X² - 8x = -10
to have a complete square, we must have this format:
a² + 2ab + b²
a² = x²
2ab = -8x ⇒ 2(x)(-4)
b² = -4² = 16
x² - 8x + 16 = -10 + 16
x² - 8x + 16 = +6
(x-4)² - 6 = 0
Both sides must have an additional value of 16.
They could have assembled total 336 different possible crews.
<em><u>Explanation</u></em>
Total number of trained pilots is 9 and geologists is 4.
The crew should be consisted of 2 pilots and 1 geologist. That means, <u>2 pilots are chosen from total 9 and 1 geologist is chosen from total 4</u>.
Number of ways for choosing 2 pilots from 9
and
Number of ways for choosing 1 geologist from 4 ![=^4C_{1}= 4](https://tex.z-dn.net/?f=%3D%5E4C_%7B1%7D%3D%204)
So, the total possible number of different crews they could have assembled ![=84*4= 336](https://tex.z-dn.net/?f=%3D84%2A4%3D%20336)
Answer:
![\large\boxed{(f-g)(x)=-3x^2-x-4}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%28f-g%29%28x%29%3D-3x%5E2-x-4%7D)
Step-by-step explanation:
![(f-g)(x)=f(x)-g(x)](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3Df%28x%29-g%28x%29)
![f(x)=-4x^2-6x-1,\ g(x)=-x^2-5x+3\\\\(f-g)(x)=(-4x^2-6x-1)-(-x^2-5x+3)\\\\(f-g)(x)=-4x^2-6x-1-(-x^2)-(-5x)-3\\\\(f-g)(x)=-4x^2-6x-1+x^2+5x-3\qquad\text{combine like terms}\\\\(f-g)(x)=(-4x^2+x^2)+(-6x+5x)+(-1-3)\\\\(f-g)(x)=-3x^2-x-4](https://tex.z-dn.net/?f=f%28x%29%3D-4x%5E2-6x-1%2C%5C%20g%28x%29%3D-x%5E2-5x%2B3%5C%5C%5C%5C%28f-g%29%28x%29%3D%28-4x%5E2-6x-1%29-%28-x%5E2-5x%2B3%29%5C%5C%5C%5C%28f-g%29%28x%29%3D-4x%5E2-6x-1-%28-x%5E2%29-%28-5x%29-3%5C%5C%5C%5C%28f-g%29%28x%29%3D-4x%5E2-6x-1%2Bx%5E2%2B5x-3%5Cqquad%5Ctext%7Bcombine%20like%20terms%7D%5C%5C%5C%5C%28f-g%29%28x%29%3D%28-4x%5E2%2Bx%5E2%29%2B%28-6x%2B5x%29%2B%28-1-3%29%5C%5C%5C%5C%28f-g%29%28x%29%3D-3x%5E2-x-4)
David's pumpkin cost $8.22
His sister's pumpkin cost $4.98
They paid $13.20