Question

algebra use the figure at the right for exercises 19 and 20. 19. given: st = 3x + 3 and tu = 2x + 9. a. what is the value of st? b. what is the value of tu? 20. given: st = x + 3 and tu = 4x - 6. a. what is the value of st? b. what is the value of su? on a number line, suppose point e has a coordinate of 3, eg = 6, and ex = 12. is point g the mid - point of ex? what are possible coordinates for g and x? 15. eg and ui prentice hall gold geometry • teaching resources copyright © by pearson education, inc. or its affiliates. all rights reserved.

Explanation:

Exercise 19

a.

Step1: Set up equation

Since \(ST = 3x + 3\) and \(TU=2x + 9\), and assuming \(T\) is the mid - point of \(SU\), then \(ST = TU\). So we set up the equation \(3x+3=2x + 9\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(3x-2x+3=2x-2x + 9\), which simplifies to \(x+3 = 9\). Then subtract 3 from both sides: \(x=9 - 3=6\).

Step3: Find the value of \(ST\)

Substitute \(x = 6\) into the expression for \(ST\): \(ST=3x + 3=3\times6+3=18 + 3=21\).

Step1: Find \(TU\)

Since \(x = 6\) and \(TU=2x + 9\), then \(TU=2\times6+9=12 + 9=21\).

Step2: Find \(SU\)

Since \(SU=ST + TU\) and \(ST = TU = 21\), then \(SU=21+21 = 42\).

Step1: Set up equation

Since \(ST=x + 3\) and \(TU = 4x-6\), and assuming \(T\) is the mid - point of \(SU\), then \(ST = TU\). So we set up the equation \(x + 3=4x-6\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(x-x + 3=4x-x-6\), which gives \(3=3x-6\). Add 6 to both sides: \(3 + 6=3x-6+6\), so \(9 = 3x\). Divide both sides by 3: \(x = 3\).

Step3: Find the value of \(ST\)

Substitute \(x = 3\) into the expression for \(ST\): \(ST=x + 3=3+3=6\).

Answer:

\(21\)

b.