Question

Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, y? Is the graph of the equation continuous or discrete?

y=7.75x+4; discrete
y=7.75x+4; continuous
y=4x+7.75; discrete
y=4x+7.75; continuous

Answer 1

[AI-generated answer — Bot GPT-4o]

To determine the total length of all the yarn that Julie ends up cutting, we need to account for both the 4 pieces of yarn of equal length \(x\) and the single piece of yarn that is 7.75 inches long.

The total length of the yarn can be calculated by summing the lengths of the 4 pieces of length \(x\) and the single piece of length 7.75 inches.

So, the equation that represents the total length \(y\) is:
\[ y = 4x + 7.75 \]

Next, we need to determine if the graph of the equation is continuous or discrete.

Since \(x\) represents the length of a piece of yarn, it can take on any non-negative real number value (as you can theoretically cut yarn to any desired length), the graph of the equation should be considered continuous.

Thus, the correct equation and classification are:
\[ y = 4x + 7.75; \text{ continuous} \]