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2 years ago

Help asap! I need to solve this for my quiz and have no clue what it is

Mathematics

1 answer:

N76 [4]2 years ago

8 0

Answer:

Step-by-step explanation:

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Find an explicit rule for the nth term of the sequence.The second and fifth terms of a geometric sequence are 18 and 144, respec

vova2212 [387]

Given:

second term = 18

fifth term = 144

The nth term of a geometric sequence is:

$\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}$

Hence, we have:

$\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\ \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}$

Divide the expression for the fifth term by the expression for the second term:

$\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}$

Substituting the value of r into any of the expression:

$\begin{gathered} ar\text{ = 18} \\ a\text{ }\times\text{ 2 = 18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}$

Hence, the explicit rule for the sequence is:

$a_n\text{ = 9\lparen2\rparen}^{n-1}$

5 0

1 year ago

Nichol walks at a constant pace of 1.2 m/s and takes 15 minutes to get to school.

liraira [26]

Answer:

The difference between the distances they walked is 600 meters.

Step-by-step explanation:

Let's calculate the distance traveled by Nichol and Sakura with the following equation:

$d = v*t$

Where:

v: is the speed

t: is the time

The distance traveled by Nichol is:

$d_{n} = 1.2 m/s*15min*\frac{60 s}{1 min} = 1080 m$

And the distance traveled by Sakura is:

$d_{s} = 1.4 m/s*20 min*\frac{60 s}{1 min} = 1680 m$

Hence, the difference between the distances they walked is:

$d_{t} = d_{s} - d_{n} = 1680 m - 1080 m = 600 m$

Sakura traveled 600 meters more than Nichol.

Therefore, the difference between the distances they walked is 600 meters.

I hope it helps you!

4 0

3 years ago

Two 6 sided dice are rolled. what is the probability of rolling a 3 on either of the dice

emmasim [6.3K]

There is a 2 of 6 percent chance that one them might land on three if you add one extra dice it would be 3 of 6 percent chance and so on.

Hope this Helped!

;D
Brainliest??

7 0

3 years ago

Twenty percent of the ice melted. If 680 grams<br> remained, how many grams melted?

musickatia [10]

Answer:

−33999/50

Step-by-step explanation:

2/100−680

1/50−680

−33999/50

5 0

3 years ago

(-3x)-7+2x+9=5 what does X equal to

yKpoI14uk [10]

Answer:

Step-by-step explanation:

-3x -7 +2x + 9 = 5

-x + 2 = 5 (you are combining like terms here)

-x = 3

x = -3

Hope this helps :)

8 0

3 years ago