Answer:
165 cards left
Step-by-step explanation:
x + 221 = 386
-221 from both sides
x = 165
Answer:
Step-bgo to the doctor y-step explanation:
Answer:
868.065
Step-by-step explanation:
198.040 ÷ 98.1 + 100 x 4.3
= 2.0188 + 100 x 4.3
= 201.8756 x 4.3
= 868.065
Answer:
![x_1=-2,\ x_2=x_3=3\\ \\(x+2)(x-3)^2=0](https://tex.z-dn.net/?f=x_1%3D-2%2C%5C%20x_2%3Dx_3%3D3%5C%5C%20%5C%5C%28x%2B2%29%28x-3%29%5E2%3D0)
Step-by-step explanation:
Consider the equation
![x^3-4x^2-3x+18=0](https://tex.z-dn.net/?f=x%5E3-4x%5E2-3x%2B18%3D0)
The zeros of the equation can be the divisors of 18:
![\pm 1,\ \pm2,\ \pm3,\ \pm 6,\ \pm 9,\ \pm 18](https://tex.z-dn.net/?f=%5Cpm%201%2C%5C%20%5Cpm2%2C%5C%20%5Cpm3%2C%5C%20%5Cpm%206%2C%5C%20%5Cpm%209%2C%5C%20%5Cpm%2018)
Check them:
![1^3-4\cdot 1^2-3\cdot 1+18=1-4-3+18=10\neq 0\\ \\(-1)^3-4\cdot (-1)^2-3\cdot (-1)+18=-1-4+3+18=16\neq 0\\ \\2^3-4\cdot 2^2-3\cdot 2+18=8-16-6+18=4\neq 0\\ \\(-2)^3-4\cdot (-2)^2-3\cdot (-2)+18=-8-16+6+18=0](https://tex.z-dn.net/?f=1%5E3-4%5Ccdot%201%5E2-3%5Ccdot%201%2B18%3D1-4-3%2B18%3D10%5Cneq%200%5C%5C%20%5C%5C%28-1%29%5E3-4%5Ccdot%20%28-1%29%5E2-3%5Ccdot%20%28-1%29%2B18%3D-1-4%2B3%2B18%3D16%5Cneq%200%5C%5C%20%5C%5C2%5E3-4%5Ccdot%202%5E2-3%5Ccdot%202%2B18%3D8-16-6%2B18%3D4%5Cneq%200%5C%5C%20%5C%5C%28-2%29%5E3-4%5Ccdot%20%28-2%29%5E2-3%5Ccdot%20%28-2%29%2B18%3D-8-16%2B6%2B18%3D0)
So, x=-2 is zero. Now
![x^3-4x^2-3x+18\\ \\=x^3+2x^2-6x^2-12x+9x+18\\ \\=x^2(x+2)-6x(x+2)+9(x+2)\\ \\=(x+2)(x^2-6x+9)\\ \\=(x+2)(x-3)^2](https://tex.z-dn.net/?f=x%5E3-4x%5E2-3x%2B18%5C%5C%20%5C%5C%3Dx%5E3%2B2x%5E2-6x%5E2-12x%2B9x%2B18%5C%5C%20%5C%5C%3Dx%5E2%28x%2B2%29-6x%28x%2B2%29%2B9%28x%2B2%29%5C%5C%20%5C%5C%3D%28x%2B2%29%28x%5E2-6x%2B9%29%5C%5C%20%5C%5C%3D%28x%2B2%29%28x-3%29%5E2)
Thus, x=3 is the second root (of multiplicity 2)