Distributive property: a(b + c) = ab + ac
4n - 2 - 2n = 2(2n - 1 - n)
4n - 2 - 2n = 2n - 2 = 2(n - 1)
Hello from MrBillDoesMath!
Answer:
a^6 + 4 a^5 + 5 a^4 - 5 a^2 - 4 a - 1
Discussion:
You may need to clean things up a bit but suppose that
S(1) = a-1
S(2) = a^2 -1
Since this is a geometric series, the geometric ratio is given by
S(2)/ S(1) = (a^2 -1)/ (a-1)
= (a+1)(a-1)/ (a-1)
= a+1
Conclusion:
S(2) = (a+1) S(1) = (a+1) (a-1)
S(3) = (a+1) S(2) = (a+1) (a+1) (a-1) = (a+1)^ (3-1) (a-1)
S(4) = (a+1) S(3) = (a+1) * (a+1)^2 (a-1) ) = (a+1)^(4-1) (a-1)
in general.....
S(n) = (a+1)^ (n-1) (a-1)
So
S(6) = (a+1)^ (6-1) (a-1)
= (a-1) (a+1) ^ 5
= a^6 + 4 a^5 + 5 a^4 - 5 a^2 - 4 a - 1
Hope I didn't screw something here!
Thank you,
MrB
Answer:
The one opposite of 100°, as the bigger the angle, the bigger the opposing side, is the biggest.
By the same logic, the one opposite 45° is the next biggest.
Continuing with that, the one opposite the black one (which would equal 35°, I think) is the smallest.
<h3>Given</h3>
- Set A: A = {-26, -25, -24, -23, - 22, - 21}
- Set B: B ∈ {x: x is even, x ≥ 6 and x ≤ 20}
<h3>(a) </h3>
<em />
<em>Cardinality means the number of elements in the set.</em>
Cardinality of the set A:
n(A) = 6, since we can count 6 elements.
Set B has even numbers between 6 and 20, both included:
- B = {6, 8, 10, 12, 14, 16, 18, 20}
Then its cardinality is:
<h3>(b) </h3>
To solve this we need to compare the elements of sets A or B with numbers given:
- -22 ∈ A, True ⇒ -22 is listed as element of A
- 6 ∈ B, True ⇒ 6 is listed as element of B
- - 21 ∉ A, False ⇒ - 21 is listed as element of A
- 2 ∈ B, False ⇒ 2 is not listed as element of B
Let the smaller number be x and the larger number be y.
We can calculate this by using simultaneous equation, aka listing 2 equations out.
From given,
X + y = 43
Let this be equation no. 1
X + 19 = y
Let this number be equation 2.
We can do simultaneous equations either by substitute method or elimination. In this case I'm using substitute.
We can already obtain the value of y (in terms of x) in euqation no. 2, so all we gonna do is to put y into equation 1.
X + x + 19 = 43
Solve this by algebra.
2x = 43 - 19
X = 12
Now we know the exact value of x
Now substitute x = 12 into equation no. 2
12 + 19 = y
Y = 31
So the answer is 12 and 31
