Tell whether the following set is an empty set or not.
2 answers:
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Given:
Area of rectangular pool = 640 square feet
The length is 12 feet shorter than the width.
To find:
The length and width of the pool.
Solution:
Let width of the pool = x feet
Then, Length of the pool = (x-12) feet
Area of a rectangle is
Area of pool is 640 square feet. So,
Splitting the middle term, we get
Using zero product property, we get
Dimensions cannot be negative. So, x=32.
Now,
Width of the pool = 32 feet
Length of the pool = 32-12 = 20 feet
Therefore, the length of the pool is 20 feet and width is 32 feet.
ANSWER
EXPLANATION.
The orthocenter is the point of intersection of any two altitudes of the triangle.
First, you need to determine the slope of each side of the triangle.
△ABC has vertices A(2, 3), B(−4, −3), C(2, −3).
This line has undefined slope, which means it is a vertical line.
The slope of this line is zero, meaning the line is a horizontal line.
This implies that side BC and side AC of the given triangle are perpendicular and will intersect at C since they are the altitudes of triangle ABC.
Hence the orthocentre is
See diagram in attachment.
EXPLANATION.
The orthocenter is the point of intersection of any two altitudes of the triangle.
First, you need to determine the slope of each side of the triangle.
△ABC has vertices A(2, 3), B(−4, −3), C(2, −3).
This line has undefined slope, which means it is a vertical line.
The slope of this line is zero, meaning the line is a horizontal line.
This implies that side BC and side AC of the given triangle are perpendicular and will intersect at C since they are the altitudes of triangle ABC.
Hence the orthocentre is
See diagram in attachment.