What is the remainder when 18,049 is divided by 14
2 answers:
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Answer:
The most likely answer would be 282,240.
Step-by-step explanation:
I got a different value than the choices you've given me. But if 282,240; 14; and 21 are your only options, then the most likely answer would be 282,240. Any number followed by an exclamation point means that it will be multiplied by all whole numbers from 1 to that number. For example, 4! would be 1 * 2 * 3 * 4 = 24. In this problem, 7! equals 5,040; 8! equals 40,320; =
; and 9! = 362,880. You can tell by the listed numbers that the product will be extremely big despite the fraction, so the best choice to go with would be 282,240.
To find the solutions to the system, we need to find exactly when one expression is equal to the other. We can do this by setting both of the right sides equal to each other, so that
Subtracting x+6 from either side, we find
factoring out an x+6:
The x-coordinates of our solutions will therefore be 6 and -6. Since the question only asks for the <em>x-coordinate</em> of the midpoint, we simply need to find the number exactly halfway between 6 and -6, which is 0.
Answer:
- A. (x1, x2) = (1, 4)
- C. There is no solution.
- B. The solutions are of the form: (x1, x2, x3) = (4t+4, t-3, t)
Step-by-step explanation:
1. Subtract the first equation from twice the second to eliminate x2.
2(2x1 -x2) -(x1 -2x2) = 2(-2) -(-7)
3x1 = 3 . . . . . simplify
x1 = 1 . . . . . . .divide by 3
Substitute this value into the second equation.
2·1 -x2 = -2
4 -x2 = 0 . . . . . add 2
4 = x2 . . . . . . . add x2
The solution is (x1, x2) = (1, 4).
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2. Multiply the first equation by 3 and add the second equation.
3(-5x1 -3x2) +(15x1 +9x2) = 3(7) +(2)
0 = 23 . . . . . not true;
There is no solution.
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3. There are two equations in 3 unknowns, so there cannot be a unique solution. The equations are not dependent, so there will be an infinite number of solutions that can be written in terms of a single parameter (t).
Let x3 = t. Then the system of equations can be rewritten as
2x1 - 5x2 = 23 +3t
x1 - 4x2 = 16
Subtracting twice the second equation from the first, we have ...
(2x1 -5x2) -2(x1 -4x2) = (23 +3t) -2(16)
3x2 = 3t -9 . . . simplify
x2 = t -3 . . . . . divide by 3
Substituting this into the second equation above, we have ...
x1 -4(t -3) = 16
x1 = 16 +4t -12 . . . . . . add 4(t-3)
x1 = 4t +4 . . . . . . . . simplify
The solutions are (x1, x2, x3) = (4t+4, t-3, t).
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The attachment shows the first system solved by graphical means. This validates our answer.
