9514 1404 393
Answer:
(x, y, z) = (2+44t, 2+14t, 7-20t)
Step-by-step explanation:
One way to write parametric equations for line L is ...
L = P + t·<em>v</em>
where P is the given point and <em>v</em> is the given direction vector. Using that form, we have ...
(x, y, z) = (2+44t, 2+14t, 7-20t)
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If you like, you can remove a common factor of 2 from the coefficients of t.
(x, y, z) = (2+22t, 2+7t, 7-10t)
Answer:
9
Step-by-step explanation:
For this problem, you would use the GCF
Find the GCF of 45, 81, 63
GCF(45, 81, 63) = 9
45 = 9 * 5
81 = 9 *9
63= 9 * 7
Since 5, 9, 7 have no common factors, the GCF has to be 9.
This means that the greatest number of plants he can put in each row is 9.
The number of rows he uses for each plant will (obviously) vary.
The easiest way to find the vertex is to convert this standard form equation into vertex form, which is y = a(x - h)^2 + k.
Firstly, put x^2 - 10x into parentheses: y = (x^2 - 10x) + 30
Next, we want to make what's inside the parentheses a perfect square. To do that, we need to divide the x coefficient by 2 and square it. In this case, the result is 25. Add 25 inside the parentheses and subtract 25 outside of the parentheses: y = (x^2 - 10x + 25) + 30 - 25
Next, factor what's inside the parentheses and combine like terms outside of the parentheses, and your vertex form is: y = (x - 5)^2 + 5.
Now going back to the formula of the vertex form, y = a(x - h)^2 + k, the vertex is (h,k). Using our vertex equation, we can see that the vertex is (5,5).
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