Answer:
x = 40.7057°
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Trigonometry</u>
- [Right Triangle Only] sin∅ = opposite over hypotenuse
Step-by-step explanation:
<u>Step 1: Define</u>
We have a right triangle. We can use trig to find the angle.
<u>Step 2: Identify Variables</u>
Angle = <em>x</em>
Opposite = 15
Hypotenuse = 23
<u>Step 3: Find Angle </u><em><u>x</u></em>
- Substitute: sinx° = 15/23
- Inverse: x° = sin⁻¹(15/23)
- Evaluate: x = 40.7057°
To solve this problem, let us first assign some
variables. Let us say that:
x = pigs
y = chickens
z = ducks
From the problem statement, we can formulate the
following equations:
1. y + z = 30 --->
only chicken and ducks have feathers
2. 4 x + 2 y + 2 z = 120 --->
pig has 4 feet, while chicken and duck has 2 each
3. 2 x + 2 y + 2 z = 90 --->
each animal has 2 eyes only
Rewriting equation 1 in terms of y:
y = 30 – z
Plugging this in equation 2:
4 x + 2 (30 – z) + 2 z = 120
4 x + 60 – 2z + 2z = 120
4 x = 120 – 60
4 x = 60
x = 15
From the given choices, only one choice has 15 pigs. Therefore
the answers are:
She has 15 pigs, 12 chickens, and 18 ducks.
Answer:
y= 8(x-5)² + 6
Step-by-step explanation:
Parabolas have two equation forms, namely; the standard and vertex form.
In the vertex form, y = a(x - h)² + k, the variables h and k are the coordinates of the parabola's vertex.
In this case; a=8, h =5, and k=6
Therefore;
The vertex equation will be
y= 8(x-5)² + 6
Answer: Hello your question is poorly written attached below is the complete question
answer:
![y = \left[\begin{array}{ccc}-4\\-11\\5\end{array}\right]](https://tex.z-dn.net/?f=y%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%5C%5C-11%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
![x = \left[\begin{array}{ccc}16\\12\\-40\end{array}\right]](https://tex.z-dn.net/?f=x%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D16%5C%5C12%5C%5C-40%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
attached below is the detailed solution using LU factorization
