have one solution. Other than these equations, however, sixth-degree polynomials almost always have multiple solutions or none at all.
Use addition or substitution to find the value of x for this set of equations 2x - 3y equals -15 x equals 4y?
2x - 3y = -15x => -3y = -17x => -21y = -119x 2x - 3y = 4y => 2x = 7y => 21y = 6x so now you can add the two equations. 0 = -113x x=0 now plug back in 2*0 - 3y = -15*0 -3y = 0 y=0.
Which is the solution set for 3x2 - 4x - 15 equals 0?
3x2-4x-15 = 0 (3x+5)(x-3) = 0 x = -5/3 or x = 3
Sin x cos x equals 0?
For the product to be zero, any of the factors must be zero, so you solve, separately, the two equations: sin x = 0 and: cos x = 0 Like many trigonometric equations, this will have an infinity of solutions, since sine and cosine are periodic functions.
How would you answer the following linear equation and what would be the solution set y equals 32.25x and y equals 26.30x?
The graphs of those two equations are straight lines, each of which passes through the origin. The origin is the common solution ... the point (0, 0).
Can 0 be the solution of an equation?
Yes, zero can and is the solution of many equations.
Is 0 a solution?
Yes, zero can be a legitimate solution of many equations and functions.
If the solution to a system of equations is 2 equals 0 what does that mean?
That means there is no solution.There is no set of numbers that you can assign to the variables in the system of equationsthat will make '2' equal to '0'.
Can absolute calue equations have one solution?
Yes, for example: | x | = 0 with the only solution: x = 0
When will a homogeneous system of equations be inconsistent?
A homogeneous system of equations will be inconsistent if it has a non-trivial solution, meaning that the variables can be simultaneously set to values other than zero. This can occur when the number of equations is greater than the number of unknowns in the system.
When will be the linear equations a1x plus b1y plus c1 equals 0 and a2x plus b2y plus c2 equals 0 has unique solution?
When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..
What is an independent system of linear equations?
An independent system of linear equations is a set of vectors in Rm, where any other vector in Rm can be written as a linear combination of all of the vectors in the set. The vector equation and the matrix equation can only have the trivial solution (x=0).
Equations that have the same solution?
It is not clear what the question requires. Yes, there are plenty of equations that have the same solution. For example, each and every equation of direct proportionality has the solution (0, 0). So what? every polynomial of the form y = anxn + an-1xn-1 + ... + a1x + a0 has the solution (0, a0). Again, so what?
Which one of the following equations represents the y- axis?
X = 0
What does it mean both algebraically and graphically when an ordered pair is a solution to a system of two linear equations?
If an ordered pair is a solution to a system of linear equations, then algebraically it returns the same values when substituted appropriately into the x and y variables in each equation. For a very basic example: (0,0) satisfies the linear system of equations given by y=x and y=-2x By substituting in x=0 into both equations, the following is obtained: y=(0) and y=-2(0)=0 x=0 returns y=0 for both equations, which satisfies the ordered pair (0,0). This means that if an ordered pair is a solution to a system of equations, the x of that ordered pair returns the same y for all equations in the system. Graphically, this means that all equations in the system intersect at that point. This makes sense because an x value returns the same y value at that ordered pair, meaning all equations would have the same value at the x-coordinate of the ordered pair. The ordered pair specifies an intersection point of the equations.
The ordered pair 2 16 is a solution for which of the following equations?
y = (x + 2)2 andy = (2x)2(x-2)2 + (y-16)2 = 0
