Answer:
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Step-by-step explanation:
Samantha's weekly paycheck is $350 and she earns $12 in tips each hour. So, 12x represents the amount she earns in tips for working x hours. To find the total amount Samantha earns after working x hours, add the amount of her weekly paycheck and her amount earned in tips.
Next, to find Samantha's average hourly earnings over the course of a week, divide the total amount that she earns in a week by the number of hours that she works, x.
It is given that the average amount earned per hour for one particular week was $22. Therefore, set the above expression equal to 22 in order to create the rational equation that can be used to determine the number of hours Samantha worked that week.
1
Move everything to the left by subtracting 25 from both sides:
Both terms are squares: is the square of
, while 25 is the square of 5. So, we can apply the factoring
To factor the expression as
A multiplication is zero if and only if one of the factors is zero, so we have
2
The discriminant of the quadratic expression is defined as
So, you have
3
Similarly, we have