The greatest common factor<span>, or </span>GCF<span>, is the </span>greatest factor<span> that divides two numbers. To find the </span>GCF<span> of two numbers: List the prime </span>factors<span> of each number. Multiply those </span>factors<span> both numbers have in </span>common<span>.</span>
Answer:
its a half circle
Step-by-step explanation:
Answer:
(-2, 6)
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
- Solving systems of equations by graphing
Step-by-step explanation:
<u>Step 1: Define systems</u>
4x - 2y = -20
7x + 2y = -2
<u>Step 2: Rewrite systems</u>
4x - 2y = -20
- Add 2y to both sides: 4x = 2y - 20
- Divide 4 on both sides: x = 1/2y - 5
<u>Step 3: Redefine systems</u>
x = 1/2y - 5
7x + 2y = -2
<u>Step 4: Solve for </u><em><u>y</u></em>
<em>Substitution</em>
- Substitute in <em>x</em>: 7(1/2y - 5) + 2y = =-2
- Distribute 7: 7/2y - 35 + 2y = -2
- Combine like terms: 11/2y - 35 = -2
- Add 35 to both sides: 11/2y = 33
- Isolate <em>y</em>: y = 6
<u>Step 5: Solve for </u><em><u>x</u></em>
- Define original equation: 7x + 2y = -2
- Substitute in <em>y</em>: 7x + 2(6) = -2
- Multiply: 7x + 12 = -2
- Subtract 12 on both sides: 7x = -14
- Divide 7 on both sides: x = -2
<u>Step 6: Graph systems</u>
<em>Check the system.</em>
Answer:b
Step-by-step explanation:on edge2020
Answer: The common number is 26.
Step-by-step explanation:
We know that the n-th term of a sequence is:
aₙ = 3*n^2 - 1
And the n-th term of another sequence is:
bₙ = 30 - n^2
Remember that in a sequence n is always an integer number.
We want to find a number that belongs to both sequences, then we want to find a pair of integers x and n, such that:
aₙ = bₓ
This is:
3*n^2 - 1 = 30 - x^2
Let's isolate one of the variables, i will isolate n.
3*n^2 = 30 - x^2 + 1 = 31 - x^2
n^2 = (31 - x^2)/3
n = √( (31 - x^2)/3)
Now we can try with different integer values of x, and see if n is also an integer.
if x = 1
n = √( (31 - 1^2)/3) = √10
We know that √10 is not an integer, so we need to try with another value of x.
if x = 2:
n = √( (31 - x^2)/3) = √(27/3) = √9 = 3
Then if we have x= 2, n is also an integer, n = 3.
Then we have:
a₃ = b₂
The common number between both sequences is:
a₃ = 3*(3)^2 - 1 = 26
b₂ = 30 - 2^2 = 26