Answer:
2
Step-by-step explanation:
16f - 24 = 4f
12f = 24
f = 2
Answer:
Step-by-step explanation:
We can see the lines are parallel
The function f(x) has y-intercept of 2 at point (2, 0) and the function g(x) has y-intercept of -3 at point of (-3, 0)
If f(x) = mx + 2, then g(x) = mx - 3
<u>The value of k is the difference of y-intercepts as slopes are same due to lines being parallel:</u>
- g(x) = f(x) + k
- k = g(x) - f(x)
- k = (mx - 3) - (mx + 2)
- k = -3 - 2
- k = -5
So the answer is k = -5
Answer:
![\displaystyle d \approx 10.3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%5Capprox%2010.3)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Cartesian Planes
<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%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify points</em>
(-5, 7)
(4, 2)
<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{(4 + 5)^2 + (2 - 7)^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B%284%20%2B%205%29%5E2%20%2B%20%282%20-%207%29%5E2%7D)
- [√Radical] (Parenthesis) Simplify:
![\displaystyle d = \sqrt{9^2 + (-5)^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B9%5E2%20%2B%20%28-5%29%5E2%7D)
- [√Radical] Evaluate exponents:
![\displaystyle d = \sqrt{81 + 25}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B81%20%2B%2025%7D)
- [√Radical] Simplify:
![\displaystyle d = \sqrt{106}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20%5Csqrt%7B106%7D)
- [Distance] Approximate:
![\displaystyle d \approx 10.3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%5Capprox%2010.3)
Answer: 1
Step-by-step explanation:
Rewrite as (i^4)^6
Rewrite i^4 as 1
Rewrite i^4 as (i^2) ^2
((i^2)) ^2)6
Rewrite i^2 as -1
((-1) ^2) 6
Raise -1 to the power of 2
1^6
One to any power is 1.