The area of the triangle ABC is 207.5 square units.
Explanation:
The measurements of the sides of the triangle are ,
and
We need to determine the area of the triangle ABC.
<u>Area of the triangle:</u>
The area of the triangle can be determined using the formula,
where ,
and
Substituting these values in the above formula, we get,
Simplifying the values, we get,
Rounding off to the nearest tenth, we get,
Thus, the area of the triangle ABC is 207.5 square units.
Answer:
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Step-by-step explanation:
This question is essentially asking one to find the vertex of the parabola formed by the given equation. One could plot the equation, but it would be far more efficient to complete the square. Completing the square of an equation is a process by which a person converts the equation of a parabola from standard form to vertex form.
The first step in completing the square is to group the quadratic and linear term:
Now factor out the coefficient of the quadratic term:
After doing so, add a constant such that the terms inside the parenthesis form a perfect square, don't forget to balance the equation by adding the inverse of the added constant term:
Now take the balancing term out of the parenthesis:
Simplify:
The x-coordinate of the vertex of the parabola is equal to the additive inverse of the numerical part of the quadratic term. The y-coordinate of the vertex is the constant term outside of the parenthesis. Thus, the vertex of the parabola is: