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2 years ago

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3 lines are shown. A line with points T, R, W intersects a line with points V, R, S at point R. A line extends from point R to p

oint Z between angle V R W. Angle V R T is (5 x) degrees and angle T, R, S is (25 x + 30) degrees.
In the diagram, what is the measure of AngleWRS?

1 answer:

monitta2 years ago

3 0

Answer:

25 degrees

Step-by-step explanation:

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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

1 year ago

Answer this correct and you are a true legend 9 + 10 = ? ...

S_A_V [24]

Answer:

AcORdinG To MY CaLCulAtIoNS ItS 21

Step-by-step explanation:

Logic :)

5 0

2 years ago

If jimmy had had 9 apples and karl has 10 how mush togheter

sveticcg [70]

19? Lol........................

7 0

2 years ago

PLEASEEEEE HELPPPP ITS DUE at 11:59pm

Masja [62]

Since theres 4 numbers and 60 spins if you divide it you get the average number that all the numbers would land on. 2 would be landed on 15 times if it went exactly to the calculations. not 100% sure though

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2 years ago

Finding value of x. PQR <br> P- 2x° <br> 3<br> 3 <br> 3

Mrrafil [7]

$\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}$

Actually Welcome to the Concept of the Equilateral Triangles.

Since, we know that, all the sides of a triangle are equal, hence it is a Equilateral triangle.

Equilateral triangle has one all angles equal to 60°.

so, major angle P = 60°

hence, 2x=60°

===> x = 30°

6 0

2 years ago