a specific geographic area with a certain climate where certain types of organisms live
a. keystone species
e. ecosystem
f. biome
g. ecosystem services
f. biome
Solve the system of equations.
y = –3x + 4
x + 4y = –6
Substitute -3x + 4 for y in the second equation:
x + 4(-3x + 4) = -6
x - 12x + 16 = -6
-11x = -22
x = 2
Now substitute x = 2 in the first equation:
y = -3(2) + 4
y = -2
Therefore, the solution to the system of equations is x = 2 and y = -2, written as an ordered pair (2,-2).
John can mow his lawn in 3 hours and his sister, Julie, can mow it in 2 hours. How long will it take them to mow their lawn if they work together?
Let's use the formula:
1/time taken = work rate
If John can mow the lawn in 3 hours, his work rate is:
1/3
Similarly, Julie's work rate is:
1/2
To find out how long it would take them to mow the lawn working together, we need to add their work rates:
1/3 + 1/2 = 2/6 + 3/6 = 5/6
So, their combined work rate is 5/6. Now we can use the same formula to find the time it would take them to mow the lawn together:
1/time taken = 5/6
time taken = 6/5
time taken = 1.2 hours, or 1 hour and 12 minutes (rounded to the nearest minute).
Therefore, it would take John and Julie 1 hour and 12 minutes to mow their lawn together.
Are you able to explain this in more simple terms?
Sure, let me explain it in simpler terms.
John can mow the lawn in 3 hours, which means if he works for 1 hour, he mows 1/3 of the lawn.
Similarly, Julie can mow the lawn in 2 hours, which means if she works for 1 hour, she mows 1/2 of the lawn.
Now, when they work together, they will mow the lawn faster because they can mow more of it in the same amount of time. When they work together for 1 hour, John will mow 1/3 of the lawn and Julie will mow 1/2 of the lawn. So, the total amount mowed in 1 hour will be:
1/3 + 1/2 = 5/6
This means that every hour, together, they can mow 5/6 of the lawn. To figure out how long it will take them to mow the entire lawn, we simply need to divide the total amount of lawn by the amount they can mow in one hour:
1 / (5/6) = 6/5
So it will take them 6/5 hours to mow the entire lawn together. That's equivalent to 1 hour and 12 minutes, to be more exact.