Answer:
A. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have columns and will not have a row of the form , so the system is consistent.
Step-by-step explanation:
Based on Godel's second incompleteness theorem, a system is considered consistent only when the far-right column of the augmented matrix is not a pivot column.
However, given that every column of the coefficient matrix is a pivot column, then there are no top coefficients in the far-right column of the augmented matrix.
Hence, there is a pivot position in each row of the coefficient matrix. The augmented matrix will have columns and will not have a row of the form , so the system is consistent.
The equation x = -8 contains the two points (-8 , -3) and (-8 , 1) ⇒ 2nd answer
Step-by-step explanation:
Let us revise the equations of the horizontal and vertical lines
- The equation of a horizontal line passes through point (a , b) is y = b, because all points lie on the line have the same y-coordinate b
- If a line passes through two points have the same y-coordinates, then the line is horizontal
- The equation of a vertical line passes through point (a , b) is x = a, because all points lie on the line have the same x-coordinate a
- If a line passes through two points have the same x-coordinates, then the line is vertical
∵ The line contained the two points (-8 , -3) and (-8 , 1)
∵ The two points have the same x-coordinate = -8
- From the 4th note above
∴ The line is vertical
∵ The equation of a vertical line is x = the x-coordinate of any point
on the line
∵ The x-coordinate of the points on the line = -8
∴ The equation of the line is x = -8
The equation x = -8 contains the two points (-8 , -3) and (-8 , 1)
Learn more:
You can learn more about the equation of a line in brainly.com/question/2657284
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The simplified expression would be 2m^2 - 24m + 39
-1,2,3 B
Because those are all the outputs it can be c and d because those are inputs and outputs so then the answer would be between A and B and the answer is B
3s+b=105 subtract 3s from both sides
b=105-3s...then we are told that:
2s+2b=98, using b found above we have:
2s+2(105-3s)=98 perform indicated multiplication on left side
2s+210-6s=98 combine like term on left side
-4s+210=98 subtract 210 from both sides
-4s=-112 divide both sides by 4
s=28, since b=105-3s
b=105-3(28)
b=105-84
b=21
So a scarf costs $28 and a belt costs $21 respectively.
The wording is a little wonky, but the cost of a scarf and a belt together is:
28+21=$49