Answer:
![\left[\begin{array}{ccc}5&7\\5&-8\\3&-9\end{array}\right] \left[\begin{array}{ccc}c\\d\end{array}\right] =\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%267%5C%5C5%26-8%5C%5C3%26-9%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dc%5C%5Cd%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-16%5C%5C3%5C%5C-15%5Cend%7Barray%7D%5Cright%5D)
This tells us that:
![A=\left[\begin{array}{ccc}5&7\\5&-8\\3&-9\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%267%5C%5C5%26-8%5C%5C3%26-9%5Cend%7Barray%7D%5Cright%5D)
![b=\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right]](https://tex.z-dn.net/?f=b%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-16%5C%5C3%5C%5C-15%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
So we are saying we have scalars, c and d, such that:
![c\left[\begin{array}{ccc}5\\5\\ 3\end{array}\right]+d\left[\begin{array}{ccc}7\\-8\\-9\end{array}\right]=\left[\begin{array}{ccc}-16\\3\\-15\end{array}\right]](https://tex.z-dn.net/?f=c%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%5C%5C5%5C%5C%203%5Cend%7Barray%7D%5Cright%5D%2Bd%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%5C%5C-8%5C%5C-9%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-16%5C%5C3%5C%5C-15%5Cend%7Barray%7D%5Cright%5D)
.
So we want to find a way to express this as:
Ax=b where x is the scalar vector, ![\left[\begin{array}{ccc}c\\d\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dc%5C%5Cd%5Cend%7Barray%7D%5Cright%5D)
.
So we can write this as:
Answer:
3:1
Step-by-step explanation:
We know that the number of students who prefer cheese AND vegetable pizza is 16 cheese + 2 vegetable = 18 combined
We also know that the number of students who prefer sausage AND pepperoni pizza is 3 sausage + 3 pepperoni = 6 combined
If we take the ratio between these figures, this ratio would be 18:6 (read as 18 to 6) which simplifies to 3:1 (read as 3 to 1).
Answer:
f (x) = 4,500 + 250x; 24 months
Step-by-step explanation:
Because 10,500 - 4,500 = 6,000
6,000 / 250 = 24
Hope this helped
Answer:
608 ft^2
Step-by-step explanation:
The formula for calculating surface area of a triangular prism is
bh + 2ls + lb (b : base, h : height, l : length)
12×8 + 2×16×10 + 16×12 = 608 ft^2
