50 POINTS, HELP
2 answers:
Answer:
Option D. = 8n - 359
Step-by-step explanation:
The given sequence is -351, -343, -335, -327, -319......
As we can see there is a common difference of 8 in each successive term.
T₂ - T₁ = -343 - (-351 ) = 351 - 343 = 8
T₃ - T₂ = -335 - ( 343 ) = 343 - 335 = 8
Therefore, the given sequence is an arithmetic sequence.
Now the explicit formula of an arithmetic sequence is represented by
a = first term of the sequence
n = number of terms
d = common difference
= -351 + 8n - 8
= 8n - 359
Therefore, option D. = 8n - 359 is the answer.
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<h2>Answer:</h2>
∠ABC = 76°
BC = 20.1
CA = 28.0
<h2>Step-by-step explanation:</h2>Solving the triangle means finding all unknown angles and sides of the triangle.
(i) Two of the angles (∠BCA = 60° and ∠CAB = 44°) are given. To find the third angle (∠ABC), use one of the theorems stating <em>that the sum of angles of a triangle is equal to 180°.</em>
Therefore, the sum of angles of the triangle ABC is 180°. i.e
∠ABC + ∠BCA + ∠CAB = 180°
=> ∠ABC + 60° + 44° = 180°
=> ∠ABC + 104° = 180°
=> ∠ABC = 180° - 104°
=> ∠ABC = 76°
(ii) One side (BA) of the triangle is given. To get the other sides, we use the sine rule as follows;
=>
=>
<em>Substitute the necessary values</em>
---------------------(ii)
(a) To get side BC, use the first two terms of equation (ii)
<em>Cross multiply</em>
BC x sin 60 = 25 x sin 44
BC x 0.8660 = 25 x 0.6947
0.8660 x BC = 17.3675
BC =
BC = 20.05
=> BC = 20.1 to the nearest tenth
(b) To get CA, use any two terms of equation (ii). Using the first and third terms, we have;
<em>Cross multiply</em>
CA x sin 60 = 25 x sin 76
CA x 0.8660 = 25 x 0.9703
0.8660 x CA = 24.2575
CA =
CA = 28.01
=> CA = 28.0 to the nearest tenth