The fraction of the amount Liang has left is
To derive L (amount of money Liang will have left), add X (amount spent on a pen) and Y (amount spent on books) together, then the derived value be subtracted from M (fraction of total amount Liang has got) i.e.: M – (X + Y)
Therefore, L = M – (X + Y)
Deriving (X + Y)
= X + Y
= +
= (1 x 7) + (3 x 4) / 21
= (7) + (12) / 21
= 7 + 12 / 21
=
X + Y =
Since the lowest common denominator of the fraction of X and Y = 21, then the fraction of M =
Thus, M =
Recall, L = M – (X + Y)
Thus,
L = –
L = (1 x 21) – (1 x 19) / 21
L = (21) – (19) /21
L = 21 – 19 /21
L =
Hence, the amount Liang will have left is
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now, this parabolic graph, has two zeros/solutions/x-intercepts, at -9 and 21.
for a quadratic equation, the vertex will be right in between the x-intercepts, namely in this case between -9 and 21, right in the middle, namely at 6, and is where the axis of symmetry is at, x = 6.