4 Helen drew the pattern shown in a
1 answer:
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------------------------------------------------------------------
Equation
------------------------------------------------------------------
x² + 4x = 0
------------------------------------------------------------------
Add a constant
------------------------------------------------------------------
x² + 4x + (4/2)² - (4/2)² = 0 ← Add 2² to form perfect square
------------------------------------------------------------------
Evaluate bracket
------------------------------------------------------------------
x² + 4x + 2² - 2² = 0
------------------------------------------------------------------
Form the perfect square
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(x + 2)² = 4
------------------------------------------------------------------
Square root both sides
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(x+2) =
√4
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Evaluate the square root
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(x+2) = 2
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Solve x
------------------------------------------------------------------
x = 2 - 2 or x = -2 - 2
x = 0 or -4
------------------------------------------------------------------
Answer: The constant to add is 4 and the value of x = 0 or -4
------------------------------------------------------------------
Equation
------------------------------------------------------------------
x² + 4x = 0
------------------------------------------------------------------
Add a constant
------------------------------------------------------------------
x² + 4x + (4/2)² - (4/2)² = 0 ← Add 2² to form perfect square
------------------------------------------------------------------
Evaluate bracket
------------------------------------------------------------------
x² + 4x + 2² - 2² = 0
------------------------------------------------------------------
Form the perfect square
------------------------------------------------------------------
(x + 2)² = 4
------------------------------------------------------------------
Square root both sides
------------------------------------------------------------------
(x+2) =
------------------------------------------------------------------
Evaluate the square root
------------------------------------------------------------------
(x+2) =
------------------------------------------------------------------
Solve x
------------------------------------------------------------------
x = 2 - 2 or x = -2 - 2
x = 0 or -4
------------------------------------------------------------------
Answer: The constant to add is 4 and the value of x = 0 or -4
------------------------------------------------------------------
Answer:
The common ratio of the geometric sequence is:
Step-by-step explanation:
A geometric sequence has a constant ratio 'r' and is defined by
where
- aₙ is the nth term
- a₁ is the first term
- r is the common ratio
Given the sequence
Compute the ratios of all the adjacent terms:
The ratio of all the adjacent terms is the same and equal to
Therefore, the common ratio of the geometric sequence is: