A point (a, b) in the second Quadrant, is any point where a is negative and b is positive.
For example (-3, 5), (-189, 14) etc are all points in the 2.Quadrant
Rotating a point P(x, y) in the second Quadrant 180° counterclockwise, means rotating 180° counterclockwise about the origin, which maps point P to P'(-a, -b) in the fourth Quadrant.
The unit fraction of 7/8 is 1/8
Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.
1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.
According to this theorem,
Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then
Take positive value x. You get
2. According to the previous theorem,
Then
Answer: 
This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then
This means that you cannot find solutions of this equation. Then CD≠2 cm.
The situation with an expression involving signed numbers is w - 12 + 4 3/8 and the overall change in Sara’s weight is -7 5/8 pounds
<h3>Represent this situation with an expression involving signed numbers. </h3>
Let Sara's initial weight be w.
The given parameters are:
Lost = 12 pounds
Gain = 4 3/8 pounds
The situation with an expression involving signed numbers is represented as:
Weight = Initial - Lost + Gain
So, we have:
Weight = w - 12 + 4 3/8
<h3>What is the overall change in Sara’s weight?.</h3>
In (a), we have:
Weight = w - 12 + 4 3/8
The overall change is:
Change = - 12 + 4 3/8
Evaluate
Change = -7 5/8
Hence, the overall change in Sara’s weight is -7 5/8 pounds
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