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10. The number of people, N, employed in a chain of cafes is related to the number of cafes, n, by the equation:
N= 10n + 120
(a) Illustrate this relation by plotting a graph of N against n for 0 ≤ n ≤ 20.
(b) Hence, or otherwise, calculate the number of
(i) employees when the company has 14 cafes;
(ii) cafes when the company employs 190 people.
(c) State the values of the slope and intercept of the graph and give an interpretation.

Sagot :

Answer:

b.

i. N= 10n+120

    = 10*14+120

    = 260

ii. N = 10n+120

<=> 190=10n+120

<=> n=7

Step-by-step explanation:

MrRoyal

The given equation N= 10n + 120 is an illustration of a linear equation. The following are the results:

  • There are 260 employees when the number of cafes is 14
  • There are 7 cafes when the number of employees is 190
  • The slope of the graph is 10 and the intercept is 120

Given

[tex]N = 10n + 120[/tex]

A. The graph

See attachment for the graph of [tex]N = 10n + 120[/tex] where:

[tex]n \to[/tex] x-axis

[tex]N \to[/tex] y-axis

B. i) Employees, when there are 14 cafés.

This means that n= 14

So, we have:

[tex]N = 10n + 120[/tex]

[tex]N = 10 \times 14 + 120[/tex]

[tex]N = 140 + 120[/tex]

[tex]N = 260[/tex]

Hence, there are 260 employees

B ii) Cafés, when there are 190 employees

This means that N = 190

So, we have:

[tex]N = 10n + 120[/tex]

[tex]190 =10n + 120[/tex]

Collect like terms

[tex]10n = 190 - 120[/tex]

[tex]10n = 70[/tex]

Divide by 10

[tex]n = 7[/tex]

Hence, there are 7 cafés

C. The slope and the intercept.

A linear equation is represented as:

[tex]y = mx + b[/tex]

Where:

[tex]m \to[/tex] slope

[tex]b \to[/tex] y-intercept

Given that:

[tex]N = 10n + 120[/tex]

By comparing both equations

[tex]m = 10[/tex]

[tex]b = 120[/tex]

The slope implies that, the rate of employee per unit café is 10

The intercept of the graph implies that the initial number of employee is 120

Read more about linear graphs at:

https://brainly.com/question/20853486

View image MrRoyal
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