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2 years ago

10

The first three terms of a sequence are given. Round to the nearest thousandth (if

1 answer:

Fofino [41]2 years ago

6 0

Answer:

19683

Step-by-step explanation:

1. find the ratio

this is geometric so..

54÷18=3

18÷6=3

2. set up the problem

3(3)^9-1

3^8= 6561

6561(3)=19683

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Solution to this inequality? <br> 3(5+2n) > 7 +10n<br> Please show work , Thank you

vodka [1.7K]

$3(5+2n) \ \textgreater \ 7 +10n \\ \\ 15 + 6n \ \textgreater \ 7 + 10n \\ \\ 15 \ \textgreater \ 7 + 10n - 6n \\ \\ 15 \ \textgreater \ 7 + 4n \\ \\ 15 - 7 \ \textgreater \ 4n \\ \\ 8 \ \textgreater \ 4n \\ \\ \frac{8}{4} \ \textgreater \ n \\ \\ 2 \ \textgreater \ n \\ \\ n \ \textless \ 2 \\ \\$

The final result is: n < 2.

7 0

2 years ago

Read 2 more answers

PLs help 50 PTS!!!!! PLEASE ILL GIVE BRAINLIEST!!!!!

Nookie1986 [14]

Answer:

$\large\boxed{y=\dfrac{1}{4}x^2-x-4}$

Step-by-step explanation:

The equation of a parabola in vertex form:

$y=a(x-h)^2+k$

<em>(h, k)</em><em> - vertex</em>

The focus is

$\left(h,\ k+\dfrac{1}{4a}\right)$

We have the vertex (2, -5) and the focus (2, -4).

Calculate the value of <em>a</em> using $k+\dfrac{1}{4a}$

<em>k = -5</em>

$-5+\dfrac{1}{4a}=-4$ <em>add 5 to both sides</em>

$\dfrac{1}{4a}=1$ <em>multiply both sides by 4</em>

$4\!\!\!\!\diagup^1\cdot\dfrac{1}{4\!\!\!\!\diagup_1a}=4$

$\dfrac{1}{a}=4\to a=\dfrac{1}{4}$

Substitute

$a=\dfrac{1}{4},\ h=2,\ k=-5$

to the vertex form of an equation of a parabola:

$y=\dfrac{1}{4}(x-2)^2-5$

The standard form:

$y=ax^2+bx+c$

Convert using

$(a-b)^2=a^2-2ab+b^2$

$y=\dfrac{1}{4}(x^2-2(x)(2)+2^2)-5\\\\y=\dfrac{1}{4}(x^2-4x+4)-5$

<em>use the distributive property: a(b+c)=ab+ac</em>

$y=\left(\dfrac{1}{4}\right)(x^2)+\left(\dfrac{1}{4}\right)(-4x)+\left(\dfrac{1}{4}\right)(4)-5\\\\y=\dfrac{1}{4}x^2-x+1-5\\\\y=\dfrac{1}{4}x^2-x-4$

3 0

3 years ago

Caleb bought groceries and paid

lutik1710 [3]

Answer:

Price of Caleb's groceries before tax= $6.4

Step-by-step explanation:

Let price of groceries before tax be = $ $x$

Sales tax % = 2.5%

Sales tax applied = $2.5\% \ of\ x = \frac{25}{100}\times x = \frac{25}{100} x$

Actual sales tax paid = $1.60

∴ $\frac{25}{100}x=1.60$

Multiplying both sides by 100.

$100\times \frac{25}{100}x=1.60\times 100$

$25x=160$

Dividing both sides by 25.

$\frac{25x}{25}=\frac{160}{25}$

$x=6.4$

∴ Price of groceries before tax= $6.4

8 0

3 years ago

Read 2 more answers

Simplify the expression- <br> 3k+ -9k+ -6+10k

Nady [450]

Answer:

4k-6

Step-by-step explanation:

$3k+ -9k+ -6+10k=3k-9k-6+10k=4k-6$

8 0

3 years ago

Read 2 more answers

In 2000 the total amount of gamma ray bursts was recorded at 6.4 million for a city. In 2005, the same survey was made and the t

ratelena [41]

Let's assume

It started in 2000

so, t=0 in 2000

$P_0=6.4million$

we can use formula

$P(t)=P_0 e^{rt}$

we can plug value

$P(t)=6.4 e^{rt}$

In 2005, the same survey was made and the total amount of gamma ray bursts was 7.3 million

so, at t=2005-2000=5

P(t)=7.3 million

we can plug value and then we can solve for r

$7.3=6.4 e^{r*5}$

$r=0.02632$

now, we can plug back

$P(t)=6.4 e^{0.02632t}$

now, we have

P(t)=1 billion =1000 million

so, we can set it and then we can solve for t

$1000=6.4 e^{0.02632t}$

$t=191.924$

approximately

$t=192$

Year is 2000+192

year is 2192................Answer

4 0

2 years ago