Certainly! Let's solve each of these proportions step by step:
### 1. Solving [tex]\(\frac{6}{-24} = \frac{-n}{52}\)[/tex]:
To solve for [tex]\( n \)[/tex], we will cross-multiply:
[tex]\[ 6 \times 52 = -24 \times (-n) \][/tex]
[tex]\[ 312 = 24n \][/tex]
Divide both sides by 24:
[tex]\[ n = \frac{312}{24} \][/tex]
[tex]\[ n = 13 \][/tex]
Since the equation was [tex]\(\frac{6}{-24} = \frac{-n}{52}\)[/tex], [tex]\( n \)[/tex] should be:
[tex]\[ n = -13 \][/tex]
So, [tex]\( n = -13 \)[/tex].
### 2. Solving [tex]\(\frac{18}{90} = \frac{6}{v + 2}\)[/tex]:
First, simplify [tex]\(\frac{18}{90}\)[/tex]:
[tex]\[ \frac{18}{90} = \frac{1}{5} \][/tex]
Now, set up the proportion:
[tex]\[ \frac{1}{5} = \frac{6}{v + 2} \][/tex]
Cross-multiply:
[tex]\[ 1 \times (v + 2) = 6 \times 5 \][/tex]
[tex]\[ v + 2 = 30 \][/tex]
Subtract 2 from both sides:
[tex]\[ v = 30 - 2 \][/tex]
[tex]\[ v = 28 \][/tex]
So, [tex]\( v = 28 \)[/tex].
### 3. Solving [tex]\(\frac{10}{3d} = \frac{50}{45}\)[/tex]:
First, simplify [tex]\(\frac{50}{45}\)[/tex]:
[tex]\[ \frac{50}{45} = \frac{10}{9} \][/tex]
Now, set the proportion:
[tex]\[ \frac{10}{3d} = \frac{10}{9} \][/tex]
Cross-multiply:
[tex]\[ 10 \times 9 = 10 \times (3d) \][/tex]
[tex]\[ 90 = 30d \][/tex]
Divide both sides by 30:
[tex]\[ d = \frac{90}{30} \][/tex]
[tex]\[ d = 3 \][/tex]
So, [tex]\( d = 3 \)[/tex].
### 4. Solving [tex]\(\frac{3t - 4}{5} = \frac{-3t + 48}{15}\)[/tex]:
Cross-multiply:
[tex]\[ (3t - 4) \times 15 = (-3t + 48) \times 5 \][/tex]
[tex]\[ 45t - 60 = -15t + 240 \][/tex]
Combine like terms by adding [tex]\( 15t \)[/tex] to both sides:
[tex]\[ 45t + 15t - 60 = 240 \][/tex]
[tex]\[ 60t - 60 = 240 \][/tex]
Add 60 to both sides:
[tex]\[ 60t = 300 \][/tex]
Divide both sides by 60:
[tex]\[ t = \frac{300}{60} \][/tex]
[tex]\[ t = 5 \][/tex]
So, [tex]\( t = 5 \)[/tex].
### Summary of Solutions:
- [tex]\( n = -13 \)[/tex]
- [tex]\( v = 28 \)[/tex]
- [tex]\( d = 3 \)[/tex]
- [tex]\( t = 5 \)[/tex]
These are the solved values for the given proportions.
