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3 years ago

The product The product of 5 and a number n is at least -25

Mathematics

2 answers:

kogti [31]3 years ago

5 0

the answer is n > -5

Sophie [7]3 years ago

4 0

Answer:

$n > - 5$

Step-by-step explanation:

$5 \times n > - 25 \\ n > - 25 \div 5 \\ n > - 5$

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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

Plssss help i’m timed 6th grade math

WINSTONCH [101]

Answer:

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Find the rate of 250mm to 75cm

Kruka [31]

If you’re looking for the ratio:

75cm = 750mm

250:750
1:3

The answer is 1:3

6 0

1 year ago

Compute $14A6_{12} - 5B9_{12}$. Give your answer as a base $12$ integer.

avanturin [10]

Answer:

you need to 12 minus 5b9 as base and don’t forget to mention the integer

4 0

2 years ago

Find a irrational number between 5.2 and 5.3 .. Explain why its irrational. Include the decimal approximation of thr nearest hun

mihalych1998 [28]

$\sqrt{28}$
It is in between
$\sqrt{25}$
And
$\sqrt{36}$
There for it is in between 5 and 6
Additionally, it is closer to root 25, meaning that it is closer to 5

Rounded to the nearest hundredth is

5.29

4 0

3 years ago