Answer:
When f(x) = 7, x is equal to 5.
Step-by-step explanation:
When looking at this graph, we are looking for where the line hits a point where y is equal to 7. That's because f(x) is essentially the same thing as y.
The point in which the graph hits y = 7 is (5, 7). This means the x value we need is 5.
Answer:
![A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}](https://tex.z-dn.net/?f=A%3D%5Cbegin%7Bbmatrix%7D6%20%26%205%20%26%203%5C%5C%202%20%26%203%20%26%204%5C%5C%202%20%26%202%20%26%203%5Cend%7Bbmatrix%7D)
![B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}](https://tex.z-dn.net/?f=B%3D%5Cbegin%7Bbmatrix%7D25%5C%5C%2018%5C%5C%2035%5Cend%7Bbmatrix%7D)
Step-by-step explanation:
It is given that the snack shop makes 3 mixes of nuts in the following proportions.
Mix I: 6 lbs peanuts, 2 lbs cashews, 2 lbs pecans.
Mix II: 5 lbs peanuts, 3 lbs cashews, 2 lbs pecans.
Mix III: 3 lbs peanuts, 4 lbs cashews, 3 lbs pecans.
they received an order for 25 of mix I, 18 of mix II, and 35 of mix III.
We need to find the matrices A & B for which AB gives the total number of lbs of each nut required to fill the order.
Mix I Mix II Mix III
peanuts 6 5 3
cashews 2 3 4
pecans 2 2 2
![A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}](https://tex.z-dn.net/?f=A%3D%5Cbegin%7Bbmatrix%7D6%20%26%205%20%26%203%5C%5C%202%20%26%203%20%26%204%5C%5C%202%20%26%202%20%26%203%5Cend%7Bbmatrix%7D)
![B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}](https://tex.z-dn.net/?f=B%3D%5Cbegin%7Bbmatrix%7D25%5C%5C%2018%5C%5C%2035%5Cend%7Bbmatrix%7D)
The product of both matrices is
![AB=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}](https://tex.z-dn.net/?f=AB%3D%5Cbegin%7Bbmatrix%7D6%20%26%205%20%26%203%5C%5C%202%20%26%203%20%26%204%5C%5C%202%20%26%202%20%26%203%5Cend%7Bbmatrix%7D%5Cbegin%7Bbmatrix%7D25%5C%5C%2018%5C%5C%2035%5Cend%7Bbmatrix%7D)
![AB=\begin{bmatrix}6\cdot \:25+5\cdot \:18+3\cdot \:35\\ 2\cdot \:25+3\cdot \:18+4\cdot \:35\\ 2\cdot \:25+2\cdot \:18+3\cdot \:35\end{bmatrix}](https://tex.z-dn.net/?f=AB%3D%5Cbegin%7Bbmatrix%7D6%5Ccdot%20%5C%3A25%2B5%5Ccdot%20%5C%3A18%2B3%5Ccdot%20%5C%3A35%5C%5C%202%5Ccdot%20%5C%3A25%2B3%5Ccdot%20%5C%3A18%2B4%5Ccdot%20%5C%3A35%5C%5C%202%5Ccdot%20%5C%3A25%2B2%5Ccdot%20%5C%3A18%2B3%5Ccdot%20%5C%3A35%5Cend%7Bbmatrix%7D)
![AB=\begin{bmatrix}345\\ 244\\ 191\end{bmatrix}](https://tex.z-dn.net/?f=AB%3D%5Cbegin%7Bbmatrix%7D345%5C%5C%20244%5C%5C%20191%5Cend%7Bbmatrix%7D)
Therefore matrix AB gives the total number of lbs of each nut required to fill the order.
Answer:
-1,7
0,-3
1,-7
5,47
Step-by-step explanation:
-x-=+
Answer:
The distance between the astronomers and the moon was
meters.
Step-by-step explanation:
We have that the speed is the distance divided by the time, so:
![v = \frac{d}{t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
In this problem, we have that:
The reflected laser beam was observed by the astronomers 2.52 s after the laser pulse was sent. This means that
.
If the speed of light is 3.00 times 10^8 m/s, what was the distance between the astronomers and the moon?
We have that
m/s.
We have to find d. So:
![v = \frac{d}{t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
![d = vt](https://tex.z-dn.net/?f=d%20%3D%20vt)
![d = 3*10^{8}*2.52](https://tex.z-dn.net/?f=d%20%3D%203%2A10%5E%7B8%7D%2A2.52)
![7.56*10^{8]](https://tex.z-dn.net/?f=7.56%2A10%5E%7B8%5D)
The distance between the astronomers and the moon was
meters.