Answer:
x ≥−42
Step-by-step explanation:
x/7 ≥−6
Multiply each side by 7
x/7 * ≥−6*7
x ≥−42
Answer: 570 adult tickets and 215 children tickets were sold
Step-by-step explanation:
Let x represent the number of adult tickets that were sold for the movie Saturday.
Let y represent the number of children tickets that were sold for the movie Saturday.
One Saturday the theater sold 785 tickets. This means that
x + y = 785
The movie theater charges 5 for an adult ticket and 2 for a child's ticket. The total sales on Saturday was 3280. This means that
5x + 2y = 3280 - - - - - - - - - - --- 1
Substituting x = 785 - y into equation 1, it becomes
5(785 - y) + 2y = 3280
3925 - 5y + 2y = 3280
- 5y + 2y = 3280 - 3925
- 3y = - 645
y = - 645/- 3
y = 215
x = 785 - y = 785 - 215
x = 570
3x+2y=14
2x-4y=4
6x+4y=28
2x-4y=4
8x = 32
x = 4
2y = 14 - 12 = 2
y = 1
(x , y) = (4 , 1)
Question:How can check your solution by writing the system as a matrix equation and using the inverse matrix?.
To check the solution, represent the system of equations as a matrix equation, find the inverse of the coefficient matrix, and multiply both sides of the equation by the inverse.
To check the solution by writing the system as a matrix equation and using the inverse matrix, we need to represent the system of equations as a matrix equation. Let's consider the given system of equations:
3x + 2y = 14
2x - 4y = 4
To do this, we can write the coefficients and constants of the system of equations as matrices:
[3 2] [x] = [14]
[2 -4] [y] = [4]
Now, we can write the system of equations as a matrix equation: AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
Next, we need to find the inverse of matrix A. If the inverse exists, we can multiply both sides of the matrix equation by the inverse of A to find the solution for X.
If we find the inverse of A and multiply both sides of the equation by the inverse, we get:
X = A-1B
Substituting the values of A-1 and B, we can find X, which represents the solution to the system of equations. Therefore, we can check our solution by writing the system as a matrix equation and using the inverse matrix.
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Answer:
$26,000.
Step-by-step explanation:
We have been given that a job that pays $100,000 per year federal income taxes 19% and state income tax is 7%.
The annual total of the required deductions of federal and state income tax would be .
To find the total amount, we will find 26% of $100,000.
Therefore, the annual total of the required deductions of federal and state income tax is $26,000.
The minimum and maximum distances that Morgan’s dog may be from the house are 492 and 508 meters.
From the information given, Morgan is currently 500 meters from her house.
The minimum distance will be:
= 500 - 8 = 492
The maximum distance will be:
= 500 + 8
= 508
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