Answer:
v/2
Step-by-step explanation:
First, if we expand the expression we know that it is equal to (4/8)*(v^3/v^2)
We can simplify the numbers to get (1/2)*(v^3/v^2)
We know that division of exponents is just subtraction of them, so v³/v² = v^(3-2) = v^1 = v
So, the answer is 1/2 * v or v/2
I hope this helps!
Every time you roll you have a 1/6 chance so rolling 4 times you have a 6x4= 24 and 1x4=4 so you have a 4/24 chance of getting a 6
Answer:
1. The matrix A isn't the inverse of matrix B.
2. |B|=12, |A|=12
Step-by-step explanation:
1. We want to know if matrix A is the inverse of matrix B, this means that if you do the product between B and A you have to obtain the identity matrix.
We have:
![A=\left[\begin{array}{cc}4&-2\\-1&3\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-2%5C%5C-1%263%5Cend%7Barray%7D%5Cright%5D)
and
![B=\left[\begin{array}{cc}3&2\\1&4\end{array}\right]](https://tex.z-dn.net/?f=B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%262%5C%5C1%264%5Cend%7Barray%7D%5Cright%5D)
A and B are 2×2 matrices (2 rows and 2 columns), if you multiply them you have to obtain a 2×2 matrix.
Then if A is the inverse of B:

Where,
![I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=I%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
Observation:
If you have two matrices:
![A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\and\\B=\left[\begin{array}{cc}e&f\\g&h\end{array}\right]\\\\\\A.B=\left[\begin{array}{cc}(a.e+b.g)&(a.f+b.h)\\(c.e+d.g)&(c.f+d.h)\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D%5C%5Cand%5C%5CB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7De%26f%5C%5Cg%26h%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5CA.B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%28a.e%2Bb.g%29%26%28a.f%2Bb.h%29%5C%5C%28c.e%2Bd.g%29%26%28c.f%2Bd.h%29%5Cend%7Barray%7D%5Cright%5D)
Now:
![B.A=\left[\begin{array}{cc}3&2\\1&4\end{array}\right].\left[\begin{array}{cc}4&-2\\-1&3\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}4.3+(-2).1&4.2+(-2).4\\(-1).3+3.1&(-1).2+3.4\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}12-2&8-8\\-3+3&-2+12\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}10&0\\0&10\end{array}\right]](https://tex.z-dn.net/?f=B.A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%262%5C%5C1%264%5Cend%7Barray%7D%5Cright%5D.%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-2%5C%5C-1%263%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5CB.A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4.3%2B%28-2%29.1%264.2%2B%28-2%29.4%5C%5C%28-1%29.3%2B3.1%26%28-1%29.2%2B3.4%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5CB.A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D12-2%268-8%5C%5C-3%2B3%26-2%2B12%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5CB.A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D10%260%5C%5C0%2610%5Cend%7Barray%7D%5Cright%5D)
![B.A=\left[\begin{array}{cc}10&0\\0&10\end{array}\right]\neq \left[\begin{array}{cc}1&0\\0&1\end{array}\right]=I\\\\\\B.A\neq I](https://tex.z-dn.net/?f=B.A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D10%260%5C%5C0%2610%5Cend%7Barray%7D%5Cright%5D%5Cneq%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%3DI%5C%5C%5C%5C%5C%5CB.A%5Cneq%20I)
Then, the matrix A isn't the inverse of matrix B.
2. If you have a matrix A:
![A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D)
The determinant of the matrix is:

Then the determinant of B is:
![B=\left[\begin{array}{cc}3&2\\1&4\end{array}\right]](https://tex.z-dn.net/?f=B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%262%5C%5C1%264%5Cend%7Barray%7D%5Cright%5D)


The determinant of A is:
![A=\left[\begin{array}{cc}4&-2\\-1&3\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-2%5C%5C-1%263%5Cend%7Barray%7D%5Cright%5D)


Answer:
(p-q)(1+x)
Step-by-step explanation:
p-q-x(q-p)
p-q-xq+xp
p+xp-q-xq
p(1+x)-q(1+x)
(p-q)(1+x)
Answer:
<em>2</em><em>5</em><em>0</em><em> </em><em>in </em><em>sq</em>
Step-by-step explanation:
<em>Here's</em><em> the</em><em> solution</em>
<em>=</em><em>></em><em> </em><em>Base </em><em>=</em><em> </em><em>2</em><em>5</em><em>i</em><em>n</em><em> </em>
<em>=</em><em>></em><em> </em><em>Height</em><em> </em><em>=</em><em> </em><em>2</em><em>0</em><em>i</em><em>n</em>
<em>=</em><em>></em><em>We </em><em>need</em><em> to</em><em> </em><em>find </em><em>out</em><em> area</em><em> of</em><em> traingle</em>
<em>=</em><em>></em><em> </em><em>Area</em><em> of</em><em> </em><em>traingle </em><em>=</em><em> </em><em>1</em><em>/</em><em>2</em><em>*</em><em>base </em><em>*</em><em>height</em><em> </em>
<em>=</em><em>></em><em> </em><em>Area</em><em> </em><em>=</em><em> </em><em>1</em><em>/</em><em>2</em><em>*</em><em>2</em><em>0</em><em>*</em><em>2</em><em>5</em><em> </em>
<em>=</em><em>></em><em> </em><em>Area</em><em>=</em><em> </em><em>2</em><em>5</em><em>0</em><em> </em><em>in </em><em>sq</em>
<em>hope</em><em> it</em><em> helps</em><em>. </em><em> </em><em>^</em><em>_</em><em>^</em>