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Solve for the value of [tex]\( x \)[/tex]:

[tex]\[ (x+51)(x+10),(x+15) \text{ and } (x+209) \][/tex]

Given the following steps:

[tex]\[
\begin{array}{l}
x + x + 5 + 5 + \frac{\text{ Solve }}{10 + x + 15 + x + 20} = (n-2) \times 180 \\
55 + 4x = (n-2) \times 180 \\
55 + 4x = (5-2) \times 180 \\
55 + 4x = 540 \\
4x = 540 - 55 \\
4x = 485 \\
x = \frac{485}{4} \\
x = 121.25
\end{array}
\][/tex]

And:

[tex]\[
\begin{array}{l}
m = 36 + 85 \\
m = 121
\end{array}
\][/tex]

Lastly:

[tex]\[ 12 \][/tex]

Twice the number 37 base [tex]\( x \)[/tex] is equal to 75. Find the value of [tex]\( x \)[/tex]:

[tex]\[ \frac{\text{ Solve }}{5} \][/tex]

Sagot :

GinnyAnsweridn
To find the value of [tex]\( x \)[/tex] such that twice the number 37 in base [tex]\( x \)[/tex] is equal to 75 in base [tex]\( x \)[/tex], follow these steps:

1. Interpret the Numbers in their Respective Base [tex]\( x \)[/tex]:
- The number 37 in base [tex]\( x \)[/tex] can be written as:
[tex]\[ 3x + 7 \][/tex]
- The number 75 in base [tex]\( x \)[/tex] can be written as:
[tex]\[ 7x + 5 \][/tex]

2. Set up the Equation:
- Twice the number 37 in base [tex]\( x \)[/tex] should be equal to 75 in base [tex]\( x \)[/tex]. This gives us:
[tex]\[ 2 (3x + 7) = 7x + 5 \][/tex]

3. Expand and Simplify the Equation:
- Distribute the 2 on the left-hand side:
[tex]\[ 2(3x + 7) = 6x + 14 \][/tex]
- Now, equate this to the right-hand side:
[tex]\[ 6x + 14 = 7x + 5 \][/tex]

4. Solve for [tex]\( x \)[/tex]:
- Subtract [tex]\( 6x \)[/tex] from both sides:
[tex]\[ 14 = x + 5 \][/tex]
- Subtract 5 from both sides:
[tex]\[ 14 - 5 = x \][/tex]
[tex]\[ x = 9 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 9 \)[/tex].
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