Point S lies between points R and T on Line segment R T. A line contains points R, S, T. The space between R and S is 2 x. The space between S and T is 3 x. If RT is 10 centimeters long, what is ST? 2 centimeters 4 centimeters 6 centimeters 8 centimeters

If the space between R and S is 2x, the space between S and T is 3x, and RT is 10 centimeters long, then ST is 6 centimeters

Point S lies between points R and T on Line segment RT

RT   =  RS   +  ST

The space between R and S is 2x

That is, RS  =  2x

The space between S and T is 3x

That is, ST  =  3x

RT is 10 centimeters long

RT  =  10cm

Substitute RT = 10, ST = 3x and RS = 2x into the equation RT = RS + ST

10  =  2x  +  3x

10   =  5x

x  =  10/5

x   =  2

If x = 2, then

ST  =  3x

ST = 3(2)

ST =  6 centimeters

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6 cm

Step-by-step explanation:

Given that:

A line that contains the points R, S and T.

Distance between R and S =

Distance between S and T =

To find:

The distance between S and T = ?

Solution:

The given situation and dimensions can be represented in the form of a diagram as shown in the attached diagram.

As per given statement and in the diagram, we can deduce that the sum of distance between R and S, S and T is equal to distance between R and T.

i.e. RS + ST = RT

ST = 3 = 3 2 = 6 cm

Therefore, the answer is:

Distance between S and T is 6 cm.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1