where will her cut be located? round to the nearest tenth.\n$x = (\\frac{m}{m + n})(x_2 - x_1)+x_1$\ngeneviev…

where will her cut be located? round to the nearest tenth.\n$x = (\\frac{m}{m + n})(x_2 - x_1)+x_1$\ngenevieve is cutting a 60 - inch piece of ribbon into a ratio of 2:3. since 2 inches are frayed at one end of the ribbon, she will need to start 2 inches in. this is indicated as 2 on the number line.\n25.2 in.\n29.4 in.\n35.1 in.\n40.7 in.

where will her cut be located? round to the nearest tenth.\n$x = (\\frac{m}{m + n})(x_2 - x_1)+x_1$\ngenevieve is cutting a 60 - inch piece of ribbon into a ratio of 2:3. since 2 inches are frayed at one end of the ribbon, she will need to start 2 inches in. this is indicated as 2 on the number line.\n25.2 in.\n29.4 in.\n35.1 in.\n40.7 in.

Answer

Explanation:

Step1: Determine the length of the usable ribbon

The total length of the ribbon is 60 inches, and 2 inches are frayed at one - end. So the usable length of the ribbon is $60 - 2=58$ inches.

Step2: Use the section - formula for ratios

The ratio is $m:n = 2:3$. The formula for finding the position of a point that divides a line - segment in the ratio $m:n$ is $x=\left(\frac{m}{m + n}\right)(x_2 - x_1)+x_1$. Here, we can think of the usable part of the ribbon as a line - segment. The length of the part of the ribbon from the non - frayed end to the cut is given by $l=\frac{2}{2 + 3}\times58$. We calculate $\frac{2}{2+3}\times58=\frac{2}{5}\times58 = 23.2$ inches.

Step3: Account for the frayed part

Since we started 2 inches in from the frayed end, the position of the cut from the original starting point (including the frayed part) is $23.2+2=25.2$ inches.

Answer:

25.2 in.