2464829438
The next number is 2,464,829,439
Answer:
7
Step-by-step explanation:
Fiction books: (1/6) of 30 books = 5 books
Non-fiction books: (3/5) of (30) books = 18 books
The subtotal here is 5 + 18, or 23.
23 of the books are either fiction or non fiction.
30 - 23, or 7, of the books remain (are neither fiction nor non-fiction).
9514 1404 393
Answer:
(x, y, z) = (-3, -1, 3)
Step-by-step explanation:
Many graphing calculators can solve matrix equations handily. Here, we use a combination of methods.
Use the last equation to write an expression for z.
z = 4 -x +4y
Substitute this into the second equation:
y -4(4 -x +4y) = -13
y -16 +4x -16y = -13
4x -15y -3 = 0
In genera form, the first equation can be written as ...
3x +y +10 = 0
Now, the solution to these two equations can be found to be ...
x = (-15(10) -1(-3))/(4(1) -3(-15)) = (-150 +3)/(4+45) = -3 . . . using "Cramer's rule"
y = -(10 +3x) = -(10 -9) = -1 . . . . from the first equation
z = 4 -(-3) +4(-1) = 3 . . . . . . . . from our equation for z
The solution to the system is (x, y, z) = (-3, -1, 3).
_____
<em>Additional comment</em>
Written as an augmented matrix, the system of equations is ...
![\left[\begin{array}{ccc|c}-3&-1&0&10\\0&1&-4&-13\\1&-4&1&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D-3%26-1%260%2610%5C%5C0%261%26-4%26-13%5C%5C1%26-4%261%264%5Cend%7Barray%7D%5Cright%5D)
Answer: b) Large blue t-shirt & Medium RC jeans
<u>Step-by-step explanation:</u>
The subscript numbers attached to the matrix letter represents the:
ROW, COLUMN
![A=\left[\begin{array}{ccc}a_{1,1}&a_{1, 2}&a_{1, 3}\\a_{2,1}&a_{2, 2}&a_{2, 3}\\a_{3,1}&a_{3, 2}&a_{3, 3}\end{array}\right] \qquad B=\left[\begin{array}{ccc}a_{1,1}&b_{1, 2}&b_{1, 3}\\b_{2,1}&b_{2, 2}&b_{2, 3}\\b_{3,1}&b_{3, 2}&b_{3, 3}\end{array}\right]\\](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_%7B1%2C1%7D%26a_%7B1%2C%202%7D%26a_%7B1%2C%203%7D%5C%5Ca_%7B2%2C1%7D%26a_%7B2%2C%202%7D%26a_%7B2%2C%203%7D%5C%5Ca_%7B3%2C1%7D%26a_%7B3%2C%202%7D%26a_%7B3%2C%203%7D%5Cend%7Barray%7D%5Cright%5D%20%5Cqquad%20B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_%7B1%2C1%7D%26b_%7B1%2C%202%7D%26b_%7B1%2C%203%7D%5C%5Cb_%7B2%2C1%7D%26b_%7B2%2C%202%7D%26b_%7B2%2C%203%7D%5C%5Cb_%7B3%2C1%7D%26b_%7B3%2C%202%7D%26b_%7B3%2C%203%7D%5Cend%7Barray%7D%5Cright%5D%5C%5C)
A₁,₃ = 1st row, 3rd column
1st row is Blue, 3rd column is Large
B₃,₂ = 3rd row, 2nd column
3rd row is RC jeans, 2nd column is Medium
A₁,₃ + B₃,₂ = Large blue t-shirt & Medium RC jeans
How man bags were used?
41 / 3 = 13.7
We can say about 14 bags by rounding to the nearest whole number. Therefore, 14 bags were used.