The number of dimes is 75 coins.
The number of nickels is 1 coin.
<u>Step-by-step explanation:</u>
It is given that,
A box contains 76 coins, only dimes and nickels.
- The 10 cent coin is called a dime.
- Let, the number of dimes be x.
- The 5 cent coin is called a nickel.
- Let, the number of nickels be y.
<u>This is represented by the system of equations :</u>
x + y = 76 -------(1)
10x + 5y = 4.90 ------(2)
Multiply eq (1) by 5 and subtract eq (2) from eq (1),
5x + 5y = 380
-<u>(10x + 5y = 4.90)</u>
<u>-5x = 375.1</u>
x = 375/5
x = 75 coins.
The number of dimes is 75 coins.
Substitute x=75 in eq (1),
y = 76 - 75
y = 1 coin.
The number of nickels is 1 coin.
For x^3-11x^2+33x+45 , we can make it an equation so <span>x^3-11x^2+33x+45=0. Next, we can find out if -1 or -3 is a factor. If -1 is a factor, than (x+1) is factorable. Using synthetic division, we get
x^2-12x+45
___ ________________________
x+1 | x^3-11x^2+33x+45
- (x^3+x^2)
_________________________
-12x^2+33x+45
- (-12x^2-12x)
______________
45x+45
-(45x+45)
___________
0
Since that works, it's either B or D. We just have to figure out when
</span> x^2-12x+45 equals 0, since there are 3 roots and we already found one. Using the quadratic formula, we end up getting (12+-sqrt(144-180))/2=
(12+-sqrt (-36))/2. Since sqrt(-36) is 6i, and 6i/2=3i, it's pretty clear that B is our answer
12m-32=-80
12m=-80+32
12m=-48
m=-4
