Step-by-step explanation:
Standard form of a quadratic is f(x) = ax² + bx + c.
To convert to vertex form, the simplest method is to find the x-coordinate of the vertex using h = -b/(2a).
Then, plug back into the equation to find the y-coordinate of the vertex. k = f(h).
Finally, the leading coefficient is the same as the standard form, a.
f(x) = a(x − h)² + k
Another method is to complete the square.
1.
a.11/12=less than one
b. 77/72= greater than one
c.23/60= less than one
d. 31/56= less than one
2. <
B, because the mid segment is half the length of the third side
Answer:
g(-8) = -23
Step-by-step explanation:
g(x) = 3x + 1 <em>Plug in g(-8)</em>
g(-8) = 3(-8) + 1 <em>Multiply 3 by -8</em>
g(-8) = -24 + 1 <em>Add 1 to -24</em>
g(-8) = -23
<h3>
Answer: 31 games</h3>
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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
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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

which is equivalent to
