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irina [24]
2 years ago
6

Let $x$ be the positive number such that $2x^2 = 4x + 9.$

Mathematics
1 answer:
loris [4]2 years ago
4 0

Solve for x. I'll do it by completing the square:

2x² = 4x + 9

2x² - 4x = 9

x² - 2x = 9/2

x² - 2x + 1 = 11/2

(x - 1)² = 11/2

x - 1 = ± √(11/2)

x = 1 ± √(11/2)

x = 1 ± √22/2

x = (2 ± √22)/2

Take the solution with the positive square root. Then it follows that a = c = 2 and b = 22. So a + b + c = 26.

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Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle
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Option A is correct. If segment DC bisects segment AB, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. This can be obtained using perpendicular bisector theorem.

<h3>What is perpendicular bisector theorem ?</h3>

Perpendicular bisector theorem : In a plane, if we choose a point, say D, on the perpendicular bisector,say PQ, drawn from segment, say AB, then the point D is equidistant from the endpoints, that is A and B, of the segment.

That is, perpendicular bisector PQ of line segment AB is the line with         Q = 90° and Q is the midpoint of AB ⇒ AQ = BQ. A point on PQ say D is equidistant from A and B ⇒AD and BD.

Thus in the given question we can use perpendicular bisector theorem.

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Hence it is clear that Option A is correct.

     

Learn more about perpendicular bisector theorem:

brainly.com/question/4186530

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