Determine whether the graphs of the given equations are perpendicular, parallel, or neither.
2 answers:
1. The two equation of line are
a. y = 4 x -2
b . -x + 4 y=0→ x=4 y→y =
Slope intercept form of line is , y= m x + c
Slope of line a =4
Slope of line b =
Neither the product of slopes of two lines is -1, nor their slopes are equal.So, these two lines are neither parallel , nor perpendicular to each other.
Correct option is neither.
2. Two lines with positive slopes are parallel→Incorrect Statement
Two lines with same slope either positive or negative are parallel.
Correct Option (Sometimes)
3. Two lines with the same slope and different y-intercepts are perpendicular.→→Incorrect Statement(never)
For lines to be perpendicular , the product of their slopes should be -1.
Lines having same slope are always parallel to each other, there is no effect of y intercept.
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There are a number of ways to approach this problem, including writing all the numbers that match one of the arrangements, such as for sets of 15:
.. 14, 29, 44, 59, 74, 89, 104, 119, 134, 149, 164, 179, 194 (separated by 15)
Modulo 8, these numbers are
.. 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2
This reduces the numbers of interest to those that are 3 modulo 8:
.. 59, 179 (separated by 8*15 = 120)
Looking at these modulo 7, we have
.. 3, 4
pinpointing 179 as the number of spoons in Cheryl's collection.
_____
The attachment shows a solution via graphing calculator. We simply added the absolute values of the differences of the remainders from the desired values and looked for where that sum was zero. This method, too, pointed to 179 as the solution to the problem.
.. 14, 29, 44, 59, 74, 89, 104, 119, 134, 149, 164, 179, 194 (separated by 15)
Modulo 8, these numbers are
.. 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2
This reduces the numbers of interest to those that are 3 modulo 8:
.. 59, 179 (separated by 8*15 = 120)
Looking at these modulo 7, we have
.. 3, 4
pinpointing 179 as the number of spoons in Cheryl's collection.
_____
The attachment shows a solution via graphing calculator. We simply added the absolute values of the differences of the remainders from the desired values and looked for where that sum was zero. This method, too, pointed to 179 as the solution to the problem.