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2 years ago

Please help me asap !!

Mathematics

1 answer:

Natasha2012 [34]2 years ago

5 0

Answer:

3.5

Step-by-step explanation:

(42 - 14)/(12 - 4) = 28/8 = 7/2 = 3.5

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Elena is paid a constant rate for each hour she works. The table shows the amounts of money that Elena earned for various amount

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Constant rates are used to illustrate linear functions.

The average rate of change is $9.0 per hour
The function that models the table is: $\mathbf{f(x) = 9x }$
The amount earned in 7.5 hours is $67.5

(a) The average rate of change

This is calculated using:

$\mathbf{Rate = \frac{y_2 -y_1}{x_2 -x_1}}$

So, we have:

$\mathbf{Rate = \frac{31.5-22.50}{3.5 - 2.5}}$

$\mathbf{Rate = \frac{9}{1.0}}$

$\mathbf{Rate = 9.0}$

Hence, the average rate of change is $9.0 per hour

(b) A function that models the table of values

Let x represent hours, and y represent the earnings.

So, we have:

$\mathbf{y =m (x - x_1) + y_1}$

Where:

m =Rate = 9.0

So, we have:

$\mathbf{y = 9(x - 2.5) + 22.5}$

Expand

$\mathbf{y = 9x - 22.5 + 22.5}$

$\mathbf{y = 9x }$

Represent as a function

$\mathbf{f(x) = 9x }$

Hence, the function that models the table is: $\mathbf{f(x) = 9x }$

(c) Amount earned for 7.5 hours

This means that x = 7.5

So, we have:

$\mathbf{f(7.5) = 9 \times 7.5 }$

$\mathbf{f(7.5) = 67.5}$

Hence, the amount earned in 7.5 hours is $67.5