Question

use the number line below, where RS=7y+3, ST=2y+9, RT=14y-8
a. What is the value of y?
y=

Answer 1

From the given line, it can be concluded that:

• Segment RT is divided into RS and ST, so: $RT = RS + RT$
• This is used to find y.
• With y, it is possible to find the length of each segment.

Doing this, we get that:

• The value of y is 4.
• The lenghts of the segments are: $RS = 31, ST = 17, RT = 48$

Question a:

The length of the sides are:

• $RS = 7y + 3$
• $ST = 2y + 9$
• $RT = 14y - 8$

Since RT is RS added to ST:

$RT = RS + RT$

$7y + 3 + 2y + 9 = 14y - 8$

$9y + 12 = 14y - 8$

$5y = 20$

$y = \frac{20}{5} = 4$

The value of y is 4.

Question b:

Replacing y by 4, we find the lengths.

• $RS = 7y + 3 = 7(4) + 3 = 28 + 3 = 31$
• $ST = 2y + 9 = 2(4) + 9 = 8 + 9 = 17$
• $RT = 14y - 8 = 14(4) - 8 = 56 - 8 = 48$

Thus, the lenghts of the segments are: $RS = 31, ST = 17, RT = 48$

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Answer 2

We need to use what we know of segments to write and solve equations that will allow us to find the value of y.

The solution is y = 4.

The information given is:

RS = 7y + 3

ST = 2y + 9

RT = 14y - 8

Because S is between R and T, we know that:

RT = RS + ST

So we can replace the equations for each segment above to get:

14y - 8 = (7y + 3) + (2y + 9)

Now we can solve this for y, to do it, let's move all the terms with "y" to the left side.

14y -7y - 2y = 3 + 9 + 8

(14 - 7 - 2)*y = 20

5*y = 20

y = 20/5 = 4

y = 4

We found that the value of y is 4.

If you want to learn more, you can read:

https://brainly.com/question/11015073