The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the func
tion? a)
(1, 9) b) (8, 9) C) (−3, 3) d) (−6, −5)
(1, 9) b) (8, 9) C) (−3, 3) d) (−6, −5)
2 answers:
Answer:
Options a,b and c preserves the function
Step-by-step explanation:
Assuming the missing table is the one shown in the attachment
we know that
A <u><em>function</em></u> is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output
In this problem
If the point (-6,-5) is added, the function is not preserved, because for one input it will have two outputs
so
For x=-6
y=9 and y=-5
If the other points are added the function is preserved, because for one input it will have one output
therefore
Options a,b and c preserves the function
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The area can be found as the magnitude of the cross product of the vectors representing two adjacent sides.
area = || kl × kn || = || (0, 2, 1) × (4, 5, 0) ||
= || (-5, 4, -8) || = √105
_____
For the purpose here, kl = l - k = (1, 3, 2) - (1, 1, 1) = (0, 2, 1)
and nk = n - k = (5, 6, 1) - (1, 1, 1) = (4, 5, 0)
The cross product can be calculated using a suitable calculator. By hand, it is the determinant
where i, j, k are unit vectors in the x, y, z directions.
area = || kl × kn || = || (0, 2, 1) × (4, 5, 0) ||
= || (-5, 4, -8) || = √105
_____
For the purpose here, kl = l - k = (1, 3, 2) - (1, 1, 1) = (0, 2, 1)
and nk = n - k = (5, 6, 1) - (1, 1, 1) = (4, 5, 0)
The cross product can be calculated using a suitable calculator. By hand, it is the determinant
where i, j, k are unit vectors in the x, y, z directions.
Answer:
9
Step-by-step explanation:
81 gallons per 9 minutes
This can be thought of as a fraction:
divide the top and bottom of the fraction by 9 to make the bottom 1
remove the gallons per minute to a separate fraction
9