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Gnesinka [82]
3 years ago
10

What Is The Length Of RT?

Mathematics
1 answer:
Ulleksa [173]3 years ago
6 0

Answer:

B

Step-by-step explanation:

AS is an angle bisector, thus the ratio of the sides of the triangle is equal to the ratio of the corresponding parts of RT, that is

\frac{SR}{ST} = \frac{RA}{TA}, substituting values

\frac{7.5}{9} = \frac{3.5}{x} ( cross- multiply )

7.5x = 31.5 ( divide both sides by 7.5 )

x = 4.2

Thus

RT = 3.5 + x = 3.5 + 4.2 = 7.7 → B

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By algebra properties we find the following relationships between each pair of algebraic expressions:

  1. First equation: Case 4
  2. Second equation: Case 1
  3. Third equation: Case 2
  4. Fourth equation: Case 5
  5. Fifth equation: Case 3

<h3>How to determine pairs of equivalent equations</h3>

In this we must determine the equivalent algebraic expression related to given expressions, this can be done by applying algebra properties on equations from the second column until equivalent expression is found. Now we proceed to find for each case:

First equation

(7 - 2 · x) + (3 · x - 11)

(7 - 11) + (- 2 · x + 3 · x)

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- 4 + (1) · x

- 4 + (5 - 4) · x

- 4 - 4 · x + 5 · x

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Second equation

- 7 + 6 · x - 4 · x + 3

(6 · x - 4 · x) + (- 7 + 3)

(6 - 4) · x - 4

2 · x - 4

2 · (x - 2) → Case 1

Third equation

9 · x - 2 · (3 · x - 3)

9 · x - 6 · x + 6

3 · x + 6

(2 + 1) · x + (14 - 8)

[1 - (- 2)] · x + (14 - 8)

(x + 14) - (8 - 2 · x) → Case 2

Fourth equation

- 3 · x + 6 + 4 · x

x + 6

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(7 + 5 · x) + (- 4 · x - 1) → Case 5

Fifth equation

- 2 · x + 9 + 5 · x  + 6

3 · x + 15

3 · (x + 5) → Case 3

To learn more on algebraic equations: brainly.com/question/24875240

#SPJ1

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