1. In 2005, there were 100 rabbits in Polygon Park. The population increased by
1 answer:
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The equation of the line is
Explanation:
The given equation is
<u>Slope:</u>
Since, the equation of the line is perpendicular to the equation , then, the slope is given by
Hence, the slope is
<u>Equation of the line:</u>
The equation of the line can be determined using the formula,
Substituting the point (-2,3) and the slope , in the above formula, we get,
Simplifying, we get,
Therefore, the equation of the line is
You can see the trapezoid in the attached picture.
The data given in the problem are:
KF = 10
LK // MF
A(KLMF) = A(FMN)
We know that KLMF is a parallelogram because:
LM // KF (bases of the trapezoid)
LK // MF (hypothesis).
The area of a parallelogram is given by the formula:
A(KLMF) = b × h
= KF <span>× h</span>
= 10 × h
The area of a triangle is given by the formula:
<span>A(FMN) = (b × h) / 2
= (FN </span>× h) / 2
The problem states that the two areas are congruent, therefore:
A(KLMF) = <span>A(FMN)
</span>10 × h = FN <span>× h / 2
10 = FN </span><span>/ 2
FN = 20
Therefore we can calculate:
KN = KF + FN = 10 + 20 = 30
Hence, KN is 30 units long.</span>
The data given in the problem are:
KF = 10
LK // MF
A(KLMF) = A(FMN)
We know that KLMF is a parallelogram because:
LM // KF (bases of the trapezoid)
LK // MF (hypothesis).
The area of a parallelogram is given by the formula:
A(KLMF) = b × h
= KF <span>× h</span>
= 10 × h
The area of a triangle is given by the formula:
<span>A(FMN) = (b × h) / 2
= (FN </span>× h) / 2
The problem states that the two areas are congruent, therefore:
A(KLMF) = <span>A(FMN)
</span>10 × h = FN <span>× h / 2
10 = FN </span><span>/ 2
FN = 20
Therefore we can calculate:
KN = KF + FN = 10 + 20 = 30
Hence, KN is 30 units long.</span>