Find the gradient of the line segment between the points (-3,2) and (-2,5).

Dont really understand how to do this

bija089 [108]

Answers:

$t_{10} = -22 \ \text{ and } S_{10} = -85$

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Explanation:

$t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2$

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

$t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4$

and so on. This process may take a while to reach $t_{10}$

There's a shortcut. The nth term of any arithmetic sequence is

$t_n = t_1+d(n-1)$

We plug in $t_1 = 5 \text{ and } d = -3$ and simplify

$t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8$

Then we can plug in various positive whole numbers for n to find the corresponding $t_n$ value. For example, plug in n = 2

$t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2$

which matches with the second term we found earlier. And,

$tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}$

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The notation $S_{10}$ refers to the sum of the first ten terms $t_1, t_2, \ldots, t_9, t_{10}$

We could use either the long way or the shortcut above to find all $t_1$ through $t_{10}$ . Then add those values up. Or we can take this shortcut below.

$Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}$

The sum of the first ten terms is -85

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As a check for $S_{10}$ , here are the first ten terms:

t1 = 5
t2 = 2
t3 = -1
t4 = -4
t5 = -7
t6 = -10
t7 = -13
t8 = -16
t9 = -19
t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that $S_{10} = -85$ is correct.

6 0

2 years ago

Which best describes the solution to 4 – 7? Because –4 + (–7) is an equivalent expression, the answer is –11. Because 4 + (–7) i

ANTONII [103]

The answer to your question would be: Because 4 + (-7) is an equivalent expression, your answer is -3. The reason for this can be described using integers. So lets say you have $4. You owe your brother $7. Since you don't have enough to pay him, you can pay him all your money, but you still have to pay him $3 more. This means technically your balance is $-3, cause if he needs the money, the second you get it he will ask for it. Sorry if this isn't too great of an example, not sure what else I could think of. Pretty much remember when subtracting a number, you can add the negative of the number, because that is the same thing. Hope this helps. Please rate, leave a thanks, and mark a brainliest answer (Not necessarily mine). Thanks, it really helps! :D

3 0

3 years ago

Read 2 more answers

You are a member of a darts team and they have won £1750 prize money in a competition. £70 is to be saved for a celebration part

grandymaker [24]

Most of the information's that are required for solving this question is already given in the question. It is important to check them minutely before trying to solve the problem in hand.
Amount of prize money won by the darts team = 1750 pounds
The amount of money that needs to be saved = 70 pounds
Then
Amount of money remaining after savings = (1750 - 70) pounds
= 1680 pounds
The number of team members in the darts team = 14
So
The amount of money
that each members of the darts team gets = 1680/14
= 70 pounds
From the above deduction we can easily conclude that each member of the darts teams will get an amount of 70 pounds.

7 0

3 years ago

Read 2 more answers

ayme built a box in the shape of a rectangular prism with the dimensions shown. What is the volume of the box, in cubic inches?

Snezhnost [94]

Answer:

$64(in)^{3}$