prove that , a⁴+=47
[tex] \frac{1}{a 4} [/tex]

Answers

Answer 1

Step-by-step explanation:

Wyzant

ALGEBRA 2 ALGEBRA QUESTION

Ahnaf A. asked • 09/16/15

If a+1/a = 4, what is the of a4+1/a4 ?

IF a + 1/a = 4 . Then what is the value of a4 + 1/a4 ?

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Jon P. answered • 09/16/15

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First, notice that (a + 1/a)2 = 42 = 16. But also, (a + 1/a)2 = a2 + 2a(1/a) + 1/a2 = a2 + 2 + 1/a2 = a2 + 1/a2 + 2

So a2 + 1/a2 + 2 = 16, so a2 + 1/a2 = 14.

Now, do that again...

(a2 + 1/a2)2 = 142 = 196, but also (a2 + 1/a2)2 = a4 + 2(a2)(1/a2) + 1/a4 = a4 + 2 + 1/a4 = a4 + 1/a4 + 2

So a4 + 1/a4 + 2 = 196, so a4 + 1/a4 = 194

You can see the pattern... E.g., a8 + 1/a8 = 1942 - 2, etc.

...welcome...


Related Questions

A circle has a radius of 8. Find the area of a sector of this circle that is intercepted by central angle measuring pi over 7

Answers

Answer:

14.4 square units

Step-by-step explanation:

Keep in mind that the area here is a fraction of the area of a full circle of radius 8.

(area of sector) = (fraction)(pi)(8)^2

The fraction is the given central angle (pi over 7) divided by 2pi:

       pi            1

   --------- * ----------- = 1/14

     7             2pi

Multiply the formula     (fraction)(pi)(8)^2     found above by this fraction:

area of sector = (1/14)(pi)(8)^2  =  14.4 square units

please help!

A restaurant needs a block of ice that is exactly 480 cubic inches in volume.
The height of the ice block must be 10 inches.

Answers

Answer:

Step-by-step explanation:

Part A,

99% sure this is D

Part B

It's probably about 4 feet tall.

Part C,

4 in. x 12 in.

2 in. x 24 in.

8 in. x 6 in.

3 in. x 16 in.

Answer:

part A:   all the above

partt B:   48

part C:   4 in. x 12 in.

             2 in. x 24 in.

              8 in. x 6 in.

              3 in. x 16 in.

Step-by-step explanation:


What is the equation of the line?

Answers

Answer: x = -9

Step-by-step explanation:

When you look at the line, you can see it's plotted on the x-axis. From there you know the solution will be equal to x. Since the line passes right through the number -9 on the x-axis line, the answer would be x = -9. The line is straight which means it has no y intercept which is why x is only equal to -9.

a radioactive materal has a half- life of 60 months. How much of a 1000g sample would remain after 42 months?

Answers

Answer:

100

Step-by-step explanation:

100

Can you find the missing measure

Answers

Answer:

for which one

Step-by-step explanation:

I need help im doing IXL right now (BB.3 Complete a function table: quadratic functions)
i just need help with this final question (posted with a picture)

Answers

Answer:

0, 2, 4

Step-by-step explanation:-2 + 2 = 0 + 2= 2 + 2 = 4

The function table is solved and the quadratic equation is f ( x ) = -3x²

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

f ( x ) = -3x²

when x = -2

f ( -2 ) = -3 ( -2 )²

f ( -2 ) = -12

And , when x = 0

f ( 0 ) = 0

when x = 2

f ( 2 ) = -12

when x = 4

f ( 4 ) = -48

Hence , the function table is f ( x ) = { -12 , 0 , -12 , -48 }

To learn more about quadratic equations click :

https://brainly.com/question/25652857

#SPJ2

Find the value of x
5(x−7)=25

Answers

Answer:

x=12

Step-by-step explanation:

5(x−7)=25

Divide both sides by 5.

x−7=25/5

Divide 25 by 5 to get 5.

x−7=5

Add 7 to both sides.

x=5+7

Add 5 and 7 to get 12.

x=12

Answer:

x = 12

Step-by-step explanation:

5(x-7) = 25 (distribute)

5x-35 =25 (add 35 on both sides)

5x = 60 (divide)

x = 12

Please help due in 5 min

Answers

Answer:

nobody can see the question(s)

Car Survey: In a survey of 2,400 people who owned a certain type of​ car, 1,680 said they would buy that type of car again. What percent of the people surveyed were satisfied with the​ car?

Answers

Answer:

70 percent

Step-by-step explanation:

Pls help :( (will get reported if link)

Answers

Answer:

Step-by-step explanation:

What's the perimeter?

Answers

Answer:

the line crossing the trapezoid, the one that helps you find the S. In this case the perimeter is 4 (;

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

perimenopause is inside just count the inside of the trapezoid

hope this helps

HELPPP ASAP 10 POINTS

Answers

Answer:

43 degrees

Step-by-step explanation:

The two angles are supplementry because they form a 90 degree angle so you would subtract 47 from 90 to get 43 degrees.

Answer: 43

Step-by-step explanation: 47+ 43 = 90.  since x is a vertical angle it is 43.

Can someone please help me ⚠️

Answers

G = - h/3 + 11/3
H = 11 - 3g
I hope this helps

Simply the following expression: 12x + 5x - 8x

Answers

I don’t know but please let me know :)

Claudia was cooking breakfast for her entire family. She made double the amount of chocolate chip pancakes as she did with the regular pancakes. She only made half as many blueberry pancakes as the regular pancakes. Claudia also knows her family loves sausages, so she made triple the amount of sausage as blueberry pancakes.

How many of each breakfast item did Claudia make if she cooked 100 times in total?

Answers

Answer:

easy the answer is 0.0.0

Step-by-step explanation:

1x0=0.0.0

A sculpture at a park is in the shape of a rectangular pyramid. What is the volume of the sculpture if the length and width of the base of the pyramid are 11 feet and 5 feet respectively, while the height of the pyramid is 6 feet? ​

Answers

Answer:

40

Step-by-step explanation:

11x6=60

60-5x4= 20

=40

please help, dont answer if you dont know

Answers

Answer:

Step-by-step explanation:

A. 1/3

What is the M? Will mark brainlist if correct

Answers

14 = M each on would be *t=5

Evaluate the function.
f(x)= -x^2
find f(3)

Answers

Answer:

f(3) = - 9

Step-by-step explanation:

To evaluate f(3) , substitute x = 3 into f(x) , that is

f(3) = - (3)² = - 9

Which describes a number that cannot be irrational?
a number that can be used to solve an algebraic equation
a number that represents the ratio of the circumference to the diameter of a circle
a number that represents the length of the diagonal of a square
a number that can be written as the ratio of two integers​

Answers

1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez

If the loss incurred on selling an article is 7/20 of the cost price, then find the loss percentage.​

Answers

Answer: The loss percentage = 65%

Step-by-step explanation:

Let x be the cost price.

As per given,

Selling price = [tex]\dfrac{7}{20}x[/tex]

Loss =Cost price - Selling price

[tex]=x-\dfrac{7}{20}x\\\\=\dfrac{20-7}{20}x\\\\=\dfrac{13}{20}x[/tex]

The loss percent = [tex]\dfrac{loss}{Cost\ price}\times100[/tex]

[tex]=\dfrac{\dfrac{13}{20}x}{x}\times100\\\\=\dfrac{13}{20}\times100\\\\=13\times5\%\\\\=65\%[/tex]

Hence, the loss percentage = 65%

Is it, a solution or, NOT a solution?

Answers

Answer:

Perosnally i think it is not a solution but let me check that for you!

Step-by-step explanation:

Answer:Answer x=15 and the answer for x=6 will be false!

Step-by-step explanation:X=6 is not a solution but the correct answer is 15 .First we know that 5+5=10,then if we add 10+5 that will give us 15.

Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height, but each side of its base is 6 units long.

Answers

Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

Pyramid A

[tex]s = 4[/tex] -- base sides

[tex]V = 36[/tex] -- Volume

Pyramid B

[tex]s = 6[/tex] --- base sides

Required

Determine the volume of pyramid B [Missing from the question]

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

[tex]V = \frac{1}{3} * B * h[/tex]

Where B represents the area of the base equilateral triangle, and it is calculated as:

[tex]B = \frac{1}{2} * s^2 * sin(60)[/tex]

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

[tex]B = \frac{1}{2} * s^2 * sin(60)[/tex]

[tex]B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}[/tex]

[tex]B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}[/tex]

[tex]B = 4\sqrt 3[/tex]

The height is calculated from:

[tex]V = \frac{1}{3} * B * h[/tex]

This gives:

[tex]36 = \frac{1}{3} * 4\sqrt 3 * h[/tex]

Make h the subject

[tex]h = \frac{3 * 36}{4\sqrt 3}[/tex]

[tex]h = \frac{3 * 9}{\sqrt 3}[/tex]

[tex]h = \frac{27}{\sqrt 3}[/tex]

To calculate the volume of pyramid B, we make use of:

[tex]V = \frac{1}{3} * B * h[/tex]

Since the heights of both pyramids are the same, we can make use of:

[tex]h = \frac{27}{\sqrt 3}[/tex]

The base area B, is then calculated as:

[tex]B = \frac{1}{2} * s^2 * sin(60)[/tex]

Where

[tex]s = 6[/tex]

So:

[tex]B = \frac{1}{2} * 6^2 * sin(60)[/tex]

[tex]B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}[/tex]

[tex]B = 9\sqrt 3[/tex]

So:

[tex]V = \frac{1}{3} * B * h[/tex]

Where

[tex]B = 9\sqrt 3[/tex] and [tex]h = \frac{27}{\sqrt 3}[/tex]

[tex]V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}[/tex]

[tex]V = \frac{1}{3} * 9 * 27[/tex]

[tex]V = 81[/tex]

Answer:

81

Step-by-step explanation:

LINKS WILL BE REPORTED ALONG WITH NONSENSE ANSWERS THANK YOU
Please help me with this, I understand how to do the first equation but not the second (the one where it says he sold more accessories than phone commissions) Brainliest will be given!

Answers

what's ur ig bestie? it's making me write it longer so hihihi

ose baked 36 cookies. He wants to share them equally among 16 people. How many cookies will each person get?

Draw a line segment to connect the two whole numbers that the answer lies between.

Answers

Toes and French fire mmm it’s bussin

can someone solve this by factoring? i need to show work but don't really understand what we're doing..

the problem is:


Answers

Answer:

The answer is x = -7 and x = -8

Step-by-step explanation:

What’s a possible answer for this question?

Answers

Answer:

x-4

Step-by-step explanation:

you get the value of h(x) by dividing f(x)/g(x), so you only put they values for divide.

Which data are represented by this dot plot a 2 4 0 2 4 6 3 0 7 1 2 7 8 1 1 b 0 1 2 3 4 5 6 7 8 0 1 2

Answers

Answer:

Mean (Average) 4.0384615384615

Median 2.5

Range 24

Mode 1, appeared 5 times

Geometric Mean 0

Largest 24

Smallest 0

Sum 105

Count 26

Step-by-step explanation:

also you put 'b' in the list so i removed that

Triangle ABC has vertices with coordinates -1,-1 , 4,0 and 0,4 Prove that ABC is an isosceles triangle but not a right triangle.

Answers

can you take a picture of it

Graham wants to determine which football team is the most popular at a game between the home team and the visiting team. Which of the following methods will give him the most accurate results?

Answers

i think that your answer the answer is A
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