Part (i)
I'm going to use the notation T(n) instead of 
To find the first term, we plug in n = 1
T(n) = 2 - 3n
T(1) = 2 - 3(1)
T(1) = -1
The first term is -1
Repeat for n = 2 to find the second term
T(n) = 2 - 3n
T(2) = 2 - 3(2)
T(2) = -4
The second term is -4
<h3>Answers: -1, -4</h3>
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Part (ii)
Plug in T(n) = -61 and solve for n
T(n) = 2 - 3n
-61 = 2 - 3n
-61-2 = -3n
-63 = -3n
-3n = -63
n = -63/(-3)
n = 21
Note that plugging in n = 21 leads to T(21) = -61, similar to how we computed the items back in part (i).
<h3>Answer: 21st term</h3>
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Part (iii)
We're given that T(n) = 2 - 3n
Let's compute T(2n). We do so by replacing every copy of n with 2n like so
T(n) = 2 - 3n
T(2n) = 2 - 3(2n)
T(2n) = 2 - 6n
Now subtract T(2n) from T(n)
T(n) - T(2n) = (2-3n) - (2-6n)
T(n) - T(2n) = 2-3n - 2+6n
T(n) - T(2n) = 3n
Then set this equal to 24 and solve for n
T(n) - T(2n) = 24
3n = 24
n = 24/3
n = 8
This means 2n = 2*8 = 16. So subtracting T(8) - T(16) will get us 24.
<h3>Answer: 8</h3>
To solve this problem we want to let X equal the amount of points that team A scored. Now we want to express the amount of points that team B scored in terms of X. If team A scored 7 more points than team B then team B scored X-7 points. We know that together they scored 163 points so we can set up this equation: x + x - 7 = 163 2x - 7 = 163 2x = 155 X = 78 Team A scored 78 points
Joshua delivered 30 hives to the local fruit farm.
If the farmer has paid to use 5% of the total number of Joshua's hives.
So 30 hives is 5% of the total number of hives.
5% of hives = 30
1% of hives = 30 ÷ 5 = 6
100% of hives = 6 × 100 = 600
Thus, Joshua had 600 hives before selling.
Now, he has = 600 - 30 = 570 hives.
Now, Joshua has 570 hives.
The answer must be -52 because I added parenthesis around -3 × 6 so it won't confuse people. I multiplied -3 and 6 and got -18. Then I multiplied -18 and 3 and got -54. I add -54 and 2 and got -52. Since there's more of negative than positive, I subtracted and got -52. Hope this helps :)
Answer:
To raise exactly $240, the charity needs to sell 20 snacks.
Step-by-step explanation:
Let
s = number of seats sold
y = number of snacks sold
Seats cost $24 each, then s seats cost $24s.
Snacks cost an additional $6 each, then y snacks cost $6y.
In total, s seats and y snacks cost $(24s+6y).
The charity needs to raise $240 to consider this event a success, so
If 5 seats are sold, then
To raise exactly $240, the charity needs to sell 20 snacks.
To solve this problem graphically, plot the graph of the line and find on this line point with s-coordinate 5. This is exactly point (5,20), so the charity needs to sell 20 snacks.
