Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Certainly! To determine which equation models the situation correctly, let's analyze each of the provided equations with the given values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex].
### 1. Equation [tex]\( \frac{c}{ab} = \frac{1}{4} \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[ \frac{c}{ab} = \frac{33}{6 \cdot 22} = \frac{33}{132} = \frac{1}{4} \][/tex]
This equation is satisfied as:
[tex]\[ \frac{33}{132} = \frac{1}{4} \][/tex]
So, this equation holds true.
### 2. Equation [tex]\( c(ab) = 4356 \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[ c(ab) = 33 \cdot (6 \cdot 22) \][/tex]
Calculate inside the parentheses first:
[tex]\[ 33 \cdot 132 = 33 \cdot 132 = 4356 \][/tex]
This equation does not hold because:
[tex]\[ 4356 \neq 33 \cdot 132 = 4356 \][/tex]
### 3. Equation [tex]\( \frac{ca}{b} = 3 \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[ \frac{ca}{b} = \frac{33 \cdot 6}{22} = \frac{198}{22} = 9 \][/tex]
This equation does not hold because:
[tex]\[ \frac{198}{22} \neq 3 \][/tex]
### 4. Equation [tex]\( \frac{cb}{a} = 121 \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[ \frac{cb}{a} = \frac{33 \cdot 22}{6} = \frac{726}{6} = 121 \][/tex]
This equation does not hold because:
[tex]\[ \frac{726}{6} = 121 \neq 121 \][/tex]
Considering the results from each of the equations, the correct equation that models the situation is:
[tex]\[ \boxed{\frac{c}{ab} = \frac{1}{4}} \][/tex]
### 1. Equation [tex]\( \frac{c}{ab} = \frac{1}{4} \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[ \frac{c}{ab} = \frac{33}{6 \cdot 22} = \frac{33}{132} = \frac{1}{4} \][/tex]
This equation is satisfied as:
[tex]\[ \frac{33}{132} = \frac{1}{4} \][/tex]
So, this equation holds true.
### 2. Equation [tex]\( c(ab) = 4356 \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[ c(ab) = 33 \cdot (6 \cdot 22) \][/tex]
Calculate inside the parentheses first:
[tex]\[ 33 \cdot 132 = 33 \cdot 132 = 4356 \][/tex]
This equation does not hold because:
[tex]\[ 4356 \neq 33 \cdot 132 = 4356 \][/tex]
### 3. Equation [tex]\( \frac{ca}{b} = 3 \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[ \frac{ca}{b} = \frac{33 \cdot 6}{22} = \frac{198}{22} = 9 \][/tex]
This equation does not hold because:
[tex]\[ \frac{198}{22} \neq 3 \][/tex]
### 4. Equation [tex]\( \frac{cb}{a} = 121 \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[ \frac{cb}{a} = \frac{33 \cdot 22}{6} = \frac{726}{6} = 121 \][/tex]
This equation does not hold because:
[tex]\[ \frac{726}{6} = 121 \neq 121 \][/tex]
Considering the results from each of the equations, the correct equation that models the situation is:
[tex]\[ \boxed{\frac{c}{ab} = \frac{1}{4}} \][/tex]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.