Answer:
15.5 ft²
Step-by-step explanation:
The area (A) of a regular polygon is calculated as
A = 
pa ( p is the perimeter and a the apothem )
Here side of regular pentagon is 3 ft, thus
perimeter = 5 × 3 = 15, so
A = 0.5 × 15 × 2.06 ≈ 15.5 ft ( to the nearest tenth )
Answer:
The set of solutions is ![\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number} \}](https://tex.z-dn.net/?f=%5C%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D12%5C%5C-7-r%5C%5Cr%5Cend%7Barray%7D%5Cright%5D%3A%20%5Ctext%7Br%20is%20a%20real%20number%7D%20%20%5C%7D)
Step-by-step explanation:
The augmented matrix of the system is ![\left[\begin{array}{ccccc}3&6&6&-9\\-2&-3&-3&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D3%266%266%26-9%5C%5C-2%26-3%26-3%263%5Cend%7Barray%7D%5Cright%5D)
.
We will use rows operations for find the echelon form of the matrix.
- In row 2 we subtract
from row 1. (R2- 2/3R1) and we obtain the matrix ![\left[\begin{array}{cccc}3&6&6&-9\\0&1&1&-7\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D3%266%266%26-9%5C%5C0%261%261%26-7%5Cend%7Barray%7D%5Cright%5D)
- We multiply the row 1 by
.
Now we solve for the unknown variables:
The system has a free variable, the the system has infinite solutions and the set of solutions is
He had put in $300 and got out $336 at the end of the year.
This means an increase of $36 over a year.
10% of $300 = $30 dollars
This shows that he definitely got more than a 10% increase.
Alan got $6 more than $30 so to find 6 from 30, you divide by 5
so ( 10% = $30 ) divided by 5 = ( 2% = $6 )
Adding the amount of money and percentages gives you 12% = $36
So the amount of mpercentage increase is 12%
Overall the amount of money in his bank now compared to when he deposited it, he has 112% in the bank.
Answer:
5/18
Step-by-step explanation:
note: 5/9 is the same as 10/18 (we get this by multiplying both numerator and denominator by 2)
hence
5/9-5/18
= 10/18 - 5/18
= (10-5) / 18
= 5/18
Answer:
X=80
Y=9
Z=7
Step-by-step explanation:
