Answer: A
<u>Step-by-step explanation:</u>
f(x) = x³ + 4x² + 7x + 6
possible rational roots are ±{1, 2, 3, 6}
Try x = -2
-2 | 1 4 7 6
<u>| ↓ -2 -4 -6</u>
1 2 3 0 ← remainder is 0 so x = -2 is a root ⇒ (x + 2) = 0
The factored polynomial x² + 2x + 3 = 0 is not factorable so use the quadratic formula to find the roots.
a=1, b=2, c=3
![x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
![x=\dfrac{-(2)\pm\sqrt{(2)^2-4(1)(3)} }{2(1)}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-%282%29%5Cpm%5Csqrt%7B%282%29%5E2-4%281%29%283%29%7D%20%7D%7B2%281%29%7D)
![x=\dfrac{-2\pm\sqrt{4-12} }{2}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-2%5Cpm%5Csqrt%7B4-12%7D%20%7D%7B2%7D)
![x=\dfrac{-2\pm\sqrt{-8} }{2}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-2%5Cpm%5Csqrt%7B-8%7D%20%7D%7B2%7D)
![x=\dfrac{-2\pm2i\sqrt{2}}{2}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-2%5Cpm2i%5Csqrt%7B2%7D%7D%7B2%7D)
![x = -1 \pm i\sqrt{2}](https://tex.z-dn.net/?f=x%20%3D%20-1%20%5Cpm%20i%5Csqrt%7B2%7D)
![x = -1 - i\sqrt{2}](https://tex.z-dn.net/?f=x%20%3D%20-1%20-%20i%5Csqrt%7B2%7D)
![x - (-1 - i\sqrt{2})=0](https://tex.z-dn.net/?f=x%20-%20%28-1%20-%20i%5Csqrt%7B2%7D%29%3D0)
The factors are:
Answer:
![A=x^2+12x+27\ units^2](https://tex.z-dn.net/?f=A%3Dx%5E2%2B12x%2B27%5C%20units%5E2)
Step-by-step explanation:
we know that
The area of the model is equal to the area of a rectangle
The area of a rectangle is equal to
![A=LW](https://tex.z-dn.net/?f=A%3DLW)
we have
![L=x+9\ units](https://tex.z-dn.net/?f=L%3Dx%2B9%5C%20units)
![W=x+3\ units](https://tex.z-dn.net/?f=W%3Dx%2B3%5C%20units)
substitute
![A=(x+9)(x+3)](https://tex.z-dn.net/?f=A%3D%28x%2B9%29%28x%2B3%29)
Apply distributive property
![A=x^2+3x+9x+27](https://tex.z-dn.net/?f=A%3Dx%5E2%2B3x%2B9x%2B27)
Combine like terms
![A=x^2+12x+27\ units^2](https://tex.z-dn.net/?f=A%3Dx%5E2%2B12x%2B27%5C%20units%5E2)
That means what is the least u would spend and most so like if someone asked you how much you would pay for a product, you may say $7-$10 and 7 would be the low range and 10
would be the high range
P ( A ) = 0.45 - probability that the land has oil,
P ( B ) = 0.8 - probability that the test predicts it
P ( A ∩ B ) = P ( A ) · P ( B ) = 0.45 · 0.8 = 0.36
Answer: The probability that the land has oil and the test predicts it is 36 %.