Answer:
23.2/20
Step-by-step explanation:
Answers:
- Total equation: x+y = 80
- Legs equation: 2x+4y = 248
- How many ducks? 36
- How many cows? 44
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Further explanation:
- x = number of ducks
- y = number of cows
x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.
That equation can be solved to y = 80-x after subtracting x from both sides.
The legs equation is 2x+4y = 248 because...
- 2x = number of legs from all the ducks only
- 4y = number of legs from all the cows only
- 2x+4y = total number of legs from both types of animals combined
We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248
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Let's plug y = 80-x into the second equation and solve for x.
2x+4y = 248
2x+4( y ) = 248
2x+4( 80-x ) = 248
2x+320-4x = 248
-2x+320 = 248
-2x = 248-320
-2x = -72
x = -72/(-2)
x = 36
There are 36 ducks
Now use this x value to find y
y = 80-x
y = 80-36
y = 44
There are 44 cows.
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Check:
36 ducks + 44 cows = 80 animals total
36*2 + 44*4 = 72 + 176 = 248 legs total
The answers are confirmed.
Answer:
24xz + 28yz
Step-by-step explanation:
4z(6x + 7y) ← multiply each term in the parenthesis by 4z
= 24xz + 28yz
Answer:
6 (19 x - 2)
Step-by-step explanation:
Simplify the following:
6 - 3 (4 - 3 x) - 3 x - 6×9 x + 18×9 x - 6
-6×9 = -54:
6 - 3 (4 - 3 x) - 3 x + -54 x + 18×9 x - 6
18×9 = 162:
6 - 3 (4 - 3 x) - 3 x - 54 x + 162 x - 6
Grouping like terms, 6 - 3 (4 - 3 x) - 3 x - 54 x + 162 x - 6 = (-3 x - 54 x + 162 x) - 3 (4 - 3 x) + (6 - 6):
(-3 x - 54 x + 162 x) - 3 (4 - 3 x) + (6 - 6)
-3 x - 54 x + 162 x = 105 x:
105 x - 3 (4 - 3 x) + (6 - 6)
6 - 6 = 0:
105 x - 3 (4 - 3 x)
-3 (4 - 3 x) = 9 x - 12:
9 x - 12 + 105 x
Grouping like terms, 105 x + 9 x - 12 = (105 x + 9 x) - 12:
(105 x + 9 x) - 12
105 x + 9 x = 114 x:
114 x - 12
Factor 6 out of 114 x - 12:
Answer: 6 (19 x - 2)
