Answer:
Step-by-step explanation:
Answer:
![\large\boxed{-\bigg[(x-3)^2+2x\bigg]+1}\\\\\boxed{-x^2+4x-8}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B-%5Cbigg%5B%28x-3%29%5E2%2B2x%5Cbigg%5D%2B1%7D%5C%5C%5C%5C%5Cboxed%7B-x%5E2%2B4x-8%7D)
Step-by-step explanation:
![f(x)=(x-3)^2+2x\\\\g(x)=-x+1\\\\g\ \circ\ f\to\text{put f(x) instead of x in the function g(x)}:\\\\(g\ \circ\ f)(x)=-\bigg[\underbrace{(x-3)^2+2x}_{x}\bigg]+1](https://tex.z-dn.net/?f=f%28x%29%3D%28x-3%29%5E2%2B2x%5C%5C%5C%5Cg%28x%29%3D-x%2B1%5C%5C%5C%5Cg%5C%20%5Ccirc%5C%20f%5Cto%5Ctext%7Bput%20f%28x%29%20instead%20of%20x%20in%20the%20function%20g%28x%29%7D%3A%5C%5C%5C%5C%28g%5C%20%5Ccirc%5C%20f%29%28x%29%3D-%5Cbigg%5B%5Cunderbrace%7B%28x-3%29%5E2%2B2x%7D_%7Bx%7D%5Cbigg%5D%2B1)
-----------------------------------------
![-\bigg[(x-3)^2+2x\bigg]+1=-(x-3)^2-2x+1\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=-(x^2-(2)(x)(3)+3^2)-2x+1=-(x^2-6x+9)-2x+1\\\\=-x^2-(-6x)-9-2x+1=-x^2+6x-9-2x+1\\\\\text{combine like terms}\\\\=-x^2+(6x-2x)+(-9+1)=-x^2+4x-8](https://tex.z-dn.net/?f=-%5Cbigg%5B%28x-3%29%5E2%2B2x%5Cbigg%5D%2B1%3D-%28x-3%29%5E2-2x%2B1%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%28a-b%29%5E2%3Da%5E2-2ab%2Bb%5E2%5C%5C%5C%5C%3D-%28x%5E2-%282%29%28x%29%283%29%2B3%5E2%29-2x%2B1%3D-%28x%5E2-6x%2B9%29-2x%2B1%5C%5C%5C%5C%3D-x%5E2-%28-6x%29-9-2x%2B1%3D-x%5E2%2B6x-9-2x%2B1%5C%5C%5C%5C%5Ctext%7Bcombine%20like%20terms%7D%5C%5C%5C%5C%3D-x%5E2%2B%286x-2x%29%2B%28-9%2B1%29%3D-x%5E2%2B4x-8)
-----------------------------------
Answer:
Step-by-step explanation:
- a. -9+2, in this case, it is -7 because you take the bigger number and subtract it by the lower number. If the bigger number is negative your answer will be negative, if the bigger number is positive it will be positive it is just really a basic subtraction problem just add the sign.
- b. In multiplication +++=+ ++-=- and a -+-=+ do your problem without thinking about the signs and then add the signs with the formula I showed you.
Hope this helps :)!
Start off by using the Pythagorean Theorem: a^2 + b^2 = c^2
12^2 + 35^2 = 37^2
144 + 1,225 = 1,369
1,369 = 1,369
If the left side equals the right side than it is a right triangle.
Your answer is: Yes
Have an amazing day and stay hopeful!
