Answer:
Slope Formula: 
Step-by-step explanation:
It is wise to remember this formula. It is one of the most important formulas in Algebra and is fundamental in higher level math courses.
We use this formula to determine the slope, or the average rate of change between 2 points.
Answer:
= 5 / 12
Step-by-step explanation:
Probability is an outcome of chance. It is a measure of outcomes of events.
To solve the probability of picking a Tootsie Pop, we must comfortably know the contents of the bag.
Number of GRAPE Tootsie pops = 5
Number of CHOCOLATE Tootsie pops= 8
Total number of Tootsie pops = The sum of both Tootsie pops
Total number = 5 + 8
= 13.
Let's note that tge question said , Juan pulls a chocolate Tootsie Pop and eats. The implication is it has reduced the total number of Tootsie Pops left in the bag.
Therefore:
The probability that the next pop he pulls out will be grape will be
Probability (Grape) = 5 / (13 -1)
= 5 / 12
The probability that the next Pop he pulls out will be a grape = 5/12
<span>1/4= y-intercept
</span><span>-1/7= x intercept </span>
Find a basis for the column space and rank of the matrix ((-2,-2,-4,1),(7,-3,14,-6),(2,-2,4,-2)(2,-6,4,-3))
Novosadov [1.4K]
Answer:
- B=\{\left[\begin{array}{c}-2\\-2\\-4\\1\end{array}\right], \left[\begin{array}{c}7\\-3\\14&-6\end{array}\right], \left[\begin{array}{c}2\\-2\\4\\-2\end{array}\right] \}[/tex] is a basis for the column space of A.
- The rank of A is 3.
Step-by-step explanation:
Remember, the column space of A is the generating subspace by the columns of A and if R is a echelon form of the matrix A then the column vectors of A, corresponding to the columns of R with pivots, form a basis for the space column. The rank of the matrix is the number of pivots in one of its echelon forms.
Let ![A=\left[\begin{array}{cccc}-2&7&2&2\\-2&-3&-2&-6\\-4&14&4&4\\1&-6&-2&-3\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-2%267%262%262%5C%5C-2%26-3%26-2%26-6%5C%5C-4%2614%264%264%5C%5C1%26-6%26-2%26-3%5Cend%7Barray%7D%5Cright%5D)
the matrix of the problem.
Using row operations we obtain a echelon form of the matrix A, that is
![R=\left[\begin{array}{cccc}1&-6&-2&-3\\0&9&2&0\\0&0&-8&-21\\0&0&0&0\end{array}\right]](https://tex.z-dn.net/?f=R%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-6%26-2%26-3%5C%5C0%269%262%260%5C%5C0%260%26-8%26-21%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%5D)
Since columns 1,2 and 3 of R have pivots, then a basis for the column space of A is
![B=\{\left[\begin{array}{c}-2\\-2\\-4\\1\end{array}\right], \left[\begin{array}{c}7\\-3\\14&-6\end{array}\right], \left[\begin{array}{c}2\\-2\\4\\-2\end{array}\right] \}](https://tex.z-dn.net/?f=B%3D%5C%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-2%5C%5C-2%5C%5C-4%5C%5C1%5Cend%7Barray%7D%5Cright%5D%2C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D7%5C%5C-3%5C%5C14%26-6%5Cend%7Barray%7D%5Cright%5D%2C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C-2%5C%5C4%5C%5C-2%5Cend%7Barray%7D%5Cright%5D%20%5C%7D)
.
And the rank of A is 3 because are three pivots in R.
