The container will take 25 minutes to go from full to empty.
Explanation:
In 15 minutes, the container has lost 3 gallons of water (
5
−
2
=
3
).
Since the leak is at a constant rate, we can determine that every five minutes the container loses one gallon.
So for the container to lose the full 5 gallons will take 25 minutes (
5
×
5
=
25
)
<span>part A:
Let
t = total the liquid in the bottle including lemon juice and water
so t = lemon juice + water ( w = water, l = lemon juice) so t = l + w
but the bottle has 1 liter of water. and <span>60% lemon juice
</span>contains 60% lemon juice = 0.6, so l = 0.6t and w(water ) = 1 liter
t = l + w
substitute l = 0.6t and w = 1 into t = l + w
now you have equation
t = 0.6t + 1
part B:
from part A, you have equation t = 0.6t +1
solve for t
t = 0.6t +1
subtract 0.6t on both sides
t - 0.6t = 0.6t - 0.6t + 1
simplify
0.4t = 1
divide both sides by 0.4
0.4t/0.4 = 1/ 0.4
simplify
t = 2.5
2.5 liters is total including lemon juice and water
2.5 - 1(1 liter of water) = 1.5 <span>1 liter of lemon juice</span></span>
Call the two equations above A and B, in order to not confuse them.
A: -2x + 6y = -38
B: 3x - 4y = 32
For this system we have opposites in x and y, so Elimination (or Linear Combination) works best. Either variable works, so let's work with x first and multiply A by 3 and B by 2. This is done so we get opposites in A and B then when added together give zero.
-2x + 6y = -38 ------> multiply by 3 ----> -6x + 18y = -114
3x - 4y = 32 ------> multiply by 2 -----> 6x - 8y = 64
Now we add the new equations. The -6x and 6x are opposites and go away. We are left with
10y = -50. We divide both sides by 10 and get that y = -5.
Now we take y = -5 and put it into an original equation. Let's use A.
-2x + 6y = -38 the original equation A
-2x + 6(-5) = -38 we found y = -5
-2x + (-30) = -38 evaluating and multiplying
-2x - 30 = -38 apply the parentheses
-2x = -8 add 30 to both sides
x = 4 divide on both sides by -2
Thus x = 4 and y = -5, or (4, -5) is the solution.
Answer:
It was 26.5 degrees colder at midnight than at 2:00 pm
Step-by-step explanation:
We have that:
At 2:pm, it was 4 degrees.
The temperature dropped 2.5 degrees per hour until 9:00 pm.
From 2pm to 9pm, there are 7 hours. 2.5 per hour, it was 4 degrees at 2 pm.
So at 9 pm the temperature is:
4 - 2.5*7 = -13.5
The temperature dropped another 9 degrees by midnight.
At midnight, the temperature is -13.5 - 9 = -22.5 degrees
How much colder was it at midnight than at 2:00 pm?
2pm: 4 degrees
Midnight: -22.5 degrees
How much coldren
-22.5 - 4 = -26.5
It was 26.5 degrees colder at midnight than at 2:00 pm
Answer:
17
Step-by-step explanation:
2 sqrt(81) -1
We know the sqrt(81) = 9
2*9 -1
18-1
17
