Let f and s be the ages of the father and the son. We have
From the first equation we derive
Substitute this expression for f in the second equation and we have
The solutions to this equation are s=5 or s=37
Since the sum of the ages must be 42, the solutions would imply
We can only accept the first solution, since the second would imply a son older than his father!
Answer:
Either: 1 neg, 3 pos, 0 imaginary; 1 neg, 1 pos, 2 imaginary
Step-by-step explanation:
Look for the positive possibilities first. Count the numbe of sign changes then subtract 2, if possible, as many times as you can.
There are 3 sign changes. So the possible positive roots are either 3 or 1.
Now look for the negative possibilities. Replace each x with a -x and then count the sign changes. Replacing with -x's gives you this polynomial:
There is only one sign change here, so the possible negative roots is 1. Start with the negative roots to find the possible combinations of positive, negative, and imaginary, since there is only 1.
- 1 1
+ 3 1
i 0 2
Since this is a 4th degree, the number of roots we have has to add up to equal 4.
9514 1404 393
Answer:
$491.65
Step-by-step explanation:
The pay for the first 8 hours is $5.40 per hour × 8 hours = $43.20. Hours over 8 are paid at 1.5 × $5.40 = $8.10 per hour. There are at least 8 hours every day for the 6-day week. There are hours over 8 on Monday, Wednesday, Thursday, and Friday totaling 7 hours of overtime.
The amount of sales is more than $3000, so 4% will be paid on $3000, and 5% will be paid on the $1115 in excess of $3000.
So, the gross pay is ...
$43.20 × 6 + 8.10 × 7 = $315.90 . . . . wages
$3000 × .04 +1115 × .05 = $175.75 . . . commission
$315.90 +1.75.75 = $491.65 . . . . gross pay for the week
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It can be less tedious to let a spreadsheet do the calculations.
