Answer:
hope this helps you out good luck
Answer:
![y=4x^2-8x-4](https://tex.z-dn.net/?f=y%3D4x%5E2-8x-4)
Step-by-step explanation:
<u>Quadratic Function</u>
The quadratic function can be expressed in the following form:
![y=a(x-x_1)(x-x_2)](https://tex.z-dn.net/?f=y%3Da%28x-x_1%29%28x-x_2%29)
Where a is a real number different from 0, and x1, x2 are the roots or zeroes of the function.
From the conditions stated in the problem, we know
x_1=1+\sqrt{2}, \ x_1=1-\sqrt{2}
Substitute in the general formula above:
![y=a[x-(1+\sqrt{2})][x-(1-\sqrt{2})]](https://tex.z-dn.net/?f=y%3Da%5Bx-%281%2B%5Csqrt%7B2%7D%29%5D%5Bx-%281-%5Csqrt%7B2%7D%29%5D)
Operate the indicated product
![y=a(x^2-2x-1)](https://tex.z-dn.net/?f=y%3Da%28x%5E2-2x-1%29)
To find the value of a, we use the y-intercept which is the value of y when x=0, thus
![y=a(0^2-2(0)-1)=-4](https://tex.z-dn.net/?f=y%3Da%280%5E2-2%280%29-1%29%3D-4)
It follows that
![a=4](https://tex.z-dn.net/?f=a%3D4)
Thus, the required quadratic function is
![y=4(x^2-2x-1)](https://tex.z-dn.net/?f=y%3D4%28x%5E2-2x-1%29)
Or, equivalently
![\boxed{y=4x^2-8x-4}](https://tex.z-dn.net/?f=%5Cboxed%7By%3D4x%5E2-8x-4%7D)
Answer:
The width of the trampoline is 8 feet.
Step-by-step explanation:
Area of rectangular trampoline = 112 ![ft^{2}](https://tex.z-dn.net/?f=ft%5E%7B2%7D)
let the width of the trampoline be represented by w, but,
length = w + 6
Given that the situation has been represented by the equation;
+ 6w - 112 = 0
+ 14w - 8w - 112 = 0
(
+ 14w) - (8w + 112)
w(w + 14) - 8(w + 14)
(w + 14)(w - 8)
So that;
w + 14 = 0 or w - 8 = 0
w = -14 or w = 8
Thus, w = 8
The width of the trampoline is 8 feet.
They own a total of 120 CDs.
GIVEN:
Ella: ratio of rock music to total CDs that she owns 25/40
Paolo: has 50 rock music CDs. The ratio of rock music to total CD is equal to Ella's ratio.
Proportion: a/b = c/d where ad = bc
25/40 = 50/x
25x = 40 * 50
25x = 2000
25x / 25 = 2000 / 25
x = 80 total of Paolo's CDs
Total of Ella's CDs = 40
Total of Paolo's CDs =<u> 80</u>
Total CDs in all 120
Tan(33) = 0.6494
This is just a problem for your calculator. Most put the number in as
Tan(
3
3
=