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kifflom [539]
3 years ago
5

In a local basketball league championship total 198 games were played, where each team played exactly three games with all the o

ther teams. How many teams participated in this championship?
Mathematics
1 answer:
kifflom [539]3 years ago
6 0

Answer:

  12

Step-by-step explanation:

When n teams play each other once, the total number of games is n(n-1)/2. Since each team played every other one 3 times, the relationship between number of teams (n) and number of games is ...

  3(n(n-1)/2) = 198

  n(n-1) = 132 = 12·11 . . . . . . multiply by 2/3 and factor

  n = 12 . . . . . . n = -11 is also an extraneous solution to this quadratic equation

12 teams participated in this championship.

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3 years ago
1. answer the three questions below about the quadrilateral:
mars1129 [50]

Before we begin, note that we need to use the distanse formula for everything to reach our conclusion. With that being said, here we go:

\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = d

Using the ordered pairs \displaystyle [3, -3] and \displaystyle [4, -2] for instanse:

\displaystyle \sqrt{[-3 + 4]^2 + [3 - 2]^2} = \sqrt{1^2 + 1^2} = \sqrt{2}

Now, sinse the <em>distanse</em><em> </em>between \displaystyle [3, -3] and \displaystyle [4, -2] is \displaystyle \sqrt{2} units, then the distanse between \displaystyle [1, 1] and \displaystyle [0, 0] ALSO has to be \displaystyle \sqrt{2} units. By definition, lettre <em>c</em><em> </em>has already been answered for you because sinse it is a rectangle, if the two short sides are congruent, then the two long sides ALSO have to be congruent, but just in case you want to be sure [you do not trust your instincts], just simply re-use the distanse formula.

Using the ordered pairs \displaystyle [1, 1] and \displaystyle [4, -2] for instanse:

\displaystyle \sqrt{[-1 + 4]^2 + [-1 - 2]^2} = \sqrt{3^2 + [-3]^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}

So there you have it. The length of both of the long sides is \displaystyle 3\sqrt{2} units.

Now that we cleared all of that up, we can now find the perimetre and area of this rectangle:

\displaystyle 2w + 2l = P

\displaystyle 2[\sqrt{2}] + 2[3\sqrt{2}] = 2\sqrt{2} + 6\sqrt{2} = 8\sqrt{2}

The perimetre of this rectangle is \displaystyle 8\sqrt{2} <em>units</em>.

\displaystyle wl = A

\displaystyle [\sqrt{2}][3\sqrt{2}] = [3][2] = 6

The area of this rectangle is \displaystyle 6 <em>squared units</em>.

You have now found what you were looking for.

** All rectangles are parallelograms because they both have two pairs of parallel and congruent sides, while vice versa is falce because a parallelogram does not have <em>four congruent right angles</em>, so it is safe to say that this is both a rectangle AND parallelogram, sinse the picture displayed is a rectangle.

I am joyous to assist you at any time. ☺️

8 0
3 years ago
Read 2 more answers
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