Not sure if this is for algebra but this is the algebraic solution.
1. 5x + 1y = 25 (x meaning number of nickels) (y meaning number of pennies)
so 3 solutions could be, 5 nickels and 0 pennies, 4 nickels and 5 pennies, 3 nickels and 10 pennies.
2. First calculate how many days till the end of October, (31-14)= 17 days. then add 30 days for the entire month of November. Then add the 5 days that occurred in December. This will leave you with a total of 52 days.
The trigonometric equation <span> (sin Θ − cos Θ)^2 − (sin Θ + cos Θ)^3 can be simplified by:
</span>Using x for Θ:
<span>(sinx - cosx)^2 - (sinx + cosx)^2 </span>
<span>= (sin^2 x - 2sinxcosx + cos^2 x) - (sin^2 x + 2sinxcosx + cos^2 x) </span>
<span>= - 2 sinx cosx - 2 sinx cosx </span>
<span>= - 4 sinx cosx </span>
<span>= - 2sin(2x)
</span>
I hope it has come to your help.
The answer is B. Hope you get it.