Answer:
There are 81 band members. :-)
Step-by-step explanation:
4 rows of 20 = 80 ... with one left over = 80 + 1 (81)
6 rows of 13 = 78 ... with three left over = 78 + 3 (81)
7 rows of 11 = 77 ... with four left over = 77 + 4 (81)
Answer:
Part 1:
Part 2: 10.5 Units
Step-by-step explanation:
We can find perimeter of a rectangle using formula
. We are given
, which is 6.5. Put this into the equation.
![2l+2(6.5)=342l+13=34\\2l=21\\l=10.5](https://tex.z-dn.net/?f=2l%2B2%286.5%29%3D342l%2B13%3D34%5C%5C2l%3D21%5C%5Cl%3D10.5)
So, length(l) of the rectangle is 10.5 units.
Answer: ![3x^2 + 2x -3](https://tex.z-dn.net/?f=3x%5E2%20%2B%202x%20-3)
Step-by-step explanation:
Remove parentheses.
![3x^2 -2x + 4x -3](https://tex.z-dn.net/?f=3x%5E2%20-2x%20%2B%204x%20-3)
Collect like terms.
![3x^2 + (-2x + 4x ) -3](https://tex.z-dn.net/?f=3x%5E2%20%2B%20%28-2x%20%2B%204x%20%29%20-3)
Simplify.
![3x^2 + 2x -3](https://tex.z-dn.net/?f=3x%5E2%20%2B%202x%20-3)
Let us denote the smaller even integer by
![N](https://tex.z-dn.net/?f=N)
.
Then, the next even integer must be
![N+2](https://tex.z-dn.net/?f=N%2B2)
.
To verify, set
![N](https://tex.z-dn.net/?f=N)
as any even number, say
![174](https://tex.z-dn.net/?f=174)
.
Then, the next even integer must be 2 more than this number, i.e.
![174+2=176](https://tex.z-dn.net/?f=174%2B2%3D176)
.
The sum of these two consecutive even integers can be expressed as:
![N+(N+2)=2N+2](https://tex.z-dn.net/?f=N%2B%28N%2B2%29%3D2N%2B2)
We are told that this sum divided by four is 189.5, i.e.
![(2N+2)\div4=189.5](https://tex.z-dn.net/?f=%282N%2B2%29%5Cdiv4%3D189.5)
Multiplying both sides by 4 will reverse the division:
![(2N+2)\times1=758](https://tex.z-dn.net/?f=%282N%2B2%29%5Ctimes1%3D758)
Subtracting 2 from each side will reverse the addition:
![2N=756](https://tex.z-dn.net/?f=2N%3D756)
Dividing both sides by 2 will reverse the multiplication:
![N=378](https://tex.z-dn.net/?f=N%3D378)
Therefore, the two consecutive integers must be
378 and
380.
Check this: