Answer:
We have the system:
y > 2*x
y > 3
Now, let's find the limits:
taking y > 3, we can see the limit y = 3.
Now we replace it in the first inequality:
3 > 2*x
3/2 > x.
Then we have that:
y > 3
x < 3/2
Those two inequalities define our system.
So any ordered pair where x is smaller than 3/2 and y is larger than 3, is a solution.
or example:
(1, 3.5) is a solution.
Answer: 133.69 or 133.7
Step-by-step explanation:
The enclosed shape is that of a trapezoid. The area of a trapezoid is the product of the height of it (measured perpendicular to the parallel bases) and the average length of the two parallel bases. The formula is generally written ...
... A = (1/2)(b₁ + b₂)·h
Here, the base lengths are the y-coordinates at x=4 and x=9. The height is the distance between those two x-coordinates: 9 - 4 = 5.
You are expected to find the y-values at those two points, then use the formula for the area of the trapezoid.
You can save a little work if you realize that the average of the two base lengths is the y-coordinate corresponding to the average x-coordinate: (9+4)/2 = 6.5. That is you only need to find the y-coordinate for x=6.5 and do the area math as though you had a rectangle of that height and width 5.
Going that route, we have
... y = 2(6.5) - 1 = 13 - 1 = 12
Then the trapezoid's area is
... A = 12·5 = 60 . . . . square units.
Answer:
![\boxed {\tt 20 \ meters}](https://tex.z-dn.net/?f=%5Cboxed%20%7B%5Ctt%2020%20%5C%20meters%7D)
Step-by-step explanation:
The perimeter of a rectangle can be found using the following formula.
![p= 2l+2w](https://tex.z-dn.net/?f=p%3D%202l%2B2w)
We know the perimeter is 60 meters and the length is 10 meters.
![p=60 \ m](https://tex.z-dn.net/?f=p%3D60%20%5C%20m)
![l= 10 \ m](https://tex.z-dn.net/?f=l%3D%2010%20%5C%20m)
Substitute the values into the formula.
![60 \ m = 2(10 \ m) + 2w](https://tex.z-dn.net/?f=60%20%5C%20m%20%3D%202%2810%20%5C%20m%29%20%2B%202w)
Multiply 2 and 10.
![60 \ m = 20 \ m +2w](https://tex.z-dn.net/?f=60%20%5C%20m%20%3D%2020%20%5C%20m%20%2B2w)
Subtract 20 from both sides of the equation.
![60 \ m - 20 \ m = 20 \ m - 20 \ m +2w](https://tex.z-dn.net/?f=60%20%5C%20m%20-%2020%20%5C%20m%20%3D%2020%20%5C%20m%20-%2020%20%5C%20m%20%2B2w)
![60 \ m - 20 \ m =2w](https://tex.z-dn.net/?f=60%20%5C%20m%20-%2020%20%5C%20m%20%3D2w)
![40 \ m = 2w](https://tex.z-dn.net/?f=40%20%5C%20m%20%3D%202w)
Divide both sides of the equation by 2.
![\frac{40 \ m}{2} =\frac{2w}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B40%20%5C%20m%7D%7B2%7D%20%3D%5Cfrac%7B2w%7D%7B2%7D)
![\frac{40 \ m}{2} =w](https://tex.z-dn.net/?f=%5Cfrac%7B40%20%5C%20m%7D%7B2%7D%20%3Dw)
![20 \ m =w](https://tex.z-dn.net/?f=20%20%5C%20m%20%3Dw)
The width of the rectangle is 20 meters.
The discount offered on each backpack reduces the mean, median and mode.
<h3>What is the mean, median and mode?</h3>
The mean, median and mode are measures of central tendency. The means is the average of a set of numbers. The median is the number that is in the center of a set of numbers. The mode is the number that occurs most frequently of a set of numbers.
When the discount is applied, the prices of the backpacks become smaller. As a result, the mean, median and mode reduce also.
For example, assume that there are 3 backpacks with the following prices $12, $30 and $30. The mean is 24. The median is $30. The mode is $30. After the discount, the prices become $6, $24 and $24. The mean is 18. The median is $24. The mode is $24.
To learn more about mean, please check: brainly.com/question/25842202