Answer:
Step-by-step explanation:
Because we have 3 unknowns, we need to come up with 3 equations. If the total number of animals is 440 and that number is made up of a combination of goats (g), ducks (d), and chickens (c) the first equation is
g + d + c = 440
The next equation is found in the fact that the number of ducks is one-quarter the number of chickens:
and solving for c gives us that
c = 4d
The last equation says that of the total number of animals, 440, half the goats and half the ducks got away, leaving only 320 animals behind. The last equation, the tricky one, is:
and simplifying that:
and because nobody hates fractions more than I do, I'm going to get rid of them by multiplying everything by 2 to get:
-g - d = -240
We've got these equations now, but what I'm going to do is to sub in what c equals (c = 4d) for c in the first equation:
g + d + 4d = 440 and
g + 5d = 440 and pair that with the one right above:
-g - 1d = -240 and use elimination to solve. The g's cancel each other out, leaving us with 4d = 200 and d = 50. So there were 50 ducks originally. Now we will sub that in to solve for c:
c = 4d so
c = 4(50) and
c = 200. Now we will sub both those values into the very first equation we put together to solve for g:
g + 200 + 50 = 440 and
g + 250 = 440 so
g = 190.
Add them all together just to be sure we have the 440 that we were told we had in the beginning (and we do, so we're all done!)
Answer:
Linear function
y = 2x - 1
Step-by-step explanation:
This is a linear function because the line is straight, having no curved.
The equation for a linear graph is y=mx + b.
x and y represent points on he graph.
"m" represents the slope of the graph. Reading from left to right, if a positive slope, then the graph continues upward. If negative, then it's a graph down downwards.
"b" represents the y-intercept, when the graph hits the y-axis. It's also the initial value.
In the photo, we can see the y-intercept is (0, -1).
Slope is calculated by rise over run. Choose two random points on the graph. Count the "rise", or how many vertical units are between the points. If the point on the right is lower than the point on the left, the rise is negative. Count the "run", which is the number of horizontal units between the points.
For the point (0, -1) and (3, 5).
m = rise/run
m = 6/3
m = 2
Substitute m=2 and b= -1 into the equation of a line.
y = 2x - 1
It depends on how you define natural numbers. There are two possible definitions.
1. All non-negative integers.
one-digit natural numbers: 0 - 9 for a total of 10
first 20 natural numbers: 0 - 19 for a total of 20
10/20 = 50%
2. All positive integers.
one-digit natural numbers: 1 - 9 for a total of 9
first 20 natural numbers: 1 - 20 for a total of 20
9/20 = 45%
If u make them common denominators, then the bag would be 6/8
the bag would last 6 days
Let
x------> <span>speed on the bicycle
y------> </span><span>speed walking
we know that
</span>x=6+y------> equation 1<span>
speed=distance /time-------> time=distance/speed
1/y=2.5/x-------> y=x/2.5------> x=2.5y-------> equation 2
equals 1 and 2
6+y=2.5y-----> 2.5y-y=6------> 1.5y=6-----> y=6/1.5-----> y=4 mi/h
x=6+y-----> x=6+4-----> x=10 mi/h
the answer is
the speed walking is 4 mi/h
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