The length of a sticky note measures 77 millimeters. Express this length in millimeters and explain.

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

The temperature, t, in degrees Fahrenheit, can be found by counting the number of cricket chirps, c, heard in 14 seconds and the

AleksandrR [38]

The graph is continuous.A viable solution is (10, 50) at the function t = c + 40.

The complete question is given below:-

The temperature, t, in degrees Fahrenheit, can be found by counting the number of cricket chirps, c, heard in 14 seconds and then adding 40. The equation t = c + 40 models the relationship between the temperature and the number of cricket chirps. What is true about the graph that represents this real-world scenario? Check all that apply.

<h3>What is a graph?</h3>

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The graph is continuous.

A viable solution is (10, 50).

t = c + 40

The given equation is

t = c + 40

This equation models the relationship between the temperature and the number of cricket chirps.

Where is the temperature in degrees Fahrenheit and is the number of cricket chirps heard in 14 seconds?

According to the problem, the temperature can be found by counting the number of cricket chirps heard in 14 seconds and then adding 40.

Now, the choices to this question are

The graph is continuous.

All values of t must be positive.

A viable solution is (–2, 38).

A viable solution is (0.5, 40.5).

A viable solution is (10, 50).

The graph of the given equation is attached, it shows the linear relationship between both variables.

Notice that the graph is continuous, it doesn't have any restriction, nor "emptiness" at certain values.

Observe that the remaining choices are all solutions to the equation, but not all of them are viable because the number of cricket chirps must be positive and integer because we can't hear the sound of 0.5 cricket.

Therefore, the last choice is viable (10, 50).

To know more about graphs follow

brainly.com/question/25020119

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