Find the value of the variable and VW if V is between U and W.

UV=2,VW= 3x, UW=29
UV = r, VW = 6r, UW =42
UV = 4p - 3, VW = 5p, UW =15
UV = 3c+29, VW = -2c-4, UW = -4c

Need a site to explain how to do these.
Teacher not clear on explaining.

UV + VW = UW

8) UV + VW = UW
2 +3x = 29
3x = 27
x = 3
VW = 3x = 9

9) UV + VW = UW
r + 6r = 42
7r = 42
r = 6
VW = 6r = 36

10) UV + VW = UW
4p-3 + 5p = 15
9p = 18
p = 2
VW = 5p = 10

11) UV + VW = UW
3c+29 + -2c-4 = -4c
c - 25 = -4c
5c = 25
c = 5
VW = -2c-4 = -10-4 = -16

Question number 8- If I’m remembering my math correctly ...

3x=27
X=9

To find the value of the variable and VW if V is between U and W, we can use the property of segment addition.

Let's look at each given scenario step-by-step:

1. UV = 2, VW = 3x, UW = 29
In this case, we know that UV + VW = UW. Substituting the given values, we have:
2 + 3x = 29
Now, we can solve for x:
3x = 29 - 2
3x = 27
x = 9
Therefore, the value of the variable x is 9, and VW is 3(9) = 27.

2. UV = r, VW = 6r, UW = 42
Using the same property as before, we have:
r + 6r = 42
Simplifying the equation:
7r = 42
r = 6
Therefore, the value of the variable r is 6, and VW is 6(6) = 36.

3. UV = 4p - 3, VW = 5p, UW = 15
Applying the segment addition property:
(4p - 3) + 5p = 15
Combining like terms:
9p - 3 = 15
Adding 3 to both sides:
9p = 18
Dividing by 9:
p = 2
Hence, the value of the variable p is 2, and VW is 5(2) = 10.

4. UV = 3c + 29, VW = -2c - 4, UW = -4c
Using the segment addition property:
(3c + 29) + (-2c - 4) = -4c
Simplifying the equation:
c + 25 = -4c
Adding 4c to both sides:
5c + 25 = 0
Subtracting 25 from both sides:
5c = -25
Dividing by 5:
c = -5
Therefore, the value of the variable c is -5, and VW is -2(-5) - 4 = 6.

If you need more explanation or examples, you can refer to math websites like Khan Academy, Mathisfun, or your textbook.

To find the value of the variable and VW if V is between U and W, we need to use the information given for each scenario. Let's go through each scenario step by step:

1. UV = 2, VW = 3x, UW = 29:
Since V is between U and W, we can say that UV + VW = UW. Substituting the given values, we have:
2 + 3x = 29

To find the value of x, we need to isolate it on one side of the equation. We can do this by subtracting 2 from both sides:
3x = 27

Then, divide both sides by 3:
x = 9

So, the value of the variable x is 9. Now, we can find the value of VW by substituting x into the equation VW = 3x:
VW = 3(9) = 27

Therefore, the value of the variable x is 9, and VW is 27.

2. UV = r, VW = 6r, UW = 42:
Using the same logic as before, we have:
r + 6r = 42

Combining like terms, we get:
7r = 42

Dividing both sides by 7:
r = 6

So, the value of the variable r is 6. Substituting r into the equation VW = 6r, we get:
VW = 6(6) = 36

Therefore, the value of the variable r is 6, and VW is 36.

3. UV = 4p - 3, VW = 5p, UW = 15:
Again, using the equation UV + VW = UW:
(4p - 3) + 5p = 15

Combining like terms:
9p - 3 = 15

Adding 3 to both sides:
9p = 18

Dividing both sides by 9:
p = 2

Thus, the value of the variable p is 2. Substituting p into the equation VW = 5p, we get:
VW = 5(2) = 10

Therefore, the value of the variable p is 2, and VW is 10.

4. UV = 3c + 29, VW = -2c - 4, UW = -4c:
Using the equation UV + VW = UW:
(3c + 29) + (-2c - 4) = -4c

Simplifying, we get:
c + 25 = -4c

Adding 4c to both sides:
5c + 25 = 0

Subtracting 25 from both sides:
5c = -25

Dividing both sides by 5:
c = -5

Therefore, the value of the variable c is -5. Substituting c into the equation VW = -2c - 4, we have:
VW = -2(-5) - 4 = 6

Hence, the value of the variable c is -5, and VW is 6.

For further explanations and practice with solving equations, you can refer to websites like Khan Academy (www.khanacademy.org) or MathIsFun (www.mathisfun.com). They provide step-by-step explanations and examples to help improve your understanding of solving equations.