Answer:

Step-by-step explanation:
Given
Points (2,3) and (-3,8)
Required
Determine the gradient
Gradient (m) is calculated by dividing the change in y values by the change in x values.
i.e.

Where:


becomes



<em>Hence, the gradient is -1</em>
The line x = 0 is perpendicular to the line y = -3:
Correct. Any horizontal line (y = a) and any vertical line (x = b) intersect at some point and are perpendicular.
All lines that are parallel to the y-axis are vertical lines:
Correct. The y-axis is a vertical line, so any lines that are parallel to it must also be vertical.
All lines that are perpendicular to the x-axis have a slope of 0.
Incorrect. Lines that have a slope of 0 are horizontal, and the x-axis is horizontal as well. Any lines with a slope of 0 are <em>parallel </em>to the x-axis, not perpendicular to it.
The equation of the line parallel to the x-axis that passes through the point (2, 6) is x = 2.
Incorrect. x = 2 is a vertical line, and vertical lines cannot be parallel to the horizontal x-axis. x = 2 is perpendicular to the x-axis, however.
The equation of the line perpendicular to the y-axis that passes through the point (-5, 1) is y = 1.
Correct. The line y = 1 is horizontal, and the y-axis is a vertical line. Because the line y = 1 crosses the y-axis, the lines are perpendicular.
Answer:
The width is: 
The length is 
Step-by-step explanation:
The given rectangle has area given algebraically by the function:

The width of the rectangle is the greatest common factor of
,
and 
That is the width is: 
We now divide the area by the width to obtain the length of the rectangle:

This simplifies to:


Answer:
Step-by-step explanation:
Berto’s train was 34 miles past the egg farm .
Eduardo’s train had 12 miles to go before it reached the egg farm.
Distance between two trains = 34 + 12 = 46 miles
This distance has to be reduced to zero for their crossing each other .
Rate at which this distance is reduced = their relative velocity
= 110 - 85
= 25 miles / h [ They are moving in the same direction ]
So, time taken for them to meet each other
= 46 / relative velocity
= 46 / 25
= 1.84 hours .