5 1/2 of what number is 55?
2 answers:
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(a) The explicit rule to model the sequence formed by the number of seats in each row is
(b) The 35th row has 120 seats
Step-by-step explanation:
The rule of the nth term of an arithmetic sequence is
, where
- a is the the first term
- d is the common difference between each two consecutive terms
∵ There are 18 seats in the 1st row
∵ There are 21 seats in the 2nd row
∵ 21 - 18 = 3
∵ The number of seats is increased by 3 with each additional row
- The number of seats in each row represents an arithmetic
sequence because there is a common difference between
each two consecutive rows
∴ The number of seats in each row formed an arithmetic sequence
∵ The number of seats in the first row = 18 seats
∴ a = 18
∵ The number of seats in a row continues to increase by 3 with each
additional row
∴ d = 3
- Substitute the values of a and d in the rule of nth term
∴
- Simplify the right hand side
∴
- Add like terms
∴
(a) The explicit rule to model the sequence formed by the number of seats in each row is
∵ There are 120 seat in a row
- Substitute by 120 in the rule above
∴ 120 = 15 + 3n
- Subtract 15 from both sides
∴ 105 = 3n
- Divide both sides by 3
∴ n = 35
∴ The number of the row is 35
(b) The 35th row has 120 seats
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
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Notice that based on the diagram, all of the sides of the triangle are the same length. (The dashes on the sides of the triangle show that the sides are of congruence.) This means that the triangle is an equilateral triangle. An important thing to note about equilateral triangles is that they all have angles of 60°. All angles in equivalent triangles are 60°.
This means that we can set equal to 60 to solve for
:
- Set up
- Add 3 to both sides
- Divide both sides by 7
Our answer is x = 9.