Answer: Option C. -> not defined

Answer: Option A. -> 1

Answer: Option D. -> 10

Answer: Option B. -> 5x + 3y + 2 =0

Answer: Option A. -> x + y – 8 = 0

Answer: Option C. -> y +4 = 0

Answer: Option A. -> k = 2

Answer: Option C. -> k = 3

Given two lines 2x + ky + 7 = 0 and 27x - 18y + 25 = 0.
We need to find the value of k for which these two lines are perpendicular to each other.

Perpendicular Lines:
Two lines are said to be perpendicular, if the product of their slopes is equal to -1.
Mathematically, it can be written as:
m1*m2 = -1
Where m1 and m2 are the slopes of the two lines.

Slopes of the given lines:
To find the slopes of the given lines, we need to calculate their coefficients of x and y.
For the first line, 2x + ky + 7 = 0
Coefficient of x = 2
Coefficient of y = k
Therefore, the slope of the first line = m1 = -2/k

For the second line, 27x - 18y + 25 = 0
Coefficient of x = 27
Coefficient of y = -18
Therefore, the slope of the second line = m2 = 18/27

Product of Slopes:
Now, we need to calculate the product of the slopes of the two lines.
m1*m2 = -2/k * 18/27
m1*m2 = -2/3k
To make the product of slopes equal to -1, we need to have -2/3k = -1
Therefore, we get,
k = 3

Hence, the value of k for which the lines 2x + ky + 7 = 0 and 27x - 18y + 25 = 0 are perpendicular to each other, is k = 3.
Therefore, Option C. k = 3 is the correct answer.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option D. -> 150⁰

Answer: Option A. -> parallel
To determine whether the given lines x + 2y - 9 = 0 and 3x + 6y + 8 = 0 are parallel or perpendicular, we need to compare their slopes. The slope of a line can be found using the formula:
slope = - coefficient of x / coefficient of y
Let's find the slope of the first line x + 2y - 9 = 0:
slope = - coefficient of x / coefficient of y= -1 / 2
Now let's find the slope of the second line 3x + 6y + 8 = 0:
slope = - coefficient of x / coefficient of y= -3 / 6= -1 / 2
Since both slopes are the same (-1/2), we can conclude that the given lines are parallel to each other. Therefore, the correct answer is option A.
Here are some key points to remember about parallel lines:

• Two lines are parallel if and only if they have the same slope.
• If two lines are parallel, they never intersect, no matter how far they are extended.
• The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
• If two lines are parallel, they have the same slope but different y-intercepts.
• To find the equation of a line given its slope and a point on the line, we can use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.