There are three outcomes of 4 out of eighteen outcomes, so the fraction of angle of spinner numbered 4 is
Answer:
![x=\frac{-(-2)\±\sqrt{(-2)^2-4(3)(0)} }{2(3)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-2%29%5C%C2%B1%5Csqrt%7B%28-2%29%5E2-4%283%29%280%29%7D%20%7D%7B2%283%29%7D)
Step-by-step explanation:
Quadratic formula:
when the equation is ![0=ax^2+bx+c](https://tex.z-dn.net/?f=0%3Dax%5E2%2Bbx%2Bc)
The given equation is
. Let's first arrange this so its format looks like
:
![1=-2x+3x^2+1](https://tex.z-dn.net/?f=1%3D-2x%2B3x%5E2%2B1)
![1=3x^2-2x+1](https://tex.z-dn.net/?f=1%3D3x%5E2-2x%2B1)
Subtract 1 from both sides of the equation
![1-1=3x^2-2x+1-1\\0=3x^2-2x+0](https://tex.z-dn.net/?f=1-1%3D3x%5E2-2x%2B1-1%5C%5C0%3D3x%5E2-2x%2B0)
Now, we can easily identify 3 as a, -2 as b and 0 as c. Plug these into the quadratic formula:
![x=\frac{-b\±\sqrt{b^2-4ac} }{2a}\\x=\frac{-(-2)\±\sqrt{(-2)^2-4(3)(0)} }{2(3)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D%5C%5Cx%3D%5Cfrac%7B-%28-2%29%5C%C2%B1%5Csqrt%7B%28-2%29%5E2-4%283%29%280%29%7D%20%7D%7B2%283%29%7D)
I hope this helps!
Answer:
Step-by-step explanation:
P = x^2 + 6
![(x^2+6)^2 - 21 = 4x^2 + 24\\(x^2+6)^2 - 4x^2 - 45 = 0](https://tex.z-dn.net/?f=%28x%5E2%2B6%29%5E2%20-%2021%20%3D%204x%5E2%20%2B%2024%5C%5C%28x%5E2%2B6%29%5E2%20-%204x%5E2%20-%2045%20%3D%200)
Solving for 4x^2:
P = x^2 +6
P - 6 = x^2
4(P - 6) = 4x^2
Substitution:
![p^2 - 4p - 24 - 45 = 0\\p^2 -4p - 69 = 0](https://tex.z-dn.net/?f=p%5E2%20-%204p%20-%2024%20-%2045%20%3D%200%5C%5Cp%5E2%20-4p%20-%2069%20%3D%200)
Answer:
<em>Yes</em>
Step-by-step explanation:
g(x) = -
x +
y = -
x +
....... <em>(1)</em>
<em>(1)</em> × 4
4y = - x + 1
x = - 4y + 1
y = - 4x + 1
f(x) = - 4x + 1
∴ f(x) and g(x) <em>are inverses</em>
Answer:
4,800 loaves.
Step-by-step explanation:
Solve by utilizing ratios and cross-multiplication.