2x + 5y = 8
5x + 2y = 1
Are the line parrallel, perpendicular, or neither the answer I got was parrallel someone please help me if I am wrong.
Find the domain of the function
g(x) = 2/1-5x
solve both of the equations for y if the slopes are recipricals of one another the lines are perpendicular otherwise if they are the same slope they are parallel
which expression is equivalent to 3x + 2y - 8 - 5x + y
To determine whether the given system of equations is made up of parallel lines, perpendicular lines, or neither, we need to compare the slopes of the equations.
1. Start by writing the given equations in slope-intercept form, which is in the form of y = mx + b, where m represents the slope.
For the first equation, 2x + 5y = 8:
- Rearrange the equation to isolate y on one side: 5y = -2x + 8
- Divide both sides by 5: y = (-2/5)x + 8/5
For the second equation, 5x + 2y = 1:
- Rearrange the equation to isolate y on one side: 2y = -5x + 1
- Divide both sides by 2: y = (-5/2)x + 1/2
2. Compare the slopes of the two equations.
The slope of the first equation is -2/5, while the slope of the second equation is -5/2.
3. If the two slopes are equal, then the lines are parallel. If the product of the two slopes is -1, then the lines are perpendicular. Otherwise, they are neither.
In this case, when we multiply -2/5 and -5/2, we get 1, which means that the lines are not perpendicular. Since the slopes are not equal, the lines are also not parallel. Therefore, the answer is that the lines in the given system are neither parallel nor perpendicular.
Now let's find the domain of the function g(x) = 2/(1-5x).
The domain of a function represents the set of all possible input values (x) for which the function is defined.
In this case, the function g(x) involves division, which means we need to avoid dividing by zero.
To find the values that make the denominator zero, we set 1 - 5x = 0 and solve for x.
1 - 5x = 0
-5x = -1
x = 1/5
The value x = 1/5 makes the denominator zero, so it is not in the domain.
Therefore, the domain of the function g(x) = 2/(1-5x) is all real numbers except x = 1/5.