Answer:
Joe is 9 years old
Step-by-step explanation:
We can start by creating two different equations, one for each fact that we know about their ages.
Say that J is Joe's age
Say that T is Tim's age
Our first equation would then be:
4J + 2T = 50
J - 2 = T
Now that we know that T is J - 2, we can plug that in to the first equation.
4J + 2(J - 2) = 50
We can simplify this equation to solve for J
4J + 2J - 4 = 50
6J = 54
J = 9
Joe is 9 years old
The MN matrix is ![\left[\begin{array}{ccc}-2 & 1 & 0 \\17 & 2 & -3\\11 & 12 & -5\end{array}\right]\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%20%26%201%20%26%200%20%5C%5C17%20%26%202%20%26%20-3%5C%5C11%20%26%2012%20%26%20-5%5Cend%7Barray%7D%5Cright%5D%5C%5C)
.
What is matrix?
A matrix is a rectangular array or table with rows and columns of numbers, symbols, or expressions that is used to represent a mathematical object or an attribute of one. is a matrix having two rows and three columns, for instance.
Given ![M=\left[\begin{array}{cc} 1 & 0 \\ -4 & 3 \\ 2 & 5 \end{array}\right]](https://tex.z-dn.net/?f=M%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%201%20%26%200%20%5C%5C%20-4%20%26%203%20%5C%5C%202%20%26%205%20%5Cend%7Barray%7D%5Cright%5D)
![N=\left[\begin{array}{ccc}-2 & 1 & 0 \\3 & 2 & -1\end{array}\right]](https://tex.z-dn.net/?f=N%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%20%26%201%20%26%200%20%5C%5C3%20%26%202%20%26%20-1%5Cend%7Barray%7D%5Cright%5D)
M is a matrix with 3 * 2 dimension and N is a matrix with 2 * 3 dimension.
So finding MN is possible and the dimension will be 3 * 3.
Now,
![MN=\left[\begin{array}{cc}1 & 0 \\-4 & 3 \\2 & 5\end{array}\right] \times \left[\begin{array}{ccc}-2 & 1 & 0 \\3 & 2 & -1\end{array}\right]\\= \left[\begin{array}{ccc}1 \times (-2)+0 \times 3 & 1 \times 1+0 \times 2 & 1 \times 0+0 \times (-1) \\(-2) \times (-4)+3 \times 3 & (-4) \times 1+3 \times 2 & (-4) \times 0+3 \times (-1) \\2 \times (-2)+5 \times 3 & 2 \times 1+5 \times 2 & 2 \times 0+5 \times (-1) \\\end{array}\right]\\](https://tex.z-dn.net/?f=MN%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%20%26%200%20%5C%5C-4%20%26%203%20%5C%5C2%20%26%205%5Cend%7Barray%7D%5Cright%5D%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%20%26%201%20%26%200%20%5C%5C3%20%26%202%20%26%20-1%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%20%5Ctimes%20%28-2%29%2B0%20%5Ctimes%203%20%26%201%20%5Ctimes%201%2B0%20%5Ctimes%202%20%26%201%20%5Ctimes%200%2B0%20%5Ctimes%20%28-1%29%20%5C%5C%28-2%29%20%5Ctimes%20%28-4%29%2B3%20%5Ctimes%203%20%26%20%28-4%29%20%5Ctimes%201%2B3%20%5Ctimes%202%20%26%20%28-4%29%20%5Ctimes%200%2B3%20%5Ctimes%20%28-1%29%20%5C%5C2%20%5Ctimes%20%28-2%29%2B5%20%5Ctimes%203%20%26%202%20%5Ctimes%201%2B5%20%5Ctimes%202%20%26%202%20%5Ctimes%200%2B5%20%5Ctimes%20%28-1%29%20%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C)
![=\left[\begin{array}{ccc}-2 & 1 & 0 \\17 & 2 & -3\\11 & 12 & -5\end{array}\right]\\](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%20%26%201%20%26%200%20%5C%5C17%20%26%202%20%26%20-3%5C%5C11%20%26%2012%20%26%20-5%5Cend%7Barray%7D%5Cright%5D%5C%5C)
Therefore the MN matrix is .
To learn more about matrix from the given link
brainly.com/question/94574
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Answer: X=4
Step-by-step explanation:
Pulling out like terms :
1.1 Pull out like factors :
2x - 8 = 2 • (x - 4)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4
One solution was found :
x = 4
Answer:$9
Step-by-step explanation:
65+8x=137
137-65=72
72/8=9
50+55x=y 200+45x=y
We have a system of equations.
The answer is 875€ both in 15 months. It will take 15 months.
