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3 years ago

6y + 4 – 3y = -5 + y + 17

Mathematics

2 answers:

Zolol [24]3 years ago

7 0

Answer:

y = 4

Step-by-step explanation:

6y + 4 - 3y = -5 + y + 17

First, we have to combine like terms on each side of the equation:

3y + 4 = y + 12

Then, we have to combine the terms from both sides of the equation:

3y + 4 = y + 12

-4 -4

3y = y + 8

-y -y

2y = 8

Then, we divide so we only have y on the left side:

2y = 8

/2 /2

y = 4

Hope this helps :)

Luda [366]3 years ago

5 0

Answer:

Step-by-step explanation:

6y+4-3y=-5+y+17

6y-3y-y= -5+17-4

2y=8

y=4

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