Use cosine rule,
cos(A)=(b^2+c^2-a^2)/(2bc)
=(10^2+12^2-6^2)/(2*10*12)
=13/15
A=29.926 degrees.................................(A)
cos(B)=(c^2+a^2-b^2)/(2ca)
=(12^2+6^2-10^2)/(2*12*6)
=5/9
B=56.251 degrees.................................(B)
cos(C)=(a^2+b^2-c^2)/(2ab)
=(6^2+10^2-12^2)/(2*6*10)
=-1/15
C=93.823 degrees.................................(C)
Check:29.926+56.251+93.823=180.0 degrees....ok
Answer:
You will have $1628.16 per month in discretionary money.
Step-by-step explanation:
In order to find the amount of money you have left for discretionary purposes at the end of the money, you need to calculate the total amount of your monthly pay is going towards expenses and savings. Since there are 12 months in a year, your monthly income is $3072. Of that amount, you spend 32% on housing and 15% on savings, for a total of 47%. The remaining percentage of your income would be considered discretionary, which would account for 53%. To find the amount of money, you take your monthly income and multiply it by 53%, or .53, which gives you $1628.16.
Let x=0.208bar or 0.20888...
1000x=208.888 and 100x=20.888 so
1000x-100x=208.888-20.888
900x=188
x=47/225
A factor pair is two numbers that can be multiplied to get a number.
With any number, we know that 1*itself is a factor pair. So
1*64
The number in the ones place, 4, is even, so we know that 64 is a multiple of 2. Half of 64 is 32, so
2*32
To find out if 3 is a factor of 64, we can add 6+4. If the answer is a multiple of 3, then we know that the number itself is a multiple of 3. Because 6+4=10, and 10 is not a multiple of 3, we know that 64 is not a multiple of 3.
If 2 is not a factor of a number, then we know that 4 (2*2) cannot be a factor. Because 2 is a factor of 64, then 4 might be as well. To discover whether or not 4 is a factor of 64, we can look at the number above multiplied by 2 to equal 64 (32) and see if it divides by 2 evenly, or we can half 64 and then half it again. If either answer is a whole number, then we know that the answer*4 equals 64, and that 64 is a multiple of 4. Because half of 32 is 16, a whole number, we know that
4*16=64
Because 64 does not have a 0 or 5 in the one's place, we know that it cannot be a multiple of 5.
Because 64 is not a multiple of 3, we know it cannot be a multiple of 6, because 6 is 2*3.
I happen to be familiar with my times tables, so I can tell that the multiples of 7 are 63 and 70, but not 64.
I don't know if 64 is a multiple of 8 off the top of my head, but I can count by 8s and see if 64 comes up: 8, 16, 24, 32, 40, 48, 56, 64, 72 - I can go on, but we can already see that 64 is a multiple of 8, so 8 is a factor of 64. If we count the number of 8s I can see that there are 8 of them when we get to 64. In other words,
8*8=64
Because we have gotten to a factor pair that is the same 2 number multiplied by each other (the square root) we know that we have found all factor pairs of 64.
