Mathematics: Use the number line below, where RS = 9y +5, ST = 5y + 6, and RT = 123. a. What is the value of y? b. Find RS and ST.

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Use the number line below, where RS = 9y +5,

sydchann582

31.01.2022

y=8

RS: 77

ST: 46

Step-by-step explanation:

We know that RS and ST together make the line RT. This means the sum of their lengths will be equal to RT.

Since RT is 123, we can create the equation 9y+5+5y+6=123 .

Combining like terms gets us 14y+11=123

We can now solve for y by isolating the variable on one side of the equation.

$14y + 11 - 11 = 123-11\\\\14y=112\\\\14y\div14 = 112\div14\\\\y=8$

Now we know the value of y. We can now substitute this into the expressions for RS and ST to find their values.

RS = $9y+5\\\\(9\cdot8)+5\\\\72+5\\\\77$

ST = $5y+6\\\\(5\cdot8)+6\\\\40+6\\\\46$

We can confirm this is correct because 46+77=123 .

Hope this helped!

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