Answer:
12
Step-by-step explanation:
N:S:G
6:2:1
Nick gets 30 more sweets than Gavyn, therefore we can say that.
As Sarah gets twice the amount of sweets that Gavyn does.
Using the completing-the-square method, find the vertex of the function f(x) = 2x2 − 8x + 6 and indicate whether it is a minimum
or a maximum and at what point.
Maximum at (2, –2)
Minimum at (2, –2)
Maximum at (2, 6)
Minimum at (2, 6)
Maximum at (2, –2)
Minimum at (2, –2)
Maximum at (2, 6)
Minimum at (2, 6)
1 answer:
Answer:
Minimum at (2, -2)
Step-by-step explanation:
Factor the leading coefficient from the first two terms:
f(x) = 2(x^2 -4x) +6
Inside parentheses, add the square of half the x-coefficient. Add the opposite of that amount outside parentheses.
f(x) = 2(x^2 -4x +4) +6 -8
Rewrite in vertex form.
f(x) = 2(x -2)^2 -2
The positive leading coefficient tells you the vertex is a <em>minimum</em>. Comparing this to the vertex form for a quadratic with vertex (h, k)
f(x) = a(x -h)^2 +k
we find the <em>vertex</em> to be ...
(h, k) = (2, -2)
The function has a minimum at (2, -2).
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Answer:
First and second box had 80 and 75 lb flour originally.
Step-by-step explanation:
Let the two boxes contained x lb and y lb of the flour respectively.
Both the boxes contained 155 lb of flour in total.
So the first equation will be,
x + y = 155 --------(1)
If the 20 lb of the flour is taken out then amount of flour in first box = (x - 20) lb
and added to the second box then flour in second box = (y + 20) lb
After the mixing of flour statement says that "the first box will contain of the flour now in the second box."
For this statement equation will be
19(x - 20) = 12(y + 20)
19x - 12y = 380 + 240
19x - 12y = 620 ------(2)
Equation (1) × 12 + equation (2)
12(x + y) + (19x - 12y) = 155×12 + 620
31x = 1860 + 620
31x = 2480
x =
x = 80 lb
from equation (1)
80 + y = 155
y = 155 - 80
y = 75 lb.
Therefore, first and second boxes had 80 lb and 75 lb of flour originally.