Factor the polynomial function over the complex numbers

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively. Pl

kicyunya [14]

Hello,

$u_{0} =a\\
 u_{1} =a*r\\
 u_{2} =a*r^{2}=-6\\
 u_{3} =a*r^{3}\\
 u_{4} =a*r^{4}\\
 u_{5} =a*r^{5}=162\\
....\\
\boxed{ u_{n} =a*r^{n}} \\

\dfrac{ 162}{-6} = \dfrac{ u_{5} }{ u_{3}} = \dfrac{ a*r^{5}}{ a*r^{2}} =r^3= -27\\
==\ \textgreater \ r=-3\\

 u_{2} =a*r^{2}=-6=a*(-3)^2 \ ==\ \textgreater \ a=-\frac{6}{9} =-\frac{2}{3}\\


\boxed{ u_{n} =-\frac{2}{3}*(-3)^{n}=(-1)^{n+1}*2*3^{n-1}} \\

$

8 0

3 years ago

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What is the length of the hypotenuse of right ΔDEF shown? A) √5041 B) √2545 C) √497 D) √1063

spin [16.1K]

The length of the hypotenuse of right triangle ΔDEF is 50.44 units

<h3>How to find hypotenuse of a right triangle?</h3>

The hypotenuse side can be found using Pythagoras theorem,

Therefore,

c² = a² + b²

where

c = hypotenuse
a and b are the other legs.

Therefore,

x² = 39² + 32²

x² = 1521 + 1024

x = √2545

x = 50.4479930225

x = 50.44

learn more on right triangle here: brainly.com/question/12353375

#SPJ1

5 0

2 years ago

How to solve inequaities?

Elza [17]

$-3(-8+5m) > 5(6-3m)\qquad|\text{use distributive property}\\\\(-3)(-8)+(-3)(5m) > (5)(6)+(5)(-3m)\\\\24-15m > 30-15m\qquad|\text{add 15m to both sides}\\\\24 > 30\qquad FALSE\\\\\text{Therefore your answer:}\ \boxed{NO\ SOLUTION}\to m\in\O$

3 0

3 years ago

Maria invested $4,000 at 3.5% simple interest. She left the principal invested for 57 months. Robert invested $3,500 at 8.5% sim

Alex_Xolod [135]

Answer:

Maria have $123,75 more total money than Robert at the end of their investments.

Step-by-step explanation:

To calculate the simple interest we should multiply the Initial invest, with the interest without percentage and the time in years.

As the time is in months we have to divide it by 12 so we have the mesure of time in years, then the interest for each of the investments will be:

Maria

Invest = $4,000 Interest = 3.5/100=0.035 Time = 57/12 = 4.75

Simple Interest = 4,000 x 0.035 x 4.75 = $665

Total money at the end of the invest = $4,000 + $665 = $4,665

Robert

Invest = $3,500 Interest = 8.5/100=0.085 Time = 42/12 = 3.5

Simple Interest = 3,500 x 0.085 x 3.5 = $1,041.25

Total money at the end of the invest = $3,500 + $1,041.25 = $4,541.25

Now we have to subtract the total money of Robert from the total money of Maria to know how much money did she got over Robert after their invests

$4,665 - $4,541.25 = $123.75

At the end of the invest, Maria got $123,75 more than Robert

8 0

3 years ago

49 points, will give Brainliest! Having a lot of trouble with Determining the domains of functions. Khan Academy Algebra I.

prohojiy [21]

Domains of functions are the values that <em>can</em> be plugged into the function and not "break" it. By "break" I mean that the denominator cannot be 0, in this case. If the denominator is 0, we will get a divide by 0 error, and thus, we must restrict the domain. All values of x will work except 9/4:

$\frac{7-3x}{4x-9}$

Let's plug in 9/4 and see what happens:

$\frac{7-3(\frac{9}{4})}{4(\frac{9}{4})-9} = \frac{whatever}{0}$

So, plugging in 9/4 results in denominator equalling 0. Therefore, we must restrict the domain so that x ≠ 9/4. Your answer is All real values of x such that x ≠ 9/4.

6 0

3 years ago

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