Question

In segment cdf, cd=2x+7, df=3x+6 and cf=9x-11 what is the length of cf?

Answer 1

Answer: To find the length of CF, we can use the segment addition postulate, which states that if a point D lies on the segment CF, then CD + DF = CF. We are given the expressions for CD, DF, and CF in terms of x, so we can substitute them into the equation and solve for x.

CD + DF = CF (2x + 7) + (3x + 6) = 9x - 11 5x + 13 = 9x - 11 -4x = -24 x = 6

Now that we have the value of x, we can plug it into any of the expressions to find the length of CF. For example,

CF = 9x - 11 CF = 9(6) - 11 CF = 54 - 11 CF = 43

Answer: The length of CF is 43 units

Answer 2

length of CF = 43 units

Explanation:

Given:

CD = 2x + 7

DF = 3x + 6

CF = 9x - 11

To find:

• Length of CF

Solution:

To find the length of CF, we should set up an equation using the information given. We can start by recognizing that CF is the sum of CD and DF:

CF = CD + DF

Substitute the given expressions

9x - 11 = (2x + 7) + (3x + 6)

Simplify like terms:

9x - 11 = 2x + 3x + 7 + 6

9x - 11 = 5x + 13

Subtract both sides by 5x.

9x - 11 - 5x = 5x + 13 - 5x

4x - 11 = 13

Add 11 on both sides:

4x - 11 + 11 = 13 + 11

4x = 24

Divide both sides by 4 to solve for x:

`\sf (4x)/(4 )= (24)/(4)`

x = 6

Now that we have found the value of x (x = 6), we can find the length of CF by substituting it into the expression for CF:

CF = 9x - 11

CF = 9(6) - 11

CF = 54 - 11

CF = 43

So, the length of CF is 43 units.