Ron earned $ 840 in a week . How much will he earn in 36 days
1 answer:
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Answer:
1. (5x - 2) + (2x - 2) + x =
2. m<J =
3. m<K =
4. m<L =
Step-by-step explanation:
Generally, the sum of angles in a triangle = .
So that;
m<J + m<K + m<L =
(5x - 2) + (2x - 2) + x =
5x + 2x + x -2 -2 =
8x - 4 =
8x = + 4
8x = 184
x =
x =
Thus,
m<J = (5x - 2)
= 5(23) - 2
=
m<K = (2x -2)
= 2(23) - 2
=
m<L = x
=
The chairs in the auditorium illustrates an arithmetic sequence
- The recursive rule is: an = an-1 + 8; a1 = 26
- The explicit rule is: an = 18 + 8n
- There are 74 seats in the 7th row
- 840 chairs can fit the auditorium
From the question, we have the following sequence:
Seats: 18, 26, 34
Rewrite as:
26 = 18 + 8
34 = 26 + 8
The above means that:
The number of seats on a row is 8 added to the the number of seats on the previous row.
Hence, the recursive rule is:
an = an-1 + 8; a1 = 26
<h3>The explicit rule</h3>In (a), we have:
a1 = 26 and d = 8
The explicit rule is calculated using:
an = a1 + (n -1) * d
This gives
an = 26 + (n - 1) * 8
Expand
an = 26 - 8 + 8n
Evaluate the difference
an = 18 + 8n
Hence, the explicit rule is:
an = 18 + 8n
<h3>The number of seats in the row 7</h3>This means that n = 7.
So, we have:
a7 = 18 + 8 * 7 = 74
Hence, there are 74 seats in the 7th row
<h3>The sigma notation</h3>We have the maximum number of rows to be 12.
So, the sigma notation would be:
The total number of seats is:
Sn = n/2(2a + (n -1) * d)
This gives
S12 = 12/2(2 * 26 + (12 -1) * 8)
S12 = 840
Hence, 840 chairs can fit the auditorium
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