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gizmo_the_mogwai [7]
3 years ago
6

HELP!!!!!

Mathematics
2 answers:
antoniya [11.8K]3 years ago
8 0

Answer: 82°

Step-by-step explanation:

<CDE = far arc - near arc / 2

i.e

<CDE = arcCBE - arcCE / 2

arcCE = 98°

arcCBE = 360° - 98° = 262°

<CDE = 262° - 98° / 2

<CDE = 164 / 2

<CDE = 82°

Therefore the measure of < CDE is 82°

Bumek [7]3 years ago
3 0

Answer:

82°

Step-by-step explanation:

whenever a line is tangent to a circle, the line segment you can draw from the center to the tangent line on the circumference is always perpendicular, so angle ACD is 90° and angle AED is 90° and we already know CAE is 98° so adding the tree would result in 278° because ACDE forms a quadrilateral it's angle have a sum of 360° so subtract 278 from 360 and you get 82°

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Varvara68 [4.7K]
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Aliun [14]
<h3>Answer:  28</h3>

==========================================================

Explanation:

Method 1

Imagine a table with 8 rows and 8 columns to represent all possible match-ups. You can actually draw out this table or just think of it as a thought experiment.

There are 8*8 = 64 entries in the table. Along the northwest diagonal, we have each team pair up with itself. This is of course silly and impossible. We cross off this entire diagonal so we drop to 64-8 = 56 entries.

Then notice that the lower left corner is a mirror copy of the upper right corner. A match-up like AB is the same as BA. So we must divide by 2 to get 56/2 = 28 different matches.

----------------------------------

Method 2

There are 8 selections for the first slot, and 8-1 = 7 selections for the second slot. We have 8*7 = 56 permutations and 56/2 = 28 combinations.

----------------------------------

Method 3

Use the nCr combination formula with n = 8 and r = 2

n C r = \frac{n!}{r!(n-r)!}\\\\8 C 2 = \frac{8!}{2!*(8-2)!}\\\\8 C 2 = \frac{8!}{2!*6!}\\\\8 C 2 = \frac{8*7*6!}{2!*6!}\\\\ 8 C 2 = \frac{8*7}{2!}\\\\ 8 C 2 = \frac{8*7}{2*1}\\\\ 8 C 2 = \frac{56}{2}\\\\ 8 C 2 = 28\\\\

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Notice how the (8*7)/2 expression is part of the steps shown above in the nCr formula.

7 0
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