The area of a shape is the amount of space it can occupy.
<em>The number of isosceles triangle in the grid is: </em>
<em />
The dimension of the grid is given as:
Calculate the area
The area of each isosceles triangle is given as:
The number (n) of the triangle in an x-by-x grid is:
So, we have:
Express as products
Hence, the number of isosceles triangle in the grid is:
Read more about areas at:
brainly.com/question/16418397
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)
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![-\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)
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Answer:
For equation 21-b=11 given in the statement
the answer is b=10
Step-by-step explanation:
This is the equation: 21-b=11
If we sum '-21' to both sides of equation, we have
21-b-21=11-21, which leaves us to: -b=-10
Now lets multiply the equation from above by '-1', we obtain that b=10
