There is a giant spinning wheel at a carnival.

Response:

Each associate incurs a cost of $700 daily for the client, meaning that 'a' associates will cost the client 700a dollars each day. For each partner, the charge is $1500 daily, so 'p' partners will accumulate a cost of 1500p dollars daily. The cumulative bill amounts to 700a + 1500p = $14100:

700a + 1500p = 14100

700a + 1500p = 14100

Given that there are a total of 11 lawyers assigned (associates and partners), the equation a + p must equal 11.

a + p = 11

a + p = 11

\underline{\text{Formulate System of Equations:}}

Formulate System of Equations:

​

700a + 1500p =

700a + 1500p = 14100

14100

a + p = 11

11

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 =

Seven hundred nineteen thousand, nine hundred twenty-seven

Answer:

The cost of an ice cream cone with 5 scoops is $4.5

Step-by-step explanation:

According to the prompt:

An ice cream stand formulates the pricing for an ice cream cone containing x scoops as follows C(x) = .....[1]

Given that: x = 5 scoops

We seek to determine the cost for an ice cream cone containing 5 scoops.

Inserting x = 5 into [1] yields;

C(5) =

C(5) = = 2 + 2.5 = $4.5

Consequently, the price for an ice cream cone with 5 scoops is $4.5

Comment
Let's first tackle the simplest approach to finding the area of a triangle.

Formula for area is
A = 1/2 b * h

Substituting values
Area = 60 in^2
where b = x
and h = 2x - 1 
Thus, 60 = 1/2 * x * (2x - 1)

Now, we solve
60 = 1/2 * x (2x - 1) Multiply by 2
60 * 2 = x(2x - 1)
120 = x (2x - 1) Expand the brackets.
120 = 2x^2 - x  Subtract 120 from both sides.
2x^2 -  x - 120 = 0 which factors out to
(2x + 15)(x - 8) = 0

Now, solving for x
2x + 15 = 0
2x = - 15
thus, x = -15/2
which yields a negative value, hence discard this solution.

x - 8 = 0
gives us x = 8 

Area verification
base = 8
height = 16 - 1 = 15

thus Area = 1/2 * 8 * 15 = 60 confirming the calculation

Response
Utilize Area = 1/2 * b * h to determine both the base and height.