Triangle ABC has been rotated 90° to create triangle DEF. Using the image below, prove that lines BC and EF have the opposite an
d reciprocal slopes. You must show all of your work to receive credit.
1 answer:
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Answer:
13 sheep, 19 chicken
Step-by-step explanation:
You can start to solve this problem by assigning variables. First, let's assign the number of sheep there are as and the number of chickens there are as
.
Because each sheep has 4 legs, the number of legs for each sheep would be . Similarly, because each chicken has 2 legs, the number of legs for each chicken would be
. Each animal would have 1 head, so the number of heads would just be
and
. Because the number of legs in total are 90,
. Because the number of heads in total are 32,
There is now a system of equations with two unknown variables and two equations. There are many ways to solve this, but for me, the easiest would be elimination. First, I would double the second equation, . Then, I would subtract that from the first equation, eliminating
.
. Solving for x gives 13. We can then plug that value into the second equation, making y be
. This means that
and
, meaning that there are 13 sheep and 19 chicken.