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3 years ago

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A map uses a scale of 3 inches = 20 miles The distance on the map between two cities is 18 inches. What is the actual distance b

etween the two cities?

1 answer:

jeka943 years ago

7 0

120 miles Bc 18 divided by 3 is 6
6 times 20 is 120

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

5 0

3 years ago

Plzzz explain this question in detail

Svet_ta [14]

Step-by-step explanation:

hi sis !! please ask me if u dont understand

6 0

3 years ago

50 POINTS!!!!! HELP ASAP!

hram777 [196]

Answer:

The inequality for Part A: −6 °F < −2 °F

Step by step-

The reason for that us because the -2 is closer to zero on the number line

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2 years ago

Questions and Answers<br>1.<br>A is 40% of B. what percentages<br>Discuss<br>A<br>6090<br>B.

ratelena [41]

Answer:

yeah thats right good job keep up the good work and keep doing ur thing good job

Step-by-step explanation:

5 0

2 years ago

Determine the point on the graph of the linear equation 2x + 5y = 19, whose ordinate is 1 1/2 times its abscissa.

rosijanka [135]

Answer:

(2, 3)

Step-by-step explanation:

2x + 5y = 19

5y = -2x + 19

y = $-\frac{2}{5} x + \frac{19}{5}$

P(abscissa, ordinate)

P(x, 1.5x)

P(2, 3)

$3 = -\frac{2}{5} (2) + \frac{19}{5}$

$3 = -\frac{4}{5} + \frac{19}{5}$

3 = 15/5

3 = 3

8 0

3 years ago