The scale on a map shows that 200 miles is represented by 5 inches on a map. Which proportion can be used to find the distance o
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Yes. The situation is defined by a linear function.
<u>Solution:</u>
Given, The weekly salary of a store manager includes a $30 bonus plus the number of hours the manager works multiplied by the managers earnings per hour.
Is this situation defined by a linear function?
Yes, the above given situation is defined by a linear function.
Now, let us see the linear equation for above situation
Let the number of hours worked by manager be "x", and cost per hour be "c" and total salary be "y"
Then, total salary is given as,
Total salary = $ 30 bonus + number of hours worked cost per hour
Above equation is a linear equation as "c" is constant ( cost per hour )
Hence, the given situation can be defined by linear function.
We need to find the base x in the following equation:
First, lets convert 365 from base 7 to base 10. This is given by
where the upperindex denotes the position of eah number. This gives
that is, 365 based 7 is equal to 194 bases 10.
Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:
where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives
Now, we have all number in base 10. Then, our first equation can be written in base 10 as
For simplicity, we can omit the 10 and get
so, we can solve this equation for x. By combining similar terms. we have
and by moving 197 to the right hand side, we obtain
Finally, we get
Therefore, the solution is x=5