Answer:
Step-by-step explanation:
y = (x² - 8x) + 10
Complete the square
coefficient of the x term: -8
divide it in half: -4
square it: (-4)² = 4²
use 4² to complete the square and keep the equation balanced:
y = (x²-8x + 4²) - 4² + 10
y = (x-4)² - 6
Answer:
Step-by-step explanation:
<u>Given rectangle ABCD with coordinates:</u>
- A(1, 2), B(3, 2), C(3, 4), D(1, 4)
The rectangle is rotated 90 degrees clockwise.
<u>The rule for this rotation is:</u>
<u>Point B mapped to B' as per above rule:</u>
Answer:
The function (gof)(x) is;
![(g\circ f)(x)=8x^2+36x+49](https://tex.z-dn.net/?f=%28g%5Ccirc%20f%29%28x%29%3D8x%5E2%2B36x%2B49)
Explanation:
Given the functions;
![\begin{gathered} f(x)=2x+3 \\ g(x)=2x^2+6x+13 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20f%28x%29%3D2x%2B3%20%5C%5C%20g%28x%29%3D2x%5E2%2B6x%2B13%20%5Cend%7Bgathered%7D)
Solving for the function;
![(g\circ f)(x)=g(f(x))](https://tex.z-dn.net/?f=%28g%5Ccirc%20f%29%28x%29%3Dg%28f%28x%29%29)
so, we have;
![\begin{gathered} g(f(x))=2(f(x))^2+6(f(x))+13 \\ g(f(x))=2(2x+3)^2+6(2x+3)+13 \\ g(f(x))=2(4x^2+12x+9)^{}+6(2x)+6(3)+13 \\ g(f(x))=8x^2+24x+18^{}+12x+18+13 \\ g(f(x))=8x^2+24x^{}+12x+18+18+13 \\ g(f(x))=8x^2+36x+49 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20g%28f%28x%29%29%3D2%28f%28x%29%29%5E2%2B6%28f%28x%29%29%2B13%20%5C%5C%20g%28f%28x%29%29%3D2%282x%2B3%29%5E2%2B6%282x%2B3%29%2B13%20%5C%5C%20g%28f%28x%29%29%3D2%284x%5E2%2B12x%2B9%29%5E%7B%7D%2B6%282x%29%2B6%283%29%2B13%20%5C%5C%20g%28f%28x%29%29%3D8x%5E2%2B24x%2B18%5E%7B%7D%2B12x%2B18%2B13%20%5C%5C%20g%28f%28x%29%29%3D8x%5E2%2B24x%5E%7B%7D%2B12x%2B18%2B18%2B13%20%5C%5C%20g%28f%28x%29%29%3D8x%5E2%2B36x%2B49%20%5Cend%7Bgathered%7D)
Therefore, the function (gof)(x) is;
![(g\circ f)(x)=8x^2+36x+49](https://tex.z-dn.net/?f=%28g%5Ccirc%20f%29%28x%29%3D8x%5E2%2B36x%2B49)
Answer:
The mean of the density curve is greater than the median.
Step-by-step explanation:
The distribution is skewed right. So the mean is greater than the median. And of course, the curve is not symmetrical.
Answer:
no its a scalene triangle
Step-by-step explanation: