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Solve for \( x \):

[tex]\[ 3x = 6x - 2 \][/tex]

---

Efectúa las siguientes operaciones:

[tex]\[
\begin{array}{rr}
36^{\circ} 24^{\prime} 23^{\prime \prime} & 36^{\circ} 45^{\prime} 23^{\prime \prime} \\
+\quad 45^{\circ} 52^{\prime} 36^{\prime \prime} & +53^{\circ} 32^{\prime} 18^{\prime \prime} \\
\hline
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Sure! Let's solve these angle addition problems step by step.

### First Set of Angles

Given:
1. \(36^\circ 24' 23''\)
2. \(45^\circ 52' 36''\)

#### Step 1: Adding the Seconds
First, add the seconds:
[tex]\[23'' + 36'' = 59''\][/tex]

Since the total seconds are less than 60, there's no need to convert to minutes.

#### Step 2: Adding the Minutes
Now, add the minutes:
[tex]\[24' + 52' = 76'\][/tex]

Since \(76'\) exceeds \(60'\), we need to convert the excess into degrees:
[tex]\[76' = 1^\circ 16'\][/tex]
Thus, carry over \(1^\circ\) to the degrees, leaving \(16'\).

#### Step 3: Adding the Degrees
Finally, add the degrees:
[tex]\[36^\circ + 45^\circ + 1^\circ = 82^\circ\][/tex]

Putting it all together:
[tex]\[36^\circ 24' 23'' + 45^\circ 52' 36'' = 82^\circ 16' 59''\][/tex]

### Second Set of Angles

Given:
1. \(36^\circ 45' 23''\)
2. \(53^\circ 32' 18''\)

#### Step 1: Adding the Seconds
First, add the seconds:
[tex]\[23'' + 18'' = 41''\][/tex]

Since the total seconds are less than 60, there's no need to convert to minutes.

#### Step 2: Adding the Minutes
Now, add the minutes:
[tex]\[45' + 32' = 77'\][/tex]

Since \(77'\) exceeds \(60'\), we need to convert the excess into degrees:
[tex]\[77' = 1^\circ 17'\][/tex]
Thus, carry over \(1^\circ\) to the degrees, leaving \(17'\).

#### Step 3: Adding the Degrees
Finally, add the degrees:
[tex]\[36^\circ + 53^\circ + 1^\circ = 90^\circ\][/tex]

Putting it all together:
[tex]\[36^\circ 45' 23'' + 53^\circ 32' 18'' = 90^\circ 17' 41''\][/tex]

### Final Answer
So the results for the given angle addition problems are:
1. [tex]\[36^\circ 24' 23'' + 45^\circ 52' 36'' = 82^\circ 16' 59''\][/tex]
2. [tex]\[36^\circ 45' 23'' + 53^\circ 32' 18'' = 90^\circ 17' 41''\][/tex]

That concludes our calculation.
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