Answer:
First, we have rounded numbers A and B, and we know that:
A + B = 11000
A - B = 3000
Now we can solve this system of equations as:
Isolating one variable in one of the equations, i will choose A in the second equation:
A = 3000 + B.
Now we can replace this into the other equation:
3000 + B + B = 11000
2*B = 11000 - 3000 = 8000
B = 8000/2 = 4000
and:
A - 4000 = 3000
A = 3000 + 4000 = 7000.
But remember that our original numbers are not exactly whole numbers, they are rounded up, so we could write them as:
A = 6999.8 (that would be rounded up to 7000)
B = 3999.7 (that would be rounded up to 4000)
The sum is:
A + B = 10999.5 (notice that this would be rounded up to 11000)
A - B = 3000.1 (this would be rounded down to 3000)
What percent means x/100.
The word "of" means times.
The word "is" means equals.
So we have x/100 · 60 = 15 or 60x/100 = 15.
The rest of the work is attached below, just solve the equation.
Answer:
<h2>
The solution to the system of equation is x = 8, y = 13</h2>
Step-by-step explanation:
The system of equation using matrix equation can be solved using crammers rule. Given the equation;
7x-4y=4
10x-6y=2
The equation will be rewritten in the format AX = B
matrix A will be 2*2 matrix
X will be a column matrix containing the variables
B will be a column matrix
![\left[\begin{array}{cc}7&-4\\10&-6\\\end{array}\right] \left[\begin{array}{c}x&y\\\\\end{array}\right] = \right] \left[\begin{array}{c}4&2\\\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%26-4%5C%5C10%26-6%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%26y%5C%5C%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%262%5C%5C%5C%5C%5Cend%7Barray%7D%5Cright%5D)
first we will find the determinant of the matrix A

To get the value of x, we will substitute the column matrix at the right hand side to replace the first column pf matrix A, then we look for the determinant and divide the determinant by the determinant of matrix A itself.
![|X|=\left[\begin{array}{cc}4&-4\\2&-6\\\end{array}\right]\\|X|= -24+8\\|X|=-16](https://tex.z-dn.net/?f=%7CX%7C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-4%5C%5C2%26-6%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%7CX%7C%3D%20-24%2B8%5C%5C%7CX%7C%3D-16)
x = |X|/|A|
x = -16/-2
x = 8
Similarly for y, we will substitute the column matrix at the right hand side to replace the second column of matrix A, then we look for the determinant and divide the determinant by the determinant of matrix A itself.
![|Y|=\left[\begin{array}{cc}7&4\\10&2\\\end{array}\right]\\|Y|= 14-40\\|Y|=-26](https://tex.z-dn.net/?f=%7CY%7C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%264%5C%5C10%262%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%7CY%7C%3D%2014-40%5C%5C%7CY%7C%3D-26)
y = |Y|/|A|
y = -26/-2
y = 13
The solution to the system of equation is x = 8, y = 13
Answer: 24
Step-by-step explanation: 6 x 4=24
Answer:
a) Math and Dance
b) 3 students (Chau, Juan, Ivan)
c) Tome, Jose, Josh, Rita
Step-by-step explanation:
That was so easy homework :-) write in comments if it helped