Question

3 fill in the blank 1 point
if rt = 36, find the value of x.
diagram: r---s---t, rs labeled 6x + 1, st labeled x + 7
x = type your answer...

4 fill in the blank 1 point
if df = 9x - 39, find ef.
diagram: d---e---f, de labeled 47, ef labeled 3x + 10
ef = type your answer...

Explanation:

Question 3

Step1: Set up the equation

Since \( RT = RS + ST \), we have \( 6x + 1 + x + 7 = 36 \).

Step2: Combine like terms

Combine the \( x \)-terms and constant terms: \( 7x + 8 = 36 \).

Step3: Solve for \( x \)

Subtract 8 from both sides: \( 7x = 36 - 8 = 28 \). Then divide by 7: \( x = \frac{28}{7} = 4 \).

Step1: Set up the equation

Since \( DF = DE + EF \), we have \( 9x - 39 = 47 + 3x + 10 \).

Step2: Combine like terms

Simplify the right side: \( 9x - 39 = 3x + 57 \).

Step3: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 6x - 39 = 57 \). Add 39 to both sides: \( 6x = 57 + 39 = 96 \). Divide by 6: \( x = \frac{96}{6} = 16 \).

Step4: Find \( EF \)

Substitute \( x = 16 \) into \( EF = 3x + 10 \): \( EF = 3(16) + 10 = 48 + 10 = 58 \).

Answer:

\( x = 4 \)

Question 4