Answer:
![\displaystyle d = 2\sqrt{13}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%202%5Csqrt%7B13%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
<u>Algebra II</u>
- Distance Formula:
![\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
Point (11, 4) → x₁ = 11, y₁ = 4
Point (5, 8) → x₂ = 5, y₂ = 8
<u>Step 2: Find distance </u><em><u>d</u></em>
Simply plug in the 2 coordinates into the distance formula to find distance <em>d</em>
- Substitute in points [Distance Formula]:
![\displaystyle d = \sqrt{(5-11)^2+(8-4)^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B%285-11%29%5E2%2B%288-4%29%5E2%7D)
- [√Radical] (Parenthesis) Subtract:
![\displaystyle d = \sqrt{(-6)^2+(4)^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B%28-6%29%5E2%2B%284%29%5E2%7D)
- [√Radical] Evaluate exponents:
![\displaystyle d = \sqrt{36+16}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B36%2B16%7D)
- [√Radical] Add:
![\displaystyle d = \sqrt{52}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B52%7D)
- [√Radical] Simplify:
![\displaystyle d = 2\sqrt{13}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%202%5Csqrt%7B13%7D)
parallel: g(x) = -5/3x + 1
perpendicular: h(x) = 3/5x - 5
neither: j(x) = 2x + 3
37
Line up the data, separate into quarters
Take the highest number in the 3rd quarter from the lowest in the 2nd
The function f(x) is vertically compressed to form g(x) while the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
<h3>How to compare both functions?</h3>
The functions are given as
f(x) =x^2
g(x) =3x^2
h(x) = -3x^2
Substitute f(x) =x^2 in g(x) =3x^2 and h(x) = -3x^2
g(x) =3f(x)
h(x) = -3f(x)
This means that the function f(x) is vertically compressed to form g(x)
Also, the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
See attachment for the functions g(x) and h(x)
Also, functions f(x) and g(x) have the same domain and range
While functions f(x) and h(x) have the same domain but different range
The complete table is:
x -2 -1 0 1 2
g(x) 12 3 0 3 12
h(x) -12 -3 0 -3 -12
Read more about function transformation at:
brainly.com/question/13810353
#SPJ1