Answers:
- Total equation: x+y = 80
- Legs equation: 2x+4y = 248
- How many ducks? 36
- How many cows? 44
====================================================
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
------------
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.
------------
Check:
36 ducks + 44 cows = 80 animals total
36*2 + 44*4 = 72 + 176 = 248 legs total
The answers are confirmed.
9 sheets of paper I believe
Have a good day :)
Answer:
bacteria
Step-by-step explanation:
The generic form of an exponential function is: 
, where a is the initial amount, r is the rate, and n is the time.
In this case, the initial amount is 1000, so a = 1000. Also, the rate is 2 because the culture doubles in size every 5 minutes. However, our n is not just n; it's actually n/5 because the rate is doubling per 5 minutes, not per 1 minute. If it was per 1 minute, then the time would simply be n. Unfortunately, that's not the case here, so the exponent of r should be n/5, where n is the number of minutes that have passed.
Now, we have: 
Since n is the number of minutes, we need to convert 2 hours to minutes:
2 hours * 60 min/hour = 120 minutes.
Thus, the answer is bacteria.
Hope this helps!
The key word here is *square* in "square flower garden".
So we need to find the area of the flower garden, and subtract it from the overall area of the yard. The remainder will be how much grass covers the yard.
Area of the Square flower garden:
7.5 * 7.5 = 56.25
Area of the Entire yard:
25 * 18 = 450
450 - 56.25 = 393.75 square feet of grass
Answer:
zero slope
y-intercept at y = -4
Step-by-step explanation:
-4y = 16 (divide both sides by -4)
y = 16 / (-4)
y = -4
y = -4 represents a horizontal line that is parallel to the x-axis that crosses the y-axis at y = -4
hence the slope of a horizontal line is zero, and the y-intercept is -4
