Answer:
(x, y) = (2, 1)
Step-by-step explanation:
Adding the two equations gives ...
2y = 2
y = 1 . . . . . divide by 2
Subtracting the second equation from the first gives ...
0 = 6x -12
0 = x -2 . . . . divide by 6
2 = x
The solution is (x, y) = (2, 1).
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The attached graph verifies this solution.
Answer: pi (4) squared (12)
Step-by-step explanation: Because like you said pi r squared h
Answer: Choice B) The expression (10-2x)(30-2x)x represents the volume of the box
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The original width is 10 inches. The width reduces to 10-2x inches after we cut off the top two corners of the rectangle. We can think of it as taking 10 and subtracting off two copies of x like so: 10-x-x = 10-2x
Similarly, the length goes from 30 inches to 30-2x inches. This time we're taking off the top and bottom corners (focus on either side it doesn't matter).
The height of the box is x inches due to this portion being folded up.
Volume of box = (width)*(length)*(height)
Volume of box = (10-2x)(30-2x)x
Note: the units for the answer are in cubic inches which can be written as "in^3" (inches cubed).
Step-by-step explanation:
A. D(t) = -25t + 160
this is the correct answer because if you substitute 3 you get 85
Answer:
It takes 20 weeks to empty the lake
Step-by-step explanation:
Some rate, let's call it 
empties the lake in 10 weeks and a river (with rate 
can fill the lake in 20 weeks. The idea behind the solution of this type of problem is always set the rate to the same units. Let's see this:
which implies that this rate empties 0.1 of the lake per week, thus, 
.
Using the same idea, we can obtain that the filling rate of the river is:
Since both rates are acting at the same time, the total rate of flowing water (either in or out the lake) would be given by:
, which means that the lake is being empty at a rate of -0.05 week and using the rule of three:
Thus, It takes 20 weeks to empty the lake.
