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In Exercises 1-4, use the figure shown. Find the length of each segment.
U
-6-5-4-3-2-1
0
1
2 3
4 5
6 7
8
1. RS =
2. RT =
3. ST
4. RU=
oooo
For Exercises 5-7, use the figure shown.
5. What is PQ?
6. What is QR?
7. What is PR?
Points A, B, C, and D on the figure below are collinear. Use the figure for
Exercises 8 and 9
A
3x
4x
13
8. If AC = 24, what is AB?
9. If BC = 15, what is BD?
Use the figure shown for Exercises 10-13.
10. What is m_PTR?
11. What is m_PTQ?
12. What is m2QTS?
13. Understand Luis said that m2 QTR = 80
Explain Luis's error

Answer 1

Answer/Step-by-step Explanation:

When calculating the length of a segment on a number line, the absolute value of the difference between one point on the numberline, and another point is what we're looking for.

1. Length of RS = |-5 - (-2)| = |-5 + 2| = |-3|

RS = 3

2. Length of RT = |-5 - 2| = |-7|

RS = 7

3. Length of ST = |-2 - 2| = |-4|

ST = 4

4. Length of RU = |-5 - 8| = |-13|

RU = 13

5. Given that the following coordinates:

P = 3

Q = 8

R = 14

5. PQ = |3 - 8| = |-5| = 5

6. QR = |8 - 14| = |-6| = 6

7. PR = |3 - 14| = |-11| = 11

Given that points A, B, C, and D are collinear, and AB = x, BC = 3x, CD = 4x - 13

8. If AC = 24,

BC can be calculated as follows:

AB + BC = AC

`x + 3x = 24`

Solve for x

`4x = 24`

Divide both sides by 4

`x = 6`

Thus,, BC = 3x = 3(6) = 18

BC = 18

9. If BC = 15, BD can be calculated as follows:

Find the value of x first

BC = 3x

15 = 3x

Divide both sides by 3

5 = x

x = 5.

BD =
`3x + (4x - 13)`

Plug in the value of x

BD =
`3(5) + (4(5) - 13) = 15 + (20 - 13)`

BD =
`15 + 7 = 22`

BD = 22

10. m<PTR = 80° (taking the reading at the top from 0°)

11. m<PTQ = 45°

12. m<QTS = 128 - 45 = 83°

13. Luis read m<QTR wrongly, what he measured was the whole of <PTR.

According to the angle addition theorem, m<QTR = 80 - 45 = 35°.