Answer: point F is at <u> 0.6 </u> on the number line
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Explanation:
The ratio 2:3 scales up to 2x:3x for some positive real number x.
This means the distance from D to F is 2x units, and the distance from F to E is 3x units. Combine those two smaller distances to get 2x+3x = 5x to represent the full distance from D to E.
D is at -3 and E is at 6. This is a distance of 9 units since |-3-6| = |-9| = 9
Set this equal to the 5x from earlier and solve
5x = 9
x = 9/5
x = 1.8
This leads to 2x = 2*1.8 = 3.6
Therefore, we'll move 3.6 units from -3 to -3+3.6 = 0.6 which is the location of point F on the number line.
Notice that from 0.6 to 6 is 5.4 units and that 3x = 3*1.8 = 5.4 matches up to help confirm the answer.
Actually, she worked for seven hours, so I'll solve for that.
7.20 x 3 = 21.6
6.75 x 4 = 27
21.6 + 27 = 48.6
48.6 /2 = 24.3
Her average should be $24.3 If she did work six hours, just multiply 6.75 x 3 and do what I did.
When x = -6 the denominator = 0
There is a hole in the graph at (-6,0)