Given that f(x) =3x^2 - 6x + 11 ,find the values of a,b and c for which f(x) = a(x - b)^2 + c

1 answer:

3 0

First you have to complete the square. The first step would be 3x^2-6x=-11. Then you divide -6 by 2 and square the number you get. 3x^2-6x+9=-11+9. 3x^2-6x+9=-2. Factor out the three to get 3(x^2-2x+3)=-2. You can't factor what is in the parenthesis. You should then add two to each side. 3(x^2-2x+3)+2.A = 3B= I don't knowC = 2

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3 years ago

One member of the debate team is going to be chosen president. each member is equally likely to be chosen. the probability that

inessss [21]

Let
x-------> the probability that a boy is chosen
B------> number of boys in the debate team
G------> number of girls in the debate team

we know that
B+G=20-----> G=20-B-----> equation 1
probability that a boy is chosen=number of boys in the debate team/total of people
so
x=B/20-------> equation 2

the probability that a girl is chosen is 2/3 the probability that a boy is chosen
probability that a girl is chosen=(2/3)*x
probability that a girl is chosen=G/20
(2/3)*x=G/20-----> equation 3
substitute equation 1 in equation 3
(2/3)*x=[20-B]/20----> equation 4

resolve the equations system
x=B/20
(2/3)*x=[20-B]/20

using a graph tool
see the attached figure
the solution is
x=0.6
B=12
G=20-12-----> G=8

number of boys in the debate team is 12
number of girls in the debate team is 8
the probability that a boy is chosen is 0.6 ----> 60%
the probability that a girl is chosen is 0.6*(2/3)----> 0.4---> 40%

the answer is
number of girls in the debate team is 8