Answer:
4
Step-by-step explanation:
Equation 1
Equation 2
What is the value of 
where each variable represents a real number?
Let's expand equation 1:
Simplify each term if can:
See if we can factor a little to get some of the left hand side of equation 2:
The first two terms have 
and if I factored from first two terms I would have 
which is the first term of left hand side of equation 2.
So let's see what happens if we gather the terms together that have the same variable squared together.
Factor the variable squared terms out of each binomial pairing:
Replace the sum of those first three terms with what it equals which is 6 from the equation 2:
Combine like terms:
Subtract 6 on both sides:
Divide both sides by 3:
Answer:
See definition below
Step-by-step explanation:
Since we have to give a recursive definition, we must give a initial value f(0). Additionally, the value of f(n) must depend on the value of f(n-1) for all n≥1.
The required value of f(0) is (0+1)!=1!=1.
Now, the factorial itself is a recursive function, because (n+1)!=(n+1)n!. In terms of f, this means that f(n)=(n+1)f(n-1) for all n≥1.
Then, our definition is: f:N→N is defined by
- f(0)=1.
- For n≥1, f(n)=(n+1)f(n-1).
Answer:
No it does not
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
<u>Given AP where:</u>
<u>To find</u>
<u>Since</u>
- a₄ = a₁ + 3d
- a₂ = a₁ + d
- a₆ = a₁ + 5d
<u>Initial equations will change as:</u>
- a₁ + 3d = 2(a₁ + d) - 1 ⇒ a₁ + 3d = 2a₁ + 2d - 1 ⇒ a₁ = d + 1
- a₁ + 5d = 7 ⇒ a₁ = 7 - 5d
<u>Comparing the above:</u>
- d + 1 = 7 - 5d
- 6d = 6
- d = 1
<u>Then:</u>
- a₁ = d + 1 = 1 + 1 = 2
- a₁ = 2
The first term is 2
Answer:
1)Find the prime factorization of 242
242 = 2 × 11 × 11Step-by-step explanation:
2)Find the prime factorization of 132
132 = 2 × 2 × 3 × 11
3)To find the GCF, multiply all the prime factors common to both numbers:
Therefore, GCF = 2 × 11
The lost one 4) GCF = 22
