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 tell that a line is parallel if the lines can go on forever without crossing or intersecting. A line is perpendicular when the lines intersect at a right angle. If the slopes are either equal or negative reciprocals, they cannot be parallel or perpendicular.
Hope this helps you!
Answer:
y = -x + 4
Step-by-step explanation:
(-1,5)...x1 = -1 and y1 = 5
(1,3)....x2 = 1 and y2 = 3
slope(m) = (y2 - y1) / (x2 - x1) = (3 - 5) / (1 - (-1) = -2 / (1 + 1) = -2/2 = -1
y = mx + b
slope(m) = -1
u can use either of ur points...I will use (1,3)...x = 1 and y = 3
now we sub and find b, the y int
3 = -1(1) + b
3 = -1 + b
3 + 1 = b
4 = b
ur equation is : y = -x + 4 <===
Hello there
Actually, the correct answer is the 9
the first 0 is in the tenths spot, the 3 is in the hundredths, the second zero is in the thousandths, and the 9 is in the ten thousandths, while the 8 is in the hundred thousandths.
Therefore, the 9 is in the ten thousandths place
I hope this helped ^^
Answer:
There are 3 possible answers because you didn't state which value was base or height.
Going off the assumption that the base is 15 cm and the height is 8 cm, the area is 60 cm. (same answer if base is 8 cm and height is 15 cm)
A = 1/2(b*h)
A = 1/2(15*8)
A = 1/2(120)
A = 60
Going off the assumption that the base is 17 cm and the height is 8 cm, the area is 68 cm. (same answer if base is 8 cm and height is 17 cm)
A = 1/2(b*h)
A = 1/2(17*8)
A = 1/2(136)
A = 68
Going off the assumption that the base is 15 cm and the height is 17 cm, the area is 127.5 cm. (same answer if base is 17 cm and the height is 15 cm)
A = 1/2(b*h)
A = 1/2(15*17)
A = 1/2(255)
A = 127.5
