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3 years ago

How do we find the value of -q in the equation -q-3=7

Mathematics

1 answer:

Cloud [144]3 years ago

3 0

-q is -10. Because the number sentence equals to -q=7+3. So q = -10.

put in(recheck): --10=7+3

+10=10

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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.

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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