decide whether the pair of lines is parallel, pependicular, or neither
3x+2y=2
2x-3y=8
E-mails arrives at the Dean's office at a mean rate of three per minute.
1- What is the probability that the Dean will receive exactly one email in a random minute? 2- What is the probability that the Dean will receive tow or more emails in a random minute?
i think you have the wrong joe
To determine whether the pair of lines is parallel, perpendicular, or neither, we need to compare their slopes.
Step 1: Write the equations of the given lines in slope-intercept form, y = mx + b, where m represents the slope.
Line 1: 3x + 2y = 2
Rewrite the equation in slope-intercept form by isolating y:
2y = -3x + 2
Divide both sides by 2:
y = (-3/2)x + 1
Line 2: 2x - 3y = 8
Rewrite the equation in slope-intercept form by isolating y:
-3y = -2x + 8
Divide both sides by -3 (notice the negative sign):
y = (2/3)x - (8/3)
Step 2: Compare the slopes of the two lines.
The slope of Line 1 is -3/2, which means its slope is -1.5.
The slope of Line 2 is 2/3, which means its slope is approximately 0.67.
Step 3: Interpret the result.
If the slopes of the two lines are the same, they are parallel.
If the slopes are negative reciprocals of each other (i.e., their product is -1), they are perpendicular.
If neither of the above conditions is met, the lines are neither parallel nor perpendicular.
In this case, the slope of Line 1 is -1.5, while the slope of Line 2 is approximately 0.67. Since their slopes are not the same and their product is not -1, we can conclude that the pair of lines is neither parallel nor perpendicular.