Find X and Y and show please show calculations
1 answer:
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Answer:
x cannot be 5 or -3.
Step-by-step explanation:
The restrictions for a fraction is that the bottom cannot be 0.
So if we find when the bottom is 0 we have found the values that x cannot be.
Let's solve x^2-2x-15=0.
Since the coefficient of x^2 is 1 all we have to do is find two numbers whose product is -15 and whose sum is -2.
Those numbers are -5 and 3 since (-5)(3)=-15 and (-5)+(3)=-2.
So the factored form of the equation is:
(x-5)(x+3)=0
This means either x-5=0 or x+3=0.
We do have to solve both.
x-5=0 can be solved by adding 5 on both sides.
x-5+5=0+5
x+0=0+5
x=5
x+3=0 can be solved by subtracting 3 on both sides.
x+3-3=0-3
x+0=0-3
x=-3
So x can be any number except x=5 or x=-3.
We already factored the bottom as (x-5)(x+3).
The top is a difference of squares, x^2-a^2,
which can be factored as (x-a)(x+a).
So the top factors as (x-5)(x+5).
The fraction can then be written as:
This can further simplified assuming x is not 5 we can write it as . I canceled the common factor of (x-5).
Let
x-------> <span>the probability that a boy is chosen
B------> </span>number of boys in the debate team
G------> number of girls in the debate team<span>
we know that
B+G=20-----> G=20-B-----> equation 1
</span>probability that a boy is chosen=number of boys in the debate team/total of people
so
x=B/20-------> equation 2
t<span>he probability that a girl is chosen is 2/3 the probability that a boy is chosen
</span>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
x-------> <span>the probability that a boy is chosen
B------> </span>number of boys in the debate team
G------> number of girls in the debate team<span>
we know that
B+G=20-----> G=20-B-----> equation 1
</span>probability that a boy is chosen=number of boys in the debate team/total of people
so
x=B/20-------> equation 2
t<span>he probability that a girl is chosen is 2/3 the probability that a boy is chosen
</span>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