(i) The simultaneous equations in a, b and c are a+b+c = 7 , 4a+2b+c = 9 & 9a+3b+c = 13
(ii) Expression for nth term = n²-n+7
The first three terms of the sequence are 7, 9, 13
nth term = an²+bn+c
If we put n = 1 then,
1st term = a(1)²+b+c
⇒ a+b+c = 7 ......(1)
If we put n = 2 then,
2nd term = a(2)²+b×2+c
⇒ 4a+2b+c = 9 ........(2)
3rd term = a(3)²+b×3+c
⇒ 9a+3b+c = 13 .......(3)
Multiplying 4 with (1) and subtract (2) from (1) we get,
(4a+4b+4c)-(4a+2b+c)=28-9
⇒ 4a+4b+4c-4a-2b-c=19
⇒ 2b+3c=19 .....(4)
Multiplying 9 with (1) and subtract (3) from (1) we get,
(9a+9b+9c)-(9a+3b+c)=63-13
⇒ 9a+9b+9c-9a-3b-c=50
⇒ 6b+8c=50
⇒ 3b+4c=25 .....(5)
Multiplying 3 with (4) and multiplying 2 with (5), then subtract (5) from (4),
3(2b+3c)-2(3b+4c)=57-50
⇒ 6b+9c-6b-8c=7
⇒ c = 7
From (5),
3b+28 = 25
⇒ 3b = -3
⇒ b = -1
From (1),
a+(-1)+7 = 7
⇒ a-1=0
⇒ a=1
So, nth term = n²-n+7
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Answer:
The parallel lines are lines that are always at the same distance apart from each other and never touch. Also they must be drawn in the same plane.
Step-by-step explanation:
Consider the provided information.
The parallel lines are lines that are always at the same distance apart from each other and never touch. Also they must be drawn in the same plane.
The sketch that shows parallel lines is shown in figure.
The real life example of parallel lines.
Few examples are:
1) Railroad Tracks
2) Edges of walls
3) Zebra crossing
Answer: 2 × 12 + 2 × 3 or 2 × (12 + 3)
Step-by-step explanation:
Here, the cost of one song = $ 2
If the downloaded song on Monday was 12,
Then, the total money spend on Monday = 2 × 12
Similarly, If the downloaded song on Tuesday is 3,
Then, the total money spend on Tuesday= 2 × 3
Thus, the total cost of the songs on Monday and Tuesday = 2 × 12 + 2 × 3 Or 2 × ( 12 + 3)
Which is the required numerical expression.
By solving it we get = 2 × 15 = 30
Therefore, he spent $ 30 on Monday and Tuesday in downloading songs.
Answer:
x = 2, y = 3
Step-by-step explanation:
5x – 4y = -2
2x + 4y = 16
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<em>Solve by elimination. (-4y and +4y gives 0)</em>
7x = 14
x = 2
<em>Substitute 2 in one of the equations in order to find y.</em>
5(2) - 4y = -2
10 - 4y = -2
-4y = -12
y = 3
x = 2, y = 3
hope this helps!! p.s. i really need brainliest :)
Answer:
Yes
Step-by-step explanation:
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