Explain why partitioning a directed line segment into a ratio of 1: 3 is not the same as finding half the length of the directed line segment.

The reason is explained below.

Step-by-step explanation:

Partition means to separate or to divide. A line segment can be partitioned into smaller segments which are compared as ratios.

The ratio of 1:3 shows that the segment will actually be divided into 4 equal sections and finding half the length of the directed line segment implies that the line segment divides in the ratio 1:1 i.e  the segment will actually be divided into 2 equal sections.

Hence, partitioning a directed line segment into a ratio of 1:3 is not the same as finding half the length of the directed line segment

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b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.