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2 years ago

Write the equation of the line through the points (-6, -19) and (2, 5).

Mathematics

1 answer:

Lelechka [254]2 years ago

5 0

Answer:

y = 3x - 1

Step-by-step explanation:

The slope of a line passing through the two points

P = (x1. y1) and Q = (x2, y2) is given by

m= (y2-y1)/(x2-x1)

We have that x1= -6, y1= -19, x2= 2, y2= 5

m=3

Now, the y-intercept is b=y1 - mx1 (or b= y2 - mx2, the result is the same).

b= -19-(3)(-6)

b= -1

y = 3x - 1

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3 years ago

Can I have help on this please

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Angles C and D are supplementary, meaning they add up to 180 degrees. So, if we add 8u-48 to 5u+46, we get 13u-2. We set that equal to 180, so 13u-2=180. Add the two, so 13u=182. Divide the 13, so u=14. To double check, plug in 14 to both expressions. 8(14)-48 and 5(14)+46. 8(14)-48 is 64. 5(14)+46 is 116. If you add 64+116, you get 180, which proves your answer right! So u= 14

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3 years ago

If 32 teams participate in a standard single elimination tournament, how many games must be played to decide a champion?

SCORPION-xisa [38]

<h3>Answer: 31 games</h3>

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

Explanation:

32/2 = 16 games will happen in round 1. Afterward, 16 teams are left.
16/2 = 8 games will happen in round 2. Afterward, 8 teams are left.
8/2 = 4 games happen in round 3.
4/2 = 2 games in round 4.
2/2 = 1 game as the final championship.

Count the number of times you divide by two and we have five occurrences of this. So there five rounds overall.

To get the total number of games played, we add up the quotients

16+8+4+2+1 = 31

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

Or as a shortcut we can simply subtract off 1 since 1+2+4+...+2^n = 2^(n+1)-1

We can write that rule as

$\displaystyle \sum_{k=1}^{n}2^k = 2^{n+1}-1$

which is equivalent to

$\displaystyle \sum_{k=1}^{n}2^{k-1} = 2^n-1$

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3 years ago