*Find the value of the variable and LM if L is between N and M
9) NL = 5x, LM = 3x, and NL = 15
*Find the value of the variable and ST if S is between R and T
28) RS = 7a, ST = 12a, RS = 28
how do you work these out?
9) If NL =5x and NL=15
then 5x=15 and you solve for x.
28) Same technique, you are given RS as 28 and 7a solve for a.
I need help
To find the value of the variable and the length of the segment, you can follow these steps for each given problem:
Problem 9:
1. Start by setting up an equation using the given information. In this case, we have NL = 5x, LM = 3x, and NL = 15.
2. Since L is between N and M, we know that the sum of NL and LM should be equal to the length of NM. Therefore, we can set up the equation 5x + 3x = 15 to solve for x.
3. Combine like terms on the left side of the equation: 8x = 15.
4. Divide both sides by 8 to isolate x: x = 15/8.
5. Now that we have found the value of x, substitute it back into the original equation to find the length of LM. In this case, LM = 3x, so LM = 3 * (15/8).
6. Simplify the expression: LM = 45/8.
Therefore, the value of the variable x is 15/8 and the length of LM is 45/8.
Problem 28:
1. Start by setting up an equation using the given information. In this case, we have RS = 7a, ST = 12a, and RS = 28.
2. Since S is between R and T, we can set up the equation RS + ST = 28.
3. Substitute the given values into the equation: 7a + 12a = 28.
4. Combine like terms on the left side of the equation: 19a = 28.
5. Divide both sides by 19 to isolate a: a = 28/19.
6. Now that we have found the value of a, substitute it back into the original equation to find the length of ST. In this case, ST = 12a, so ST = 12 * (28/19).
7. Simplify the expression: ST = 336/19.
Therefore, the value of the variable a is 28/19 and the length of ST is 336/19.
To solve the given problems, we need to use the concept of a segment and its parts.
In both cases, we have a line segment where one point (L in the first problem and S in the second problem) lies between two other points (N and M in the first problem, and R and T in the second problem).
To find the value of the variable, we need to set up an equation based on the given information and solve for the unknown.
Let's solve the first problem:
1) NL = 5x (given)
2) NL = 15 (given)
Since L is between N and M, we can equate the two expressions:
3) 5x = 15 (substituting NL)
To find the value of x, we divide both sides of equation 3 by 5:
4) x = 15 / 5
x = 3
So, the value of the variable x is 3.
To find LM, we substitute the value of x into the given equation:
LM = 3x
= 3 * 3
= 9
Therefore, the value of the variable x is 3, and LM is 9.
Let's solve the second problem:
1) RS = 7a (given)
2) RS = 28 (given)
Since S is between R and T, we can equate the two expressions:
3) 7a = 28 (substituting RS)
To find the value of a, we divide both sides of equation 3 by 7:
4) a = 28 / 7
a = 4
So, the value of the variable a is 4.
To find ST, we substitute the value of a into the given equation:
ST = 12a
= 12 * 4
= 48
Therefore, the value of the variable a is 4, and ST is 48.