5.345345... can be expressed as (fraction form)

Answer:

Part A) The straight-line distance between the school and the Fire Station is

Part B) The straight-line distance between the school and the hospital is

Step-by-step explanation:

The full question can be found in the attached image.

Let

The positive x-coordinates represent the East

The positive y-coordinates represent the North

The negative x-coordinates indicate the West

The negative y-coordinates indicate the South

Treat point A (0,0) as the Middle School (reference point).

Part A) The Town Hall is situated 4.3 miles directly east of the Middle School,

thus the coordinates for Town Hall are B(4.3,0).

The Fire Station is positioned 1.7 miles directly north of Town Hall, therefore

the coordinates for the Fire Station are C(4.3,1.7).

What is the straight-line distance between the school and the Fire Station?

Keep in mind that

the distance formula between two points is indicated as

We have

A(0,0) and C(4.3,1.7).

Now substitute

Part B) Now considering

The hospital is 3.1 miles west of the fire station.

The coordinates for the hospital are D(4.3-3.1,1.7).

D(1.2,1.7)

What is the straight-line distance between the school and the hospital?

Remember that

the distance formula applies here as well,

with points A(0,0) and D(1.2,1.7).

Substituting the values gives us

In theory, each letter has an equal chance of appearing since there are 15 of each. With 5 letters available, the total count is 75 balls, and each letter has a probability of being selected.

This suggests a theoretical frequency of , meaning on average, any specific letter should be drawn 250 times, so the answer is D.

Response:

Resort A experiences a more uniform snowfall, indicating less fluctuation. In contrast, Resort B has a greater median snowfall and a higher interquartile range, making it likely for Kevin to encounter better snowfall conditions there.

Thanks:) I just completed it edg

Detailed explanation:

Answer:

To find the number of genuine solutions for a system of equations consisting of a linear equation and a quadratic equation

1) With two variables, say x and y, rearrange the linear equation to express y, then substitute this y in the quadratic equation

After that, simplify the resulting equation and determine the number of real roots utilizing the quadratic formula, for equations of the type 0 = a·x² - b·x + c.

When b² exceeds 4·a·c, two real solutions emerge; if b² equals 4·a·c, there will be a single solution.

Step-by-step explanation:

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 =