If there are 30 days and 15 are sunny then 50% are sunny.
Answer:
$996
Step-by-step explanation:
The rectangular plot has an area that is the product of its length and width. We are given the width as 12 feet, and the area as 240 ft², so we can find the length from ...
... A = L×W
... 240 ft² = L×(12 ft)
... 240 ft²/(12 ft) = L = 20 ft
Opposite sides of the rectangle are the same length, so the cost of fence for a side of a given length will be the sum of the costs of the opposites sides.
The 12 ft side has one segment that is $18 per foot, and one that is $15 per foot. For the 20 ft sides, both are $15 per foot. Then the total cost can be figured from ...
... (12 ft)·($18/ft + $15/ft) + (20 ft)·($15/ft +$15/ft) = 12·$33 +20·$30 = $996
'Vertex form', having just googled it, is another name for completing the square, which I have done extensively at school. This involved converting:
f(x) = ax^2 + bx + c --> f(x) = a(x-b)^2 + c
In the completed-square form, (b, c) are the co-ordinates of the vertex (which is the maximum/minimum point). So for part a:
- Here is the original
f(x) = x^2 + 12x + 11
- Halve the x-coefficient (the number before x) and use it as -b in the vertex form described above. You must then calculate the square of this number and minus it at the end because when you multiply it out, this is the surplus you will make along with x^2 + 12x:
f(x) = (x + 6)^2 - 36 + 11
- Tidy this up by collecting the constant (just number) terms together:
f(x) = (x + 6)^2 - 25
- Using the form a(x - b)^2 + c, we can work out that b = -6 (because -b = 6) and c = -25. This gives us the vertex (-6, -25) which is a minimum point because the graph is a positive quadratic, giving us the characteristing 'U' shape which has a bottom. If it were a negative quadratic (denoted by a negative x^2 coefficient), the vertex will be a maximum point because it has an 'n' shape instead.
- To solve the equation from here, make the function equal to zero:
(x + 6)^2 - 25 = 0
- Then take 25 to the other side:
(x + 6)^2 = 25
- Next, square-root both sides:
x + 6 = <span>±5
- Rearrange to finish:
x = -6 </span><span>± 5 = -1 or -11
- Therefore, the roots (solutions) to the equation x^2 + 12x + 11 = 0 are x = -1 or -11
This method will work the same for the other equations up there too, so I will leave them for you to do.
I hope this helps
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-3(2x-9)=-3
We have to solve this equation.
-3(2x-9)=-3
-6x+27=-3
-6x=-3-27
-6x=-30
x=(-30)/(-6)=5
answer: x=5
Answer:
Step-by-step explanation:
