Question

question 2(multiple choice worth 1 points) (04.03 mc) what point on the number line is \\(\frac{3}{5}\\) of the way from the point -9 to the point 17? \\(\bigcirc\\) 1.4 \\(\bigcirc\\) 4 \\(\bigcirc\\) 4.8 \\(\bigcirc\\) 6.6

Explanation:

Step1: Find the distance between -9 and 17

The distance \( d = 17 - (-9)=17 + 9 = 26\)

Step2: Calculate \(\frac{3}{5}\) of the distance

\(\frac{3}{5}\times26=\frac{78}{5} = 15.6\)

Step3: Add this to the starting point (-9)

The point is \(-9+15.6 = 6.6\) Wait, no, wait. Wait, maybe I made a mistake. Wait, the formula for a point \(x\) that is \(\frac{m}{n}\) of the way from \(a\) to \(b\) is \(x=a+\frac{m}{n}(b - a)\)

So \(a=-9\), \(b = 17\), \(m = 3\), \(n=5\)

So \(x=-9+\frac{3}{5}(17-(-9))=-9+\frac{3}{5}(26)=-9 + 15.6 = 6.6\)? But the options have 1.4,4,4.8,6.6. Wait, maybe I messed up the direction. Wait, maybe the problem is from -9 to 17, so the vector is \(17-(-9)=26\). \(\frac{3}{5}\) of 26 is 15.6. Then starting at -9, moving 15.6 units towards 17: \(-9+15.6 = 6.6\). So the answer is 6.6.

Answer:

6.6 (the option with 6.6)