Answer:
C. Same is not an orange belt and Kate is not a red belt.
Step-by-step explanation:
A negation is an operation that "takes a statement and changes it to a statement whose true or false value is opposite". For example, if I were to say 2 + 2 = 4, the negation would be that 2 + 2 ≠ 4.
So, if Sam is an orange belt and Kate is a red belt, the negation is C. Same is not an orange belt and Kate is not a red belt.
Hope this helps!
Pair up the terms into separate groups. Then factor each group individually (pull out the GCF). Once that is finished, you factor out the overall GCF to complete the full factorization.
8r^3 - 64r^2 + r - 8
(8r^3 - 64r^2) + (r - 8)
8r^2(r - 8) + (r - 8)
8r^2(r - 8) + 1(r - 8)
(8r^2 + 1)(r - 8)
So the final answer is (8r^2 + 1)(r - 8)
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Edit:
Problem 1b) Follow the same basic steps as in part A
28v^3 + 16v^2 - 21v - 12
(28v^3 + 16v^2) + (-21v - 12)
4v^2(7v + 4) + (-21v - 12)
4v^2(7v + 4) - 3(7v + 4)
(4v^2 - 3)(7v + 4)
The answer to part B is (4v^2 - 3)(7v + 4)
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Second Edit:
I apologize for the first edit. I misread what you were asking initially. Here is problem 2A. We follow the same basic steps as in 1a) and 1b). You'll need to rearrange terms first
27mz - 12nc + 9mc - 36nz
27mz + 9mc - 12nc - 36nz
(27mz + 9mc) + (-12nc - 36nz)
9m(3z + c) + (-12nc - 36nz)
9m(3z + c) -12n(c + 3z)
9m(3z + c) -12n(3z + c)
(9m - 12n)(3z + c)
3(3m - 4n)(3z + c)
The slope of the first equation is -2, you can see it right off.
the slope of the second equation is 2, notice both are in slope-intercept form.
both equations are the equations of a line, so is really just two lines.
because their slope differs, they're not parallel or equivalent, therefore, they lines do meet at some point, and one point only, and therefore, they have 1 solution only.
a system of equations with at least 1 solution, is a consistent system.
a consistent system with exactly 1 solution only, is not just consistent, but also independent.
