Buckle up, this one was a long one.
I set up 1 / 3(12 + x) as a fraction and set it equal to - 8(6 - x).
Get rid of the parentheses by distributing the integers on the outside. You get 1 / 36 + 3x = - 48 + 8x.
To get rid of the fraction, you multiply both sides by the (36 + 3x) polynomial to get 1 = (- 48 + 8x)(36 + 3x).
Now we do the FOIL method to get 1 = 24x^2 + 288x - 144x - 1728. Combine like terms to get 24x^2 + 144x - 1728 = 1.
Simply again by dividing each term the GCF of 24 to get 24(x^2 + 6x - 72) = 1.
Factor the inside of the parentheses to get 24(x + 12)(x - 6) = 1. Now divide both sides by 24 to isolate the x variables to get (x + 12)(x - 6) = 1/24.
Set each polynomial equal to 1/24 to get you possible answers for what x can be.
x + 12 = 1/24. Subtract 12 from both sides; you get x = - 12 + 1/24 to get x = - 11 23/24.
x - 6 = 1/24. Add 6 to both sides; you get x = 6 + 1/24 to get x = 6 1/24
Answer:
Total favourable outcomes = 36
No. of favourable outcomes of getting a sum of 2 = 1
Probability of getting a sum of 2 = 1/36
Answer:
First = 1000
Second = 10,000
Step-by-step explanation:
Given the following :
Amount invested = $11,000
A portion earns 2 1/2 % interest per year
The rest earns a rate of 2% per year
Total Interst earned after a year = $255
Amount invested at each rate
Let amount invested at 2 1/2% = a
Amount invested at 2% = 11,000 - a
Simple interest = principal * rate * time
First investment :
a * 5/2% * 1
Second :
(11000 - a) * 2%
Firat investment + second = $225
a * 0.025 + (11000 - a) * 0.02 = 225
0.025a + 220 - 0.02a = 225
0.005a = 225 - 220
0.005a = 5
a = 5 / 0.005
a = 1000
Amount in first investment = 1000
Second investment = 11000 - 1000 = 10,000
One way to solve this problem is by:
First multiply both sides by 10
30r=9
Now divide by 30
r=0.3 Final Answer
