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.
You can use the sum and difference identities which for cosine is cos(a+b)= cosacosb-sinasinb
Answer:
490/10=49
Every 10 numbers is one number. I divided by 490 because it says less then 500
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
2/5 + 3/4 = [2(4) + 3(5)]/20
= 23/20 = 1 3/20
1 3/20 = 1 9/60
1 1/6 = 1 10/60
1 1/6 > 1 3/20
First, change this equation to y-intercept form:
-4x+7=2y-3
2y = -4x+10
y= -2x + 5
The slope is -2, which is the coefficient for x in y-intercept form.
