3. Irrigation System (Rational Algebraic Expressions): - The garden will require an irrigation system that costs \( \$ 10 \) per meter of piping. The length of piping needed can be modeled by the expression \( \frac{2 l+2 w}{2} \), where \( l \) and \( w \) are the length and width of one plot, respectively. - If each plot is 4 meters by 6 meters, calculate the total cost of the piping for the entire garden using rational algebraic expressions. 4. Plant Growth Analysis (Systems of linear Equations): - Two types of plants will be grown in the garden: Type A and Type B. The growth rate of Type A is given by the equation \( y=2 x+5 \) and for Type B by \( y=-x+15 \), where \( x \) is the number of weeks since planting, and \( y \) is the height in centimeters. Determine after how many weeks the heights of Type A and Type B plants will be the same. Solve the system of linear equations to find this intersection point.

### Irrigation System (Rational Algebraic Expressions): Given: - The cost of the irrigation system is $10 per meter of piping. - The length of piping needed can be modeled by the expression \( \frac{2l+2w}{2} \), where \( l \) and \( w \) are the length and width of one plot, respectively. - Each plot is 4 meters by 6 meters. To calculate the total cost of the piping for the entire garden, we need to find the total length of piping required and then multiply it by the cost per meter. 1. Calculate the total length of piping required: - For one plot: \( \frac{2(4)+2(6)}{2} = \frac{8+12}{2} = \frac{20}{2} = 10 \) meters - Since there are multiple plots, the total length of piping required is \( 10 \times \text{number of plots} \). 2. Calculate the total cost of the piping for the entire garden: - Total cost = Total length of piping required * Cost per meter Let's calculate the total cost of the piping for the entire garden using rational algebraic expressions. Calculate the value by following steps: - step0: Calculate: \(10\times 10\) - step1: Multiply the numbers: \(100\) The total cost of the piping for the entire garden is $100. ### Plant Growth Analysis (Systems of Linear Equations): Given: - Growth rate of Type A plants: \( y = 2x + 5 \) - Growth rate of Type B plants: \( y = -x + 15 \) - \( x \) represents the number of weeks since planting, and \( y \) represents the height in centimeters. To determine after how many weeks the heights of Type A and Type B plants will be the same, we need to find the intersection point of the two growth rate equations. 1. Set the two equations equal to each other: - \( 2x + 5 = -x + 15 \) 2. Solve the equation to find the intersection point: - \( 3x = 10 \) - \( x = \frac{10}{3} \) Therefore, the heights of Type A and Type B plants will be the same after \( \frac{10}{3} \) weeks.