At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To determine which of the given equations represents a nonlinear function, we must analyze each equation in terms of its degree. The degree of an equation is defined as the highest power of the variable(s) in the equation.
Let's examine these equations one by one:
### Equation 1: [tex]\( x(y-5) = 2 \)[/tex]
Rewrite this equation in standard form:
[tex]\[ x(y-5) = 2 \][/tex]
[tex]\[ xy - 5x = 2 \][/tex]
The degree of a term is the sum of the exponents of the variables in that term:
- The term [tex]\( xy \)[/tex] has a degree of [tex]\( 1 + 1 = 2 \)[/tex]
- The term [tex]\( -5x \)[/tex] has a degree of 1
The highest degree term is [tex]\( xy \)[/tex], which is of degree 2. Therefore, this equation is nonlinear.
### Equation 2: [tex]\( y - 2(x+9) = 0 \)[/tex]
Rewrite this equation in standard form:
[tex]\[ y - 2(x+9) = 0 \][/tex]
[tex]\[ y - 2x - 18 = 0 \][/tex]
- The term [tex]\( y \)[/tex] has a degree of 1
- The term [tex]\( -2x \)[/tex] has a degree of 1
- The term [tex]\( -18 \)[/tex] is a constant with degree 0
The highest degree term is of degree 1. Therefore, this equation is linear.
### Equation 3: [tex]\( 3y + 6(2-x) = 5 \)[/tex]
Rewrite this equation in standard form:
[tex]\[ 3y + 6(2-x) = 5 \][/tex]
[tex]\[ 3y + 12 - 6x = 5 \][/tex]
[tex]\[ 3y - 6x + 12 = 5 \][/tex]
[tex]\[ 3y - 6x + 7 = 0 \][/tex]
- The term [tex]\( 3y \)[/tex] has a degree of 1
- The term [tex]\( -6x \)[/tex] has a degree of 1
- The term [tex]\( 7 \)[/tex] is a constant with degree 0
The highest degree term is of degree 1. Therefore, this equation is linear.
### Equation 4: [tex]\( 2(y + x) = 0 \)[/tex]
Rewrite this equation in standard form:
[tex]\[ 2(y + x) = 0 \][/tex]
[tex]\[ 2y + 2x = 0 \][/tex]
- The term [tex]\( 2y \)[/tex] has a degree of 1
- The term [tex]\( 2x \)[/tex] has a degree of 1
The highest degree term is of degree 1. Therefore, this equation is linear.
After evaluating all the equations:
- The first equation [tex]\( x(y-5)=2 \)[/tex] is nonlinear.
- The second equation [tex]\( y - 2(x+9)=0 \)[/tex] is linear.
- The third equation [tex]\( 3y + 6(2-x)=5 \)[/tex] is linear.
- The fourth equation [tex]\( 2(y+x)=0 \)[/tex] is linear.
Thus, the equation that represents a nonlinear function is:
[tex]\[ x(y-5) = 2 \][/tex]
Let's examine these equations one by one:
### Equation 1: [tex]\( x(y-5) = 2 \)[/tex]
Rewrite this equation in standard form:
[tex]\[ x(y-5) = 2 \][/tex]
[tex]\[ xy - 5x = 2 \][/tex]
The degree of a term is the sum of the exponents of the variables in that term:
- The term [tex]\( xy \)[/tex] has a degree of [tex]\( 1 + 1 = 2 \)[/tex]
- The term [tex]\( -5x \)[/tex] has a degree of 1
The highest degree term is [tex]\( xy \)[/tex], which is of degree 2. Therefore, this equation is nonlinear.
### Equation 2: [tex]\( y - 2(x+9) = 0 \)[/tex]
Rewrite this equation in standard form:
[tex]\[ y - 2(x+9) = 0 \][/tex]
[tex]\[ y - 2x - 18 = 0 \][/tex]
- The term [tex]\( y \)[/tex] has a degree of 1
- The term [tex]\( -2x \)[/tex] has a degree of 1
- The term [tex]\( -18 \)[/tex] is a constant with degree 0
The highest degree term is of degree 1. Therefore, this equation is linear.
### Equation 3: [tex]\( 3y + 6(2-x) = 5 \)[/tex]
Rewrite this equation in standard form:
[tex]\[ 3y + 6(2-x) = 5 \][/tex]
[tex]\[ 3y + 12 - 6x = 5 \][/tex]
[tex]\[ 3y - 6x + 12 = 5 \][/tex]
[tex]\[ 3y - 6x + 7 = 0 \][/tex]
- The term [tex]\( 3y \)[/tex] has a degree of 1
- The term [tex]\( -6x \)[/tex] has a degree of 1
- The term [tex]\( 7 \)[/tex] is a constant with degree 0
The highest degree term is of degree 1. Therefore, this equation is linear.
### Equation 4: [tex]\( 2(y + x) = 0 \)[/tex]
Rewrite this equation in standard form:
[tex]\[ 2(y + x) = 0 \][/tex]
[tex]\[ 2y + 2x = 0 \][/tex]
- The term [tex]\( 2y \)[/tex] has a degree of 1
- The term [tex]\( 2x \)[/tex] has a degree of 1
The highest degree term is of degree 1. Therefore, this equation is linear.
After evaluating all the equations:
- The first equation [tex]\( x(y-5)=2 \)[/tex] is nonlinear.
- The second equation [tex]\( y - 2(x+9)=0 \)[/tex] is linear.
- The third equation [tex]\( 3y + 6(2-x)=5 \)[/tex] is linear.
- The fourth equation [tex]\( 2(y+x)=0 \)[/tex] is linear.
Thus, the equation that represents a nonlinear function is:
[tex]\[ x(y-5) = 2 \][/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
