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Answer:
x = 14
m∠SOP = (7x - 2)° = 96°
m∠SOR = (5x + 14) = 84°
Step-by-step explanation:
`From the given picture,
Angle SOP and angle SOR are the linear pairs.
Therefore, sum of these angles will be equal to to 180°.
m∠SOP + m∠SOR = 180° -----(1)
Since, m∠SOP = (7x - 2)° and m∠SOR = (5x + 14)°
[There is a misprint in this question. There should be x in place of y in the measures of the angles]
By substituting these values in the equation (1),
(7x - 2) + (5x + 14) = 180
12x + 12 = 180
12x = 180 - 12
12x = 168
x =
x = 14
m∠SOP = (7x - 2)° = 96°
m∠SOR = (5x + 14) = 84°
Answer:
The 13th term is 81<em>x</em> + 59.
Step-by-step explanation:
We are given the arithmetic sequence:
And we want to find the 13th term.
Recall that for an arithmetic sequence, each subsequent term only differ by a common difference <em>d</em>. In other words:
Find the common difference by subtracting the first term from the second:
Distribute:
Combine like terms. Hence:
The common difference is (7<em>x</em> + 5).
To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:
Where <em>a</em> is the initial term and <em>d</em> is the common difference.
The initial term is (-3<em>x</em> - 1) and the common difference is (7<em>x</em> + 5). Hence:
To find the 13th term, let <em>n</em> = 13. Hence:
Simplify:
The 13th term is 81<em>x</em> + 59.