? cm<br> 3 cm<br> 7 cm<br> 4 cm<br> 7 cm<br> Missing length

Find the ninth term of the sequence if the second term is 12 and the fourth term is 16/3.

aleksklad [387]

with the assumption this is a geometric sequence and thus it as an "r" common ratio, so we know that the 3rd term must be 12 * r and the 4th term must be 12 * r * r, so let's make a quick table

$\begin{array}{rll} term&value\\ \cline{1-2} a_2&12\\ a_3&12\cdot r\\\cline{1-2} a_4&(12\cdot r)r\\ &12r^2\\ &\frac{16}{3}\\\cline{1-2} a_5&12r^3\\ a_6&12r^4\\ a_7&12r^5\\ a_8&12r^6\\ a_9&12r^7 \end{array}\qquad \implies \begin{array}{llll} 12r^2=\cfrac{16}{3}\implies r^2=\cfrac{16}{12\cdot 3}\implies r^2=\cfrac{4}{9}\\\\\\ r=\sqrt{\cfrac{4}{9}}\implies r=\cfrac{\sqrt{4}}{\sqrt{9}}\implies r=\cfrac{2}{3} \end{array} \\\\[-0.35em] ~\dotfill$

$a_9=12\left( \cfrac{2}{3} \right)^7\implies a_9=12\cdot \cfrac{128}{2187}\implies a_9=\cfrac{512}{729}$

6 0

2 years ago

A company's stock was selling at $28 a share. A month later, it was selling at $21 a share. What is the PERCENT decrease.

xz_007 [3.2K]

You can use the formula ...

... (percent change) = ((new amount) - (original amount))/(original amount) × 100%

Filling in the given information, this tells you ...

... (percent change) = ($21 -$28)/($28) × 100%

... = (-7/28) × 100%

... (percent change) = -25%

A negative percent change is a decrease, so the change in price is a ...

... 25% decrease

4 0

3 years ago

Find the simple interest

Pavlova-9 [17]

Answer:

$81 of interest would be earned

Step-by-step explanation:

A=prt

A= (900)(0.03)(3)

A = 81

8 0

3 years ago

Tanya is printing a report. There are 96 sheets of paper in the printer, and the number of sheets p left after t minutes of prin

AleksandrR [38]

Answer:

$0 = -8t + 96\\\\\Rightarrow\ 8t=96\\\\\Rightarrow\ t=\dfrac{96}{8}\\\\=12$

<h3>Hence, it will take 12 minutes by the printer to use all 96 sheets of paper.</h3>

Step-by-step explanation:

Given :

Tanya is printing a report.

There are 96 sheets of paper in the printer, and the number of sheets of paper p left after t minutes of printing is given by the function

$p(t) = -96 - 8t$

When all the 96 sheets printed , then the number of sheets will left to print =0

Substitute p(t)=0 in the given function, to find the value of t, we get

$0 = -8t + 96\\\\\Rightarrow\ 8t=96\\\\\Rightarrow\ t=\dfrac{96}{8}\\\\=12$

<h3>Hence, it will take 12 minutes by the printer to use all 96 sheets of paper.</h3>

4 0

3 years ago

HELP ASAP PLZ i need help !<br>help me :((

kodGreya [7K]

Answer:

(1) $g[f(x)]=\frac{8x-1}{12x-4}$

(2) $g^{-1}(x)=\frac{x+1}{(3x-2)}$

(3) $x=\frac{9+\sqrt{129} }{6}, \frac{9-\sqrt{129} }{6}$

Step-by-step explanation:

Given functions f(x) = (4x-1)

are $g(x)=\frac{2x+1}{3x-1}$

(1) $g[f(x)]=\frac{2(4x-1)+1}{3(4x-1)-1}$

$=\frac{8x-2+1}{12x-3-1}$

$=\frac{8x-1}{12x-4}$

(2) for $g^{-1}(x)$ , rewrite the function g(x) in terms of an equation

$y=\frac{2x+1}{3x-1}$

Substitute y in place of x and x in place of y, then solve for y.

$x=\frac{2y+1}{3y-1}$

(3y-1)x = 2y+1

3xy - x = 2y + 1

3xy - 2y = x + 1

y(3x-2) = x + 1

$y=(\frac{x+1}{3x-2} )$

⇒ $g^{-1}(x)=\frac{x+1}{(3x-2)}$

(3) $f[g(x)]=(x-1)$

$f[g(x)]=4[\frac{2x+1}{3x-1}] =(x-1)$

⇒ $\frac{(8x+4)-(3x-1)}{3x-1}=(x-1)$

⇒ $\frac{8x-3x+4+1}{3x-1}=(x-1)$

⇒ $\frac{5x+5}{(3x-1)}=(x-1)$

⇒ $5x+5=(3x-1)(x-1)$

⇒ $5x+5=3x^2-3x-x+1$

⇒ $5x+5=3x^2-4x+1$

⇒ $3x^2-9x-4=0$

⇒ $x=\frac{9\pm\sqrt{(-9)^2-4(-4)\times3} }{2\times3}$

$x=\frac{9\pm\sqrt{81+48} }{6}$

$x=\frac{9\pm\sqrt{129} }{6}$

$x=\frac{9+\sqrt{129} }{6}, \frac{9-\sqrt{129} }{6}$

4 0

3 years ago

? cm 3 cm 7 cm 4 cm 7 cm Missing length