Answer:
![l=31+20(y-2007)](https://tex.z-dn.net/?f=l%3D31%2B20%28y-2007%29)
where
is the number of laptops, and
is the year.
in 2017: ![l=231](https://tex.z-dn.net/?f=l%3D231)
Step-by-step explanation:
I will define the variable
as the number of years that passed since 2007.
Since the school buys 20 lapts each year, after a number
of years, the school will have
more laptops.
and thus, since the school starts with 31 laptops, the equation to model this situation is
![l=31+20*x](https://tex.z-dn.net/?f=l%3D31%2B20%2Ax)
where
is the number of laptops.
since x is the number of years that have passed since 2007, it can be represented like this:
![x=y-2007](https://tex.z-dn.net/?f=x%3Dy-2007)
where
can be any year, so the equation to model the situation using the year:
![l=31+20(y-2007)](https://tex.z-dn.net/?f=l%3D31%2B20%28y-2007%29)
and this way we can find the number of laptos at the end of 2017:
![y=2017](https://tex.z-dn.net/?f=y%3D2017)
and
![l=31+20(y-2007)](https://tex.z-dn.net/?f=l%3D31%2B20%28y-2007%29)
![l=31+20(2017-2007)\\l=31+20(10)\\l=31+200\\l=231](https://tex.z-dn.net/?f=l%3D31%2B20%282017-2007%29%5C%5Cl%3D31%2B20%2810%29%5C%5Cl%3D31%2B200%5C%5Cl%3D231)
17,19,23 are the prime numbers
<h2>
Explanation:</h2><h2 />
The complete question is shown in the figure below. As you can see one square units is well shown in the graph. So we can conclude that the distance between two consecutive points is 1 unit. If so, then we can calculate the area of the parallelogram as follows:
![A=b\times h \\ \\ A:Area \\ \\ b:Base \\ \\ h:Height \\ \\ \\ CB=b \\ \\ AB=h](https://tex.z-dn.net/?f=A%3Db%5Ctimes%20h%20%5C%5C%20%5C%5C%20A%3AArea%20%5C%5C%20%5C%5C%20b%3ABase%20%5C%5C%20%5C%5C%20h%3AHeight%20%5C%5C%20%5C%5C%20%5C%5C%20CB%3Db%20%5C%5C%20%5C%5C%20AB%3Dh)
Then, finding CB by Pythagorean Theorem:
![CB=\sqrt{6^2+4^2} \\ \\ CB=2\sqrt{13}](https://tex.z-dn.net/?f=CB%3D%5Csqrt%7B6%5E2%2B4%5E2%7D%20%5C%5C%20%5C%5C%20CB%3D2%5Csqrt%7B13%7D)
And:
![AB=4](https://tex.z-dn.net/?f=AB%3D4)
Therefore:
![A=(2\sqrt{13})(4) \\ \\ \boxed{A=8\sqrt{13} \ units^2}](https://tex.z-dn.net/?f=A%3D%282%5Csqrt%7B13%7D%29%284%29%20%5C%5C%20%5C%5C%20%5Cboxed%7BA%3D8%5Csqrt%7B13%7D%20%5C%20units%5E2%7D)
In this question, the volume of the cone is needed. The equation used to determine the volume of the cone is (1/3)π(r²)h
To solve for the volume,
V = (1/3)π(3²)(10)
= (1/3)(9)(10)π
= (3)(10)π
= 30π cm³
The correct answer is the first option which is 30π cm³.