FIND THE MEAN: GRADES GIVEN 81, 70, 65, 89,70
2 answers:
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We are asked to describe the variation 
,
that is
for x≠0, in which case x=y=0, we distinguish the following intervals:
I = (-infinity, -1]
II = (-1, 0)
III = (0, 1)
III = [1, infinity)
Case I, consider the cases (examples) x= -5, and x= -6
, so we can conclude that the greater the x, the smaller the y.
Case II, consider x= -1/2 < x=-1/3
thus, the greater the x, the smaller the y.
Case III, consider the cases (examples) x= 5, and x= 6
, so we can conclude that the greater the x, the greater the y.
Case III, consider x= 1/3 < x=1/2
thus, the greater the x, the greater the y.
Conclusion:
y=0 only if x is 0. Otherwise y>0 always:
for x<0, x and y are inversely proportional
for x>0, x and y are directly proportional.
Remark, an other possible consideration in cases could be x<0 and x>0 only.
Remark, another approach is considering the graph of y=5x^2, which is a parabola, with the vertex at (0, 0) opening upwards.
From the graph we can find the same conclusion. That is we can see that the farer we get away from the y-axis, in both direction, the larger the values of y become.
that is
for x≠0, in which case x=y=0, we distinguish the following intervals:
I = (-infinity, -1]
II = (-1, 0)
III = (0, 1)
III = [1, infinity)
Case I, consider the cases (examples) x= -5, and x= -6
Case II, consider x= -1/2 < x=-1/3
thus, the greater the x, the smaller the y.
Case III, consider the cases (examples) x= 5, and x= 6
Case III, consider x= 1/3 < x=1/2
thus, the greater the x, the greater the y.
Conclusion:
y=0 only if x is 0. Otherwise y>0 always:
for x<0, x and y are inversely proportional
for x>0, x and y are directly proportional.
Remark, an other possible consideration in cases could be x<0 and x>0 only.
Remark, another approach is considering the graph of y=5x^2, which is a parabola, with the vertex at (0, 0) opening upwards.
From the graph we can find the same conclusion. That is we can see that the farer we get away from the y-axis, in both direction, the larger the values of y become.
1:
notice that each part is divisible by 3
÷ 3 =
9n ÷ 3 = 3n
6 ÷ 3 = 2
so it becomes
3n can be rewritten as 2n+n
-you want to rewrite it into two numbers that multiply to the number that's alone (in this case 2)
which would get you
Now that it's rewritten, you can factor out n + 2 from the equation.
<u><em>the answer is </em></u>
3(n+2)(n+1)
And you can check that by multiplying (n+2)(n+1) which is and then each of those by 3, which is
or
, our origional equation
2:
So I rewrote this as (it's the same thing, just reordered using the commutative property)
now -11x can be rewritten as -4x-7x
(remember, the two numbers should multiply to equal 28, which is our constant.)
now we can factor out x from the first expression and -7 from the second
and lastly you factor out x-4,
<u><em>which would give you</em></u>
(x-4)(x-7)
Make sure to check your work and make sure it multiplies to
3:
The first thing I notice when looking at this problem is that both 9 and 4 are perfect squares. Not only that, but they are the squares of 2 and 3, which are products of -12
So if you rewrite 9 as and 4 as
, the equation becomes
now that is ugly so it can be turned into
and -12x can be rewritten as
so our equation now looks like
There's a rule that says
In our case, a=3x and b=2
<u><em>so the final answer is</em></u>