Answer:
Shown
Step-by-step explanation:
Given that twelve basketball players, whose uniforms are numbered 1 through 12, stand around the center ring on the court in an arbitrary arrangement.
Let us consider consecutive numbers in this set.
After this we find the totals are more than 20.
When 1 to 12 are arbitrarily arranged, there are chances that numbers from 6 and above are having consecutive numbers.
These totals are greater than 20
Hence shown that some three consecutive players have the sum of their numbers at least 20.
(i.e. starting from if we take)
Let the two integers be x and x+1
(x+1)^2-x^2=21
x^2+2x+1-x^2=21
2x+1=21
2x=20
x=10
then x=10, x+1
10+1=11
the two integers are 10, 11
Answer:
y = -4/3x - 3
Step-by-step explanation:
I'll do the first one to get you started
The equation y = x^2+16x+64 is the same as y = 1x^2+16x+64
Compare that to y = ax^2+bx+c and we see that
a = 1
b = 16
c = 64
Use the values of 'a' and b to get the value of h as shown below
h = -b/(2a)
h = -16/(2*1)
h = -8
This is the x coordinate of the vertex.
Plug this x value into the original equation to find the corresponding y value of the vertex.
y = x^2+16x+64
y = (-8)^2 + 16(-8) + 64
y = 0
Since the y coordinate of the vertex is 0, this means k = 0.
The vertex is (h,k) = (-8, 0)
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So we found that a = 1, h = -8 and k = 0
Therefore,
f(x) = a(x-h)^2 + k
f(x) = 1(x-(-8))^2 + 0
f(x) = (x+8)^2
is the vertex form
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<h3>Final answer to problem 1 is f(x) = (x+8)^2 </h3>
