Answer:
See below, I will let graphing part to yourself.
Step-by-step explanation:
First function: domain:
, range:
, decreasing
Second function: domain:
, range:
, increasing
Third function: domain:
, range:
, increasing
The answer is a, -40 + 7 = -33
Answer:
A. 200 packages
Step-by-step explanation:
The number of packages per roll can be found by dividing the length of a roll by the length of tape needed for each package.
__
For each package:
(2.375 in/piece)×(4 piece/package) = 9.5 in/package
Per roll:
(1900 in/roll) / (9.5 in/package) = (1900/9.5) packages/roll
= 200 packages/roll
The machine can seal 200 packages with a roll of tape 1900 inches long.
![\left[ \begin{matrix} 2 & a \\ -1 & -2 \end{matrix} \right] + \left[ \begin{matrix} b & 4 \\ -2 & 1 \end{matrix} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Bmatrix%7D%202%20%26%20a%20%5C%5C%20-1%20%26%20-2%20%5Cend%7Bmatrix%7D%20%5Cright%5D%20%2B%20%5Cleft%5B%20%5Cbegin%7Bmatrix%7D%20b%20%26%204%20%5C%5C%20-2%20%26%201%20%5Cend%7Bmatrix%7D%20%5Cright%5D)
This addition of matrices can be combined into one matrix.
To add matrices, add the corresponding components of each matrix.
After adding, we'll have the following
![\left[ \begin{matrix} 2+b & a+4 \\ -3 & -1 \end{matrix} \right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%20%5Cbegin%7Bmatrix%7D%202%2Bb%20%26%20a%2B4%20%5C%5C%20-3%20%26%20-1%20%5Cend%7Bmatrix%7D%20%5Cright%5D%20)
This matrix should be equal to the matrix on the right-hand side of the equation. This means that each corresponding component of this matrix and the other matrix should be equivalent.
This means that
![2+b=1](https://tex.z-dn.net/?f=2%2Bb%3D1)
AND
![a+4=0](https://tex.z-dn.net/?f=a%2B4%3D0)
Solving these one-step equations will give the values of a = -4 and b = -1. That's answer choice D.