Example: Find the coordinates of point P along the directed line segment AB, A (3,4) and B (8, 14), so that the ratio of AP to PB is 3/2
Step 1: Graph the line segment and label the points.
Step 2: Find the whole number of equal parts
you will be partitioning.
Ratio of AP to PB is 3/2

.
This means...
AP will have
parts

PB will have
parts

So, the whole number of equal
parts will be 5. This means we will cut the line segment AB into 5 parts.

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.

x=6 and x=3

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x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15