To find the 20th term in this sequence, we can simply keep on adding the common difference all the way until we get up to the 20th term.
The common difference is the number that we are adding or subtracting to reach the next term in the sequence.
Notice that the difference between 15 and 12 is 3.
In other words, 12 + 3 = 15.
That 3 that we are adding is our common difference.
So we know that our first term is 12.
Now we can continue the sequence.
12 ⇒ <em>1st term</em>
15 ⇒ <em>2nd term</em>
18 ⇒ <em>3rd term</em>
21 ⇒ <em>4th term</em>
24 ⇒ <em>5th term</em>
27 ⇒ <em>6th term</em>
30 ⇒ <em>7th term</em>
33 ⇒ <em>8th term</em>
36 ⇒ <em>9th term</em>
39 ⇒ <em>10th term</em>
42 ⇒ <em>11th term</em>
45 ⇒ <em>12th term</em>
48 ⇒ <em>13th term</em>
51 ⇒ <em>14th term</em>
54 ⇒ <em>15th term</em>
57 ⇒ <em>16th term</em>
60 ⇒ <em>17th term</em>
63 ⇒ <em>18th term</em>
66 ⇒ <em>19th term</em>
<u>69 ⇒ </u><u><em>20th term</em></u>
<u><em></em></u>
This means that the 20th term of this arithemtic sequence is 69.
Answer:
The solution to the inequality is 0.
It's a linear function. We need only two points to draw a graph.
We choose any values of x and calculate the value of y.
for x= 0 → y = 3(0) - 1 = 0 - 1 = -1 → (0, -1)
for x = 2 → y = 3(2) - 1 = 6 - 1 = 5 → (2, 5)
for x = 0 → y = 3(0) - 1/3 = 0 - 1/3 = -1/3 → (0, -1/3)
for x = 2 → y = 3(2) - 1/3 = 6 - 1/3 = 5 2/3 → (2, 5 2/3)
Step-by-step explanation:
LHS= sin 3x/sin x - cos 3x/cosx
Taking LCM,
<u>=</u><u>sin3xcosx- cos3xsinx</u>
sinxcosx
<u>=</u><u>sin(3x-x)</u>
sinxcosx
= <u>2sin2x</u>
2sinxcosx
=<u> </u><u>2sin2x</u><u> </u>
sin2x
=2
= RHS.
Proved.
Let's call the angles x and y. We know that supplementary angles must add to 180 degrees, so x+y=180.
Furthermore, we know that x is 75% more than 2y. We can write "75% more than" numerically as 1.75, so x = 1.75(2y).
We can simplify the second equation by multiplying 1.75 and 2 together to get x = 3.5y.
Now we can solve the system of equations by substitution by plugging 3.5y in for x in x+y=180.
(3.5y) + y = 180
Combine like terms.
4.5y = 180
Divide by 4.5
y = 40
Plug y = 40 in and solve for x.
x + 40 = 180
x = 140
The answer is 40 and 140. Hope this helps :)
