There are 5
hope that this helps and good luck
Answer: Inconsistent
<u>Step-by-step explanation:</u>
y = 3x + 4 → m = 3, b = 4
y = 3x + 3 → m = 3, b = 3
These equations have the same slope but different y-intercepts so they are parallel lines <em>which means they will never intersect.</em>
NOTES
- one solution: consistent & independent <em>lines cross</em>
- infinite solutions: consistent & dependent <em>same line</em>
- no solution: inconsistent <em>parallel lines</em>
Given:
The two vectors are:
To find:
The value of 
.
Solution:
We have,
The cross product of these two vectors is:
![\overrightarrow{a}\times \overrightarrow{b}=\hat{i}[(-1)(5)-(1)(-3)]-\hat{j}[(2)(5)-(1)(1)]+\hat{k}[(2)(-3)-(-1)(1)]](https://tex.z-dn.net/?f=%5Coverrightarrow%7Ba%7D%5Ctimes%20%5Coverrightarrow%7Bb%7D%3D%5Chat%7Bi%7D%5B%28-1%29%285%29-%281%29%28-3%29%5D-%5Chat%7Bj%7D%5B%282%29%285%29-%281%29%281%29%5D%2B%5Chat%7Bk%7D%5B%282%29%28-3%29-%28-1%29%281%29%5D)
![\overrightarrow{a}\times \overrightarrow{b}=\hat{i}[-5+3]-\hat{j}[10-1]+\hat{k}[-6+1]](https://tex.z-dn.net/?f=%5Coverrightarrow%7Ba%7D%5Ctimes%20%5Coverrightarrow%7Bb%7D%3D%5Chat%7Bi%7D%5B-5%2B3%5D-%5Chat%7Bj%7D%5B10-1%5D%2B%5Chat%7Bk%7D%5B-6%2B1%5D)
Now the magnitude of the cross product is:
Therefore, the value of is 
.
Answer:
First awnser
Step-by-step explanation:
4x(7-v2)+v7(7-v2)
28-4v2+7v7-v14
Answer:
0.343
Step-by-step explanation:
First, find the different ways one can chose a professor or instructor. In this case, there are 8 professors and 4 instructors. So there are a total of 12 ways you can choose a professor or instructor.
Second, you want to find the different ways you can choose any member of the faculty. In this example, since you are only choosing one person, then you just find the total number of people in the faculty, which is 8 + 11 + 12 + 4 = 35.
Third, all you do is divide the different ways you can get a professor or instructor by the total different ways you can choose. So it's 12/35, or 0.343.
