Answer: The value of x is 3.5
Explanation:
<u>Equation</u>:
y = 2x - 7
When the equation's Line intersects the x-axis, the value of y shall be always 0
<u>Insert y = 0, to find x intercept</u>
⇒ 0 = 2x - 7
⇒ 2x - 7 = 0
⇒ 2x = 7
⇒ x = 3.5
So coordinates: (x, y) → (3.5, 0)
Answer:
![\displaystyle -x^3+10x^2-48x+64](https://tex.z-dn.net/?f=%5Cdisplaystyle%20-x%5E3%2B10x%5E2-48x%2B64)
Step-by-step explanation:
We want to find the minimum-degree polynomial with real coefficients and zeros at:
![x= 4+4i\text{ and } x = 2](https://tex.z-dn.net/?f=x%3D%204%2B4i%5Ctext%7B%20and%20%7D%20%20x%20%3D%202)
As well as a <em>y-</em>intercept of 64.
By the Complex Root Theorem, if <em>a</em> + <em>b</em>i is a root, then <em>a</em> - <em>b</em>i is also a root.
So, a third root will be 4 - 4i.
The factored form of a polynomial is given by:
![P(x)=a(x-p)(x-q)...](https://tex.z-dn.net/?f=P%28x%29%3Da%28x-p%29%28x-q%29...)
Where <em>a</em> is the leading coefficient and <em>p</em> and <em>q</em> are the zeros. More factors can be added if necessary.
Substitute:
![P(x)=a(x-(2))(x-(4+4i))(x-(4-4i))](https://tex.z-dn.net/?f=P%28x%29%3Da%28x-%282%29%29%28x-%284%2B4i%29%29%28x-%284-4i%29%29)
Since we want the minimum degree, we won't need to add any exponents.
Expand the second and third factors:
![\displaystyle \begin{aligned} (x-(4+4i))(x-(4-4i))&=(x-4-4i)(x-4+4i) \\ &= x(x-4-4i)-4(x-4-4i)+4i(x-4-4i)\\ &=x^2-4x-4ix-4x+16+16i+4ix-16i-16i^2\\ &= x^2-8x+32\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20%28x-%284%2B4i%29%29%28x-%284-4i%29%29%26%3D%28x-4-4i%29%28x-4%2B4i%29%20%5C%5C%20%26%3D%20x%28x-4-4i%29-4%28x-4-4i%29%2B4i%28x-4-4i%29%5C%5C%20%26%3Dx%5E2-4x-4ix-4x%2B16%2B16i%2B4ix-16i-16i%5E2%5C%5C%20%26%3D%20x%5E2-8x%2B32%5Cend%7Baligned%7D)
Hence:
![P(x)=a(x-2)(x^2-8x+32)](https://tex.z-dn.net/?f=P%28x%29%3Da%28x-2%29%28x%5E2-8x%2B32%29)
Lastly, we need to determine <em>a</em>. Since the <em>y-</em>intercept is <em>y</em> = 64, this means that when <em>x</em> = 0, <em>y</em> = 64. Thus:
![64=a(0-2)(0^2-8(0)+32)](https://tex.z-dn.net/?f=64%3Da%280-2%29%280%5E2-8%280%29%2B32%29)
Solve for <em>a: </em>
![-64a=64\Rightarrow a=-1](https://tex.z-dn.net/?f=-64a%3D64%5CRightarrow%20a%3D-1)
Our factored polynomial is:
![P(x)=-(x-2)(x^2-8x+32)](https://tex.z-dn.net/?f=P%28x%29%3D-%28x-2%29%28x%5E2-8x%2B32%29)
Finally, expand:
![\displaystyle \begin{aligned} P(x) &=-(x^2(x-2)-8x(x-2)+32(x-2)) \\&=-(x^3-2x^2-8x^2+16x+32x-64)\\&=-(x^3-10x^2+48x-64)\\&= -x^3+10x^2-48x+64\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20P%28x%29%20%26%3D-%28x%5E2%28x-2%29-8x%28x-2%29%2B32%28x-2%29%29%20%5C%5C%26%3D-%28x%5E3-2x%5E2-8x%5E2%2B16x%2B32x-64%29%5C%5C%26%3D-%28x%5E3-10x%5E2%2B48x-64%29%5C%5C%26%3D%20-x%5E3%2B10x%5E2-48x%2B64%5Cend%7Baligned%7D)
Answer:
32w+10
Step-by-step explanation:
add all the w's then just add 10
Answer:
The answer is 350.
Step-by-step explanation:
Sorry, I tried to answer this question before but I had to do some family stuff, so I can't really give a detailed explanation. But in order to find it you need to know how to work with proportions or samples in probability.
Once again sorry.