Answer:
Step-by-step explanation:
Given equation is,
y = 3x² - 6x + 11
a). y = 3x² - 6x + 11
= 3(x² - 2x) + 11
= 3(x² -2x + 1 - 1) + 11
= 3(x² - 2x + 1) - 3 + 11
= 3(x - 1)² + 8
Comparing this equation with y = a(x - b)² + c
a = 3, b = 1 and c = 8
b). For minimum value of x,
Since, vertex of the graph is given by (b, c),
Minimum value of x will be,
x = b
x = 1
c). Vertex of the parabola → (b, c)
→ (1, 8)
For y-intercept,
By substituting x = 0 in the equation,
y = 3(0 - 1)² + 8
y = 11
Now we can sketch the graph by using the table of input - output values.
x -2 -1 0 1 2 3
y 35 20 11 8 11 20
-31x is the answer to the problem
The perimeter will be:
P = 2x + y
100 = 2x + y
The area is:
A = x * y
We write the area as a function of x:
A (x) = x * (100-2x)
Rewriting:
A (x) = 100x - 2x ^ 2
We derive:
A '(x) = 100 - 4x
We equal zero and clear x:
0 = 100 - 4x
4x = 100
x = 25 feet
The other dimension is:
y = 100-2x
y = 100-2 (25)
y = 100-50
y = 50 feet
The area will be:
A = (25) * (50)
A = 1250 feet ^ 2
Answer:
the maximum area that the farmer can enclose with 100 ft of fence is:
A = 1250 feet ^ 2
The dimensions of the garden to give this area should be:
x = 25 feet
y = 50 feet
It can be simplified by dividing 10 on both the numerator and the denominator.
100/10=10
2670/10=267
So the simplified answer is 10/267.
1) If the hats cost $12.50 each and the materials cost $5.50, then the fashion designer makes ($12.50 - $5.50 =) $7 per hat. So, to work out how many hats you must make, you need to divide how much you spend on advertising by how much you make per hat so, $1,400 ÷ $7 = 200 hats.
$12.50 - $5.50 = $7
$1,400 ÷ $7 = 200 hats
and your variable and equation is:
y = number of hats needed to sell
advertising = earnings of 1 hat x number of hats
1,400 = 7y
1,400÷7 = y
200 = y
∴ The fashion designer must make and sell 200 hats to break even and get back her $1,400 spent on advertising.
2) So, you do the same on this one as well. If he makes $2 per book, and binding and packaging cost $0.80, then you need to $2 - $0.80 to find how much each book will make you, the answer is $1.20 per book. Then you need to $864 ÷ $1.20 which equals 720 books.
$2 - $0.80 = $1.20
$864 ÷ $1.20 = 720 books.
and your variable and equation would be:
y = unknown number of books needed to sell
initial costs = earnings of 1 book x number of books
864 = 1.20y
864 ÷ 1.20 = y
720 = y
∴ The puzzle expert must sell 720 books to break even and earn back his initial costs of $864.
** I hope that's what you meant (putting it in an algebraic equation) and I hope is correct **