Six times the difference of a number and 9 is 54. Find the number.
2 answers:
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First we need to determine the type of progression in the question.
That's geometric progression. Because the pattern from one sequence to the others are about multiplying.
Second, determine the ratio of the progression
r = a₂/a₁
r = a₂ ÷ a₁
r = 1/2 ÷ 2
r = 1/2 × 1/2
r = 1/4
Third, determine the formula to know the recursive rule
a₂ = a × 1/4
a₂ = 1/4 × a
Fourth, determine a₁. a₁ is the first term of the progression
a₁ = 2
Final answer:
Recursive rule
a₁ = 2
That's geometric progression. Because the pattern from one sequence to the others are about multiplying.
Second, determine the ratio of the progression
r = a₂/a₁
r = a₂ ÷ a₁
r = 1/2 ÷ 2
r = 1/2 × 1/2
r = 1/4
Third, determine the formula to know the recursive rule
a₂ = a × 1/4
a₂ = 1/4 × a
Fourth, determine a₁. a₁ is the first term of the progression
a₁ = 2
Final answer:
Recursive rule
a₁ = 2
Answer:
<h2>The dependent variable is distance, the equation is y = 20x, and the dragonfly will travel 480 miles.</h2>Step-by-step explanation:
According to the graph, the dependent variable is Distance in miles, because it's on the vertical axis. Additionally, the independent variable is time in hours, because it's on the horizontal axis. However, you always put time as independent, because nothing affects time.
To find the equation, we just need to find the slope, using two points (0,0) and (2,40).
Therefore, the equation is , which shows a direct proportion between variables.
Now, in 24 hours, it would travel
It would travel 480 miles.
Therefore, the right answer is the second choice.