What is the greatest common factor of 72 and 112

Answer: x1 = 251/26, x2 = -111/26

Step-by-step explanation:

Greetings!

As illustrated in the diagram, the point you seek is where the two lines intersect.

This intersection point is found by solving the system of linear equations (both equations must be satisfied by the point):

You can approach solving it using the substitution method:

Then substitute x1 into equation 2 to resolve x2:

After which, utilize the x2 value to establish x1:

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 =

Response:

Step-by-step breakdown:

N

Answer:

28.4 cm

Step-by-step explanation:

The perimeter of the triangular wall is determined by adding all sides of the right triangle.

The triangle's height is given as 6 cm.

The hypotenuse measures 12 cm.

Using the Pythagorean theorem to find the third side:

Hypotenuse² = opposite² + adjacent²

Assigning the height as opposite = 6 cm, we find:

12² = 6² + adj²

Thus, adj² = 12² - 6²

Which gives us adj² = 144 - 36

So, adj² = 108

Leading to adj = √108

Thus, adj = 10.39 cm

The perimeter totals = 6 cm + 12 cm + 10.39 cm

= 28.39 cm

= 28.4 cm when rounded to the nearest tenth.

Answer: c. We can state with 95 percent confidence that the percentage of individuals surveyed who regard climate change as a significant issue is between 0.146 and 0.214.

Step-by-step explanation:

Interpretation of the 95% confidence interval :

This means one can be 95% certain that the actual proportion in the broader population falls within this range.

From the provided details, we identify the population parameter as p (the proportion of individuals that believe in climate change )

As a result, the 95 percent confidence interval is represented as (0.146, 0.214)

Interpretation: We can assert with 95% confidence that the actual population proportion of individuals who perceive climate change as a problem ranges from 0.146 to 0.214.

c. We are 95 percent confident that the proportion of people in the sample who think climate change is a problem is between 0.146 and 0.214.