The vertices of a hyperbola are located at (0-4) and (0, 12). The foci of the same hyperbola are located at (0-6)

Find the distance between the following two points: (-1, -2) and (-1, 3)

scZoUnD [109]

5 because -2+5=3 explanation

6 0

3 years ago

Read 2 more answers

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

2.8 meters linen divided into 45 cm pieces = # of pieces and waste

pogonyaev

2.8 meter= 2800cms

To solve this, we can create a simple algebraic equation:
45x=2800
Divide both sides by 45.
(45x)/45=(2800)/45
x=62.222

You can make 62 full pieces.

To find the waste, multiply the numbers of pieces by the length of each.
62*45
=2790
2800-<span>2790
=10 centimeters

There would be 10 centimeters of wasted linen.

Hope this helps!
-Benjamin</span>

6 0

3 years ago

Can 11/100 be reduced?

kiruha [24]

No it can not be reduced

7 0

3 years ago

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The trail to a waterfall is 4 1/5 miles long .The trail to an overlook is 1 2/3 times as long as the trail to the waterfall. Whi

erica [24]

I believe the correct answer to your question would be choice B. The trail is no more than 6 miles long.

4 0

3 years ago