The University of Sydney
Faculty of Economics and Business  
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Algebraic Manipulation - Quiz 1   Last unanswered question  Question  Next unanswered question

Question 1 lion

Which of the following correctly makes y  the subject of  3x + 2y = 7?
a)        3
y = 7- 2x .    b) y = 7--3x-.
      2
c)        3
y = 7 +-x.
       2    d)     7+ 3x
y = --2---.

 

Not correct. Choice (a) is false.
Try again, you haven’t performed the operations in the right order.
Your answer is correct.
If   3x+ 2y = 7  then 2y = 7- 3x
and     7- 3x
y = ------.
      2
Not correct. Choice (c) is false.
Try again, you haven’t performed the operations in the right order, watch the signs.
Not correct. Choice (d) is false.
Try again, watch the signs.
Question 2 lion

Which of the following factorizes the expression     2
3x y+ 2xy + 5x+ 4y+ 4    correctly?
a) xy(3x +2) +4(y + 1) + 5x .
b) x(3xy+ 5)+ 2y(x+ 2)+ 4 .
c)     2
y(3x + 2x + 4)+ 5x+ 4.
d) All of the above.

 

Not correct. Choice (a) is false.
Try again, have you looked at all of the possibilities.
Not correct. Choice (b) is false.
Try again, have you looked at all of the possibilities.
Not correct. Choice (c) is false.
Try again, have you looked at all of the possibilities.
Your answer is correct.
They all correctly factorize the expression.
xy(3x+ 2)+ 4(y+ 1)+ 5x  =3x2y + 2xy+ 4y +4 + 5x
and x(3xy+ 5)+ 2y(x+ 2)+ 4  =3x2y + 5x+ 2xy + 4y + 4
and y(3x2 +2x + 4)+ 5x+ 4  =3x2y + 2xy+ 4y +5x + 4.
Question 3 lion

Which of the following makes y  the subject of   ad+ c+ aex - bx- afy - y = 0?
a) y = ad+ c+ aex - bx - afy.
b)     ad+ c+ aex - bx
y = ----af-+-1-----.
c)     ad-+c-+-aex---bx--y-
y =         af         .
d) None of the above.

 

Not correct. Choice (a) is false.
Try again, you don’t have all of the terms involving y  on the left hand side.
Your answer is correct.
First collect all terms involving y  and add to both sides to give
afy+ y = y(af + 1) = ad + c+ aex- bx.
Then divide both sides by af + 1  to give
    ad+-c-+aex---bx
y =      af + 1    .
Not correct. Choice (c) is false.
Try again, you don’t have all of the terms involving y  on the left hand side.
Not correct. Choice (d) is false.
Try again, there is a correct answer.
Question 4 lion

Which of the following correctly represents x  if   x- μ
-----= z?
 σ
a)     z - μ
x = -----.
      σ    b) x = (z + μ)σ.
c) x = μ + zσ.    d) x = μ- zσ .

 

Not correct. Choice (a) is false.
Try again, you can’t just swap x  and z.
Not correct. Choice (b) is false.
Try again, you must multiply both sides by σ  first.
Your answer is correct.
If     x--μ-
z =   σ    then   zσ = x- μ    and   μ+ zσ = x.
Not correct. Choice (d) is false.
Try again, looking carefully at the signs.
Question 5 lion

Which of the following makes n  the subject of the formula        ∘ ---
       σ2-
e = z  n ?
a)     (zσ )2
n =  -e-  .    b)     (z σ2)
n =   -e-  .
c)    ( e )2
n =  ---  .
     zσ    d)      ∘ σ2-
n = z  ---.
        e

 

Your answer is correct.
If       ∘ ---
       σ2
e = z  n--    then   2    2σ2
e  = z n--    and       2σ2
n = z e2-.
Hence      (zσ )2
n =  -e-  .
Not correct. Choice (b) is false.
Try again, you haven’t dealt with the square root sign.
Not correct. Choice (c) is false.
Try again, you have found  1
--.
n
Not correct. Choice (d) is false.
Try again, you can’t just swap n  and e .