Question

1. what is the constant of proportionality in the equation y = 5x?
2. what is the constant of proportionality in the equation y = 0.41x?
3. the equation p = 3s represents the perimeter p of an equilateral triangle with side length s. is there a proportional relationship between the perimeter and the side length of an equilateral triangle? explain.
4. model with math in a chemical compound, there are 3 parts zinc for every 16 parts copper, by mass. a piece of the compound contains 320 grams of copper. write and solve an equation to determine the amount of zinc in the chemical compound.

Explanation:

7.

Step1: Recall proportional - equation form

The equation of a proportional relationship is $y = kx$, where $k$ is the constant of proportionality.

Step2: Identify the constant

In the equation $y = 5x$, comparing with $y=kx$, we can see that $k = 5$.

Step1: Recall proportional - equation form

The equation of a proportional relationship is $y = kx$, where $k$ is the constant of proportionality.

Step2: Identify the constant

In the equation $y = 0.41x$, comparing with $y = kx$, we can see that $k=0.41$.

Step1: Recall the definition of proportional relationship

A proportional relationship between two variables $y$ and $x$ can be written in the form $y = kx$, where $k$ is a non - zero constant.

Step2: Analyze the given equation

The equation for the perimeter $P$ of an equilateral triangle with side length $s$ is $P = 3s$. Here, $P$ is the dependent variable and $s$ is the independent variable. The ratio $\frac{P}{s}=3$ (a non - zero constant). So, there is a proportional relationship between the perimeter and the side length of an equilateral triangle.

Answer:

5

8.