The range is: B. {12, 4, -6}
Step-by-step explanation:
Given
12x + 6y = 24
Here x is the input and y is the output
So,
Replacing y with f(x)
![12x +6f(x) = 24\\6f(x) = 24 - 12x\\\frac{6f(x)}{6} = \frac{24-12x}{6}\\f(x) = \frac{24-12x}{6}](https://tex.z-dn.net/?f=12x%20%2B6f%28x%29%20%3D%2024%5C%5C6f%28x%29%20%3D%2024%20-%2012x%5C%5C%5Cfrac%7B6f%28x%29%7D%7B6%7D%20%3D%20%5Cfrac%7B24-12x%7D%7B6%7D%5C%5Cf%28x%29%20%3D%20%5Cfrac%7B24-12x%7D%7B6%7D)
Domain = {-4, 0, 5},
We will put the elements of domain, one by one, to find range
![f(-4) = \frac{24-12(-4)}{6}\\=\frac{24+48}{6}\\= \frac{72}{6}\\=12\\\\f(0) = \frac{24-12(0)}{6}\\=\frac{24}{6}\\= 4\\\\f(5) = \frac{24-12(5)}{6}\\=\frac{24-60}{6}\\=\frac{-36}{6}\\=-6](https://tex.z-dn.net/?f=f%28-4%29%20%3D%20%5Cfrac%7B24-12%28-4%29%7D%7B6%7D%5C%5C%3D%5Cfrac%7B24%2B48%7D%7B6%7D%5C%5C%3D%20%5Cfrac%7B72%7D%7B6%7D%5C%5C%3D12%5C%5C%5C%5Cf%280%29%20%3D%20%5Cfrac%7B24-12%280%29%7D%7B6%7D%5C%5C%3D%5Cfrac%7B24%7D%7B6%7D%5C%5C%3D%204%5C%5C%5C%5Cf%285%29%20%3D%20%5Cfrac%7B24-12%285%29%7D%7B6%7D%5C%5C%3D%5Cfrac%7B24-60%7D%7B6%7D%5C%5C%3D%5Cfrac%7B-36%7D%7B6%7D%5C%5C%3D-6)
Hence,
The range is: B. {12, 4, -6}
Keywords: Range, Domain, functions
Learn more about functions at:
#LearnwithBrainly
Perimeter of rectangle is calculated by taking the sum of all the sides of the rectangle. In rectangles the 2 opposite sides are equal
length - 3x - 1
breadth - 3x - 3
the formula used to calculate perimeter for rectangle
perimeter = (2 x length) + (2 x breadth)
substituting length and breadth
perimeter = {2 x (3x - 1)} + {2 x (3x - 3)}
= 6x - 2 + 6x - 6
= 12x - 8
therefore correct answer is
<span>b.12x-8</span>
Answer:
debt
Step-by-step explanation: hope this helps
Answer:
The shape of the data in the histogram is Symmetrical.
Step-by-step explanation:
This is because the distribution, or data set is the same to the left and right of the center point.
Answer:
x = 8√2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Trigonometry</u>
- [Right Triangles Only]: Pythagorean Theorem: a² + b² = c²
Step-by-step explanation:
<u>Step 1: Define</u>
We are given a right triangle. We can use PT to solve for the missing length.
<u>Step 2: Identify Variables</u>
Leg <em>a</em> = 8
Leg <em>b</em> = 8
Hypotenuse <em>c</em> = <em>x</em>
<u>Step 3: Solve for </u><em><u>x</u></em>
- Substitute [PT]: 8² + 8² = x²
- Exponents: 64 + 64 = x²
- Add: 128 = x²
- Isolate <em>x</em>: 8√2 = x
- Rewrite: x = 8√2