Answer:
About 2.6 pizza's each. (round it however you see fit)
Step-by-step explanation:
Hope this helps!! Have a good day and remember to be tiger fierce!! :)
Step-by-step explanation:
(x + 8)(x - 1) = x^2 - x + 8x - 8 = x^2 + 7x - 8.
Hence a = 1, b = 7, c = -8. (Options A, D and E)
Answer:
1353 ft
Step-by-step explanation:
The cliff height and the distance from its base to the boat form the legs of a right triangle. The cliff height is the leg opposite the elevation angle, and the distance to the boat is the leg adjacent. Given these two legs of the triangle, the tangent relation seems useful:
Tan = Opposite/Adjacent
We want to find the cliff height (opposite), so we can multiply this equation by Adjacent:
Opposite = Adjacent×Tan
cliff height = (2994 ft)(tan(24°19')) ≈ 1353 ft
The cliff is about 1353 feet high.
An hour and 15 minutes I believe which would be 1 and 1/4
'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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