Answered

From health tips to tech hacks, find it all on IDNLearn.com. Get timely and accurate answers to your questions from our dedicated community of experts who are here to help you.

Find the length of RT and ST.

Given:
[tex]\[ RT = 8x - 6 \][/tex]
[tex]\[ RS = 16 \][/tex]
[tex]\[ ST = 2x - 4 \][/tex]

Sagot :

GinnyAnsweridn
Let's solve the problem step-by-step. We are given the following:

- RT = 8x - 6
- RS = 16
- ST = 2x - 4

We know that RT is the sum of RS and ST:

RT = RS + ST

Substitute the given expressions into this equation:

8x - 6 = 16 + 2x - 4

Now, let's simplify and solve for [tex]\( x \)[/tex]:

8x - 6 = 12 + 2x

To isolate [tex]\( x \)[/tex], we first subtract [tex]\( 2x \)[/tex] from both sides:

8x - 2x - 6 = 12

6x - 6 = 12

Next, we add 6 to both sides to further isolate [tex]\( x \)[/tex]:

6x - 6 + 6 = 12 + 6

6x = 18

Now, we divide by 6:

x = 18 / 6

x = 3

Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into the expressions for RT and ST to find their lengths.

RT = 8x - 6

RT = 8(3) - 6

RT = 24 - 6

RT = 18

Similarly, for ST:

ST = 2x - 4

ST = 2(3) - 4

ST = 6 - 4

ST = 2

So, the lengths are:

- RT = 18
- ST = 2

Thus, using these calculations, we have determined that the length of RT is 18 units and the length of ST is 2 units.
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.