1a) x = 5, y = 2
b) x = 2, y = -1
2a) x = 2, y = 1
b) x = -0.3, y = 2.4
3 don’t know sorry
4a) x = -7, y = 3
b) x = -3.2, y = -23.8
How many of each animal do you have
By the polynomial remainder theorem,
will be a factor of
if the remainder upon division is 0, and this remainder is given by
:
Since
, it follows that
. But notice that if
, then we have
and since
, the equation above requires that either
or
, which is impossible. So
.
So we have 8 cases to check:
(1) Notice that if
, we have
. This is only possible for
.
(2) If
, then
, and so we can have
.
(3) If
, then
, and so
.
(4) If
, then
.
(5) If
, then
.
(6) If
, then
.
(7) If
, then
.
(8) If
, then
.
At the same time, we have 8 cases to consider to find how many options there are for
.
(1)
. We have only one choice of
.
(2)
. This is the same as when
, which we found to be 2 choices.
(3) Same as
; 3 choices.
(4) Same as
; 4 choices.
(5) 5.
(6) 4.
(7) 3.
(8) 2.
In total, there are
ways to choose
such that
is a factor of
, so the answer is B.
Note the symmetry of the sum above. You can easily give a slightly briefer combinatorial argument for this answer, but I figured a more brute-force approach would be easier to follow.
Answer:
y = - 2x - 7
Step-by-step explanation: