Answer:
x ≈ 25.5°
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] tanθ = opposite over adjacent
Step-by-step explanation:
<u>Step 1: Identify Variables</u>
Angle θ = <em>x</em>°
Opposite Leg = 10
Hypotenuse = 21
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute [tangent]: tanx° = 10/21
- Inverse trig: x° = tan⁻¹(10/21)
- Evaluate: x = 25.4633°
- Round: x ≈ 25.5°
Write the coeeficientes of the polynomial in order:
| 1 - 5 6 - 30
|
|
|
------------------------
After some trials you probe with 5
| 1 - 5 6 - 30
|
|
5 | 5 0 30
-----------------------------
1 0 6 0 <---- residue
Given that the residue is 0, 5 is a root.
The quotient is x^2 + 6 = 0, which does not have a real root.
Therefore, 5 is the only root. You can prove it by solving the polynomial x^2 + 6 = 0.
I think the answer is B.
But my second choice would be C.
<h3>
Answer: 126</h3>
=====================================================
Work Shown:
Let x and y be the two numbers.
We're given x = 162 and the variable y is unknown.
We're also given LCM = 1134 and HCF = 18
So,
LCM = (x*y)/HCF
1134 = 162*y/18
1134 = (162/18)y
1134 = 9y
9y = 1134
y = 1134/9
y = 126
The other number is 126
---------------------
Notice that
showing that 18 is the highest common factor (HCF) of the numbers 162 and 126. This partially confirms the answer.
Now let,
- A = multiples of 162
- B = multiples of 126
So,
- A = 162, 324, 486, 648, 810, 972, 1134, 1296, ...
- B = 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, ...
We see that 1134 is in each list of multiples and the smallest such common item. So the lowest common multiple (LCM) of 162 and 126 is 1134. This helps fully confirm the answer.
Answer:
How many groups are there or how many people are in each group
Step-by-step explanation:
