A painter built a ladder using 18 rungs. The rungs on the ladder were 5.7 inches apart and 1.1 inches thick. What is the distanc

Response:

D. The sidelines are parallel because they are perpendicular to a common line.

Justification:

According to the perpendicular transversal theorem, when a line is perpendicular to one of two parallel lines, it is also perpendicular to the other line. Furthermore, the converse of the theorem states that if two lines are perpendicular to the same line, they must be parallel. Therefore, the sidelines are indeed parallel and also perpendicular to this single line.

Result:

20.19°

Detailed explanation:

Refer to the attached diagram related to the question. We need to determine <CAB

Utilizing the sine rule on triangle ABC:

cross-multiply

Thus, the angle <CAB measures 20.19°

To find out the number of days, we should create equations based on the values provided. The total distance Kayla aims to travel combines both her running distance and her biking distance.

200 miles = (6 miles/day)x + (10 miles/day)y

where x signifies the days she spent running and y represents the days bike riding.

If the minimum biking days are set to be 15, indicated by y = 15, we have:

200 miles = (6 miles/day)x + (10 miles/day)(15 days)

Solving for x gives:
200 = 6x + 150
50 = 6x
x = 8.3333 days

Total days = 15 days biking + 8.3333 days running = 23.3333 days, approximately making it 24 days.

Answer:

Step-by-step explanation:

Given that lines l and m are parallel and there is a transversal cutting through these lines.

5). (9x + 2)° = 119° [by alternate interior angles]

    9x = 117 ⇒ x = 13

6). (12x - 8)° + 104° = 180°

     12x = 180 - 96

     x = ⇒ x = 7

7). (5x + 7) = (8x - 71) [by alternate exterior angles]

    8x - 5x = 71 + 7

    3x = 78

     x = 26

8). (4x - 7) = (7x - 61) [by corresponding angles]

    7x - 4x = -7 + 61

    3x = 54

     x = 18

9). (9x + 25) = (13x - 19) [by corresponding angles]

    13x - 9x = 25 + 19

    4x = 44

     x = 11

   (13x - 19)° + (17y + 5)° = 180° [linear pairs of angles sum to supplementary]

    (13×11) - 19 + 17y + 5 = 180

    129 + 17y = 180

    17y = 180 - 129

     y = 3

10). (3x - 29) + (8y + 17) = 180 [linear pairs of angles sum to supplementary]

     3x + 8y = 180 + 12

     3x + 8y = 192 -----(1)

     (8y + 17) = (6x - 7) [by alternate exterior angles]

     6x - 8y = 24

     3x - 4y = 12 -----(2)

     From equation (1) subtract equation (2)

     (3x + 8y) - (3x - 4y) = 192 - 12

     12y = 180

     y = 15

     Plugging into equation (1),

     3x + 8(15) = 192

     3x + 120 = 192

    x = 24

11). (3x + 49)° = (7x - 23)° [by corresponding angles]

    7x - 3x = 49 + 23

    4x = 72 ⇒ x = 18

    (11y - 1)° = (3x)° [by corresponding angles]

    11y = 3×18 + 1

     11y = 55 ⇒ y = 5

12). (5x - 38)° = (3x - 4)° [by corresponding angles]

     5x - 3x = 38 - 4

     2x = 34

     x = 17

     (7y - 20)° + (5x - 38)° + 90° = 180°

     [The angles within a triangle sum to 180°]

     7y + 5x - 58 = 90

     5x + 7y = 148

     5×17 + 7y = 148

     85 + 7y = 148

     7y = 148 - 85

     y =