For the sequence 2, 6, 18, 54, ..., the explicit formula is: an = a1 ! rn"1 = 2 ! 3n"1 , and the recursive formula is: a1 = 2, an+1 = an ! 3 . In each case, successively replacing n by 1, 2, 3, ... will yield the terms of the sequence. See the examples below.
1. 8c^2-26c+15= (4c-3) (2c-5). Break the expression into groups: =(8c^2-6c)+(-20c+15). Factor out 8c^2-6c: 2c(4c-3). Factor out -5 from -20c+ 15: -5(4c-3). Lastly factor out common term (4c-3) and thats how you'll get your answer (4c-3) (2c-5).
2. common factors for 270 and 360 is 90.To find this write the factors of each and find the largest one.270: 1, 270, 2, 135, 3, 90, 5, 54, 6, 45, 9, 30, 10, 27, 15, 18360: 1, 360, 2, 180, 3, 120, 4, 90, 5, 72, 6, 60, 8, 45, 9, 40, 10, 36, 12, 30, 15, 24, 18, 20
3. The factors for 8 a3b2 and 12 ab4 is 4. because 8: 1, 2, 4, 812: 1, 2, 3, 4, 6, 12.
4. 81a^2+36a+4= (9a+2)^2. Break down the expression into groups: (81a^2+18a)+(18a+4). Factor out 9a from 81a^2 +18a: 9a(9a+2). Factor out 2 from 18a+4: 2(9a+2). so the groups you got are now 9a(9a+2)+2(9a+2). Lastley factor out common term (9a+2) to get (9a+2) (9a+2). Finally you get the answer (9a+2)^2.
5. mn-15+3m-5n= (n+3)(m-5). factor out m from nm+3m: m(n+3). Factor out -5 from -5n-15: -5(n+3). And thats how you get the number (n+3)(m-5)
Hope this helped :) Have a great day
Answer: 3/5
Step-by-step explanation: To find the reciprocal of 1 and 2/3, we first need to convert 1 and 2/3 to an improper fraction.
To write a mixed number as an improper fraction, first multiply the denominator times the whole number, then add the numerator.
So here, we multiply the denominator, 3, times the whole number, 1, then we add the numerator. So we have (3 x 1) + 2 or 3 + 2 which is 5.
Now we put our new number over our old denominator and we get 5/3.
However, we're not done yet. We still need to find the reciprocal.
The reciprocal describes a fraction so when we're asked to find the reciprocal of 5/3, we want to switch the numerator and denominator.
So if we switch 5/3, we get the proper fraction 3/5.
Therefore, the mixed number 1 and 2/3 is equivalent to the improper fraction 5/3, and if we switch the top and bottom numbers, we get 3/5.
Answer:
1: 5/2 = 2.5 eggs
2: 25 1/3 bags of gravel
Step-by-step explanation:
