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bixtya [17]
3 years ago
5

If u = , v = , and w = , which operation gives the result represented in the graph? Thank you so much in advance!

Mathematics
1 answer:
Roman55 [17]3 years ago
4 0

Answer:B

Step-by-step explanation:

Plato Users

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Dont really understand how to do this
bija089 [108]

Answers:

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

========================================================

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}

---------------------

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

-----------------------

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
Write<br> 17/3<br> as a mixed number.<br> O A. 3<br> O-B. 3<br> © C.53<br> O D. 53
IRINA_888 [86]

Answer:

5 2/3

Step-by-step explanation:

15 ÷ 3 = 5.

with 2 leftover, you will have 2/3

5 + 2/3 = 5 2/3

<em>Good Luck!</em>

<em>-kiniwih426</em>

3 0
3 years ago
Read 2 more answers
X+5/2 + x−3/3 =3 1/6
Nataly [62]
The answer is x=-1/2
3 0
3 years ago
Read 2 more answers
-4x -7 - 3x + 4 = 25
zimovet [89]

Answer:

x=-4

Step-by-step explanation:

-4x -7 - 3x + 4 = 25

-7x=25-4+7

x=-28/7

x=-4

7 0
3 years ago
Read 2 more answers
7 times as many as 3,073
mestny [16]

if your wondering what 7 times 3073 is then your answer is 21511. If your looking for something else I don't understand it then. Hope this helps!

8 0
2 years ago
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