given that n is an integer greater than 1, explain why the largest prime factor of 2(7^n) - 2(7^(n-1)) + 7^(n+1) is 61.

Answers

Answer 1

When we put the value of 1 in place of n in the equation, the value obtained will be equal to the largest prime factor that is 61.

What is a Prime number?

A prime number is any whole number that is greater than 1 and cannot be created by combining other whole numbers. Consequently, a prime number's only factors are 1 and the actual number.

As per the given expression in the question,

2(7ⁿ) - 2(7ⁿ⁻¹) + 7ⁿ⁺¹

Use exponent rule:

[tex]a^b.a^c=a^b^+^c[/tex]

Put the values accordingly,

2(7ⁿ) - 2(7ⁿ⁻¹) + 7ⁿ . 7¹

So,

[tex]\frac{a^b}{a^c}= a^b^-^c[/tex]

⇒ 2(7ⁿ) - 2(7ⁿ/7¹) + 7ⁿ . 7¹

Simplify the above equation,

2(7ⁿ) - 2/7(7ⁿ) + (7)7ⁿ

Take out 7ⁿ as common,

(2 - 2/7 + 7)7ⁿ

Therefore,

61/7(7ⁿ)

Put n = 1 to check for the largest prime number,

61/7(7¹)

= 61

To know more about Prime number:

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Related Questions

step by step please :(
Convert the equation to Standard Form.

y=2(x+1)^(2)-4

Answers

Answer:

y = 2x^2 + 4x - 2

Step-by-step explanation:

y=2(x+1)^(2)-4 is in vertex form. We want the same equation in standard form, which looks like y = ax^2 + bx + c.

Perform the indicated multiplication (squaring of x + 1):

y = 2(x^2 + 2x + 1) - 4, or

y = 2x^2 + 4x + 2 - 4, or

y = 2x^2 + 4x - 2 This is in the standard form of a quadatic.

Cheryl painted her living room walls with two different colors. She painted part of the room yellow and another part green. If the surface area of the walls in her room is 720 ft2 and she painted 288 ft2 yellow, what percent of the room did she paint green?

Answers

Answer:

Total percent of the room did she paint green = 60%

Step-by-step explanation:

Given - Cheryl painted her living room walls with two different colors. She painted part of the room yellow and another part green. If the surface area of the walls in her room is 720 ft² and she painted 288 ft² yellow.

To find - What percent of the room did she paint green ?

Proof -

Given that,

The surface area of the walls in her room = 720 ft²

Total area painted in yellow color = 288 ft²

So,

Total area painted in green color would be = 720 - 288 = 432 ft²

Now,

Let the total percent green color painted = x

So,

720 × x% = 432

⇒[tex]720*\frac{x}{100} = 432[/tex]

⇒ x = [tex]\frac{432*100}{720}[/tex] = 60

∴ we get

Total percent of the room did she paint green = 60%

Neptune has a diameter of about 3 x 10^4 miles. Earth has a diameter
of about 8 x 10^3 miles.
Earth's diameter is about__
the size of Neptune's diameter.
2.67 times
37.5 times
0.267 times
26.7 times

Answers

Answer:

0.267 times

Step-by-step explanation:

(8×10³) ÷ (3×10⁴) = 0.2666666667

Valentina's family is planning to have a party for her quinceanera. They are considering two different locations to rent for her party. Casa Lucia charges a $200 one-time rental fee plus $500 per hour. The Silver Fox charges $200 per hour plus a $1,100 one-time rental fee. Explain what the solution to the system of equations represents in this real-world context.

Answers

Answer:

number of hours = 3 hours

Step-by-step explanation:

Let

x = number of hours

Casa Lucia = 200 + 500x

Silver Fox = 1,100 + 200x

To solve the equation, equate both cost of rent

Casa Lucia = Silver Fox

200 + 500x = 1,100 + 200x

200 - 1,100 = 200x - 500x

-900 = - 300x

x = -900 / -300

x = 3 hours

number of hours = 3 hours

The solution to the system of equations in this real-world context represents the number of hours both locations can be rented with the same cost.

It means both locations cost the same if rented for 3 hours each

Margo can purchase tile at a store for $0.59 per tile and rent a tile saw for $72. At another store she can
borrow the tile saw for free if she buys tiles there for $1.39 per tile. How many tiles must she buy for the
cost to be the same at both stores?

Answers

Solve the system of linear equations by substitution.

Answers

[tex] \large{\red{\underline{\bf{Required \: Solution \: : }}}} [/tex]

Here we have been provided with two equations and we have to solve them by substitution method and get the value of x and y.

y = x - 4 (Equation No 1)y = 4x - 10 (Equation No 2)

Here we have been already provided a temporary value of y in first equation so let us substitute in the second equation.

[tex]: \implies \: \sf{y \: = \: 4x \: - \: 10}[/tex]

[tex]: \implies \: \sf{x \: - \: 4 \: = \: 4x \: - \: 10}[/tex]

[tex]: \implies \: \sf{x \: = \: 4x \: - \: 10 \: + \: 4}[/tex]

[tex]: \implies \: \sf{x \: = \: 4x \: - 6}[/tex]

[tex]: \implies \: \sf{x \: - 4x \: = \: - 6}[/tex]

[tex]: \implies \: \sf{ - 3x \: = \: - 6}[/tex]

[tex]: \implies \: \sf{ \cancel - \: 3x \: = \: \cancel- \: 6}[/tex]

[tex]: \implies \: \sf{ 3x \: = \: 6}[/tex]

[tex]: \implies \: \sf{ x \: = \: \dfrac{6}{3} }[/tex]

1/36 for the first need the questions for the second

What is the output is 2 less than twice the input.

Answers

Answer:

Step-by-step explanation:

at least I don't think so be cause it hard to explain

Will give brainliest!

Answers

Answer:

Step-by-step explanation:

multiply 0.83 by 0.06 = 0.0498

multiply 0.17 by 0.52 and add that to the first one

which gives you the prob of winning of 0.1382

Greg is four feet tall. how many inches tall is Greg?

Answers

Answer:

48 inches

Step-by-step explanation:

Answer:

it is the wrong answer

Step-by-step explanation: he is 5 feet and 10 inches

You get a brand new car for your 16th birthday, valued at $25,875. Each year you
own the car it decreases in value by 15%. How much will the car be worth when you
turn 21?

Answers

Answer: $25,875 - 15% = 21 993.75 0r $25,875 + 15% = 29 756.25

Step-by-step explanation:

NEED HELP ASAP PLS

polygon ABCD, shown in the figure is dilated by a scale factor of 8 with the origin as the center of dilation , resulting in the image of ABCD .
The slope of CD is ____?

Answers

Answer:

2/1 or 2overrun

Step-by-step explanation:

You can see that the rais/run for C to D is 2/1. So that would be the slope.

DUE IN A BIT PLEASE HELP WILL MARK BRAINLIEST JUST PLEASE HELP!! :((

Answers

Answer: D

Step-by-step explanation:

2. Find the area of the trapezoid.

A. 44^3 ft
B. 52^3 ft
C. 44^3 - 24ft
D. 60^3 ft

Answers

Answer:

i think the answer is b i hope it helps

Step-by-step explanation:

help me plss im beeging

Answers

Answer:

1. x = 12

2. x= 9

3.x = 14

4.x=18

Step-by-step explanation:

Please show work

I'll give brainliest

Answers

Answer:

Step-by-step explanation:

a right angle is 90 degrees so

90=76+2x subtract 76 from both sides

-76 -76

________

14=2x divide 2 from both sides

_ ___

2 2

7=x

Check:

76+(2*7)=90 correct

Answer:

x=7

Step-by-step explanation:

76°+2n=90°

2x=90-76

[tex] \frac{2x}{2} = \frac{14}{2} [/tex]

[tex]x = 7[/tex]

hope it helps...

in a right triangle, if sin(theta)= 8/17, what is tan (theta)?

Answers

sin θ = perpendicular/ hypotenuse

tan θ = perpendicular/base

By applying Pythagoras theorem, you get the base as 15

So, your answer is 8/15

There are 9 cars in the parking lot. 2 cars are parked on the left and the other cars are
parked on the right. What fraction of the cars are parked on the right?

Answers

7/9

Explanation:
There are 7 cars out of the total of 9 on the right

A plane traveled 1092 miles to Riyadh and back. The trip there was with the wind. It took 6
hours. The trip back was into the wind. The trip back took 7 hours. Find the speed of the plane
in still air and the speed of the wind.

Answers

Answer:

Step-by-step explanation:

p and s was are the speeds of the plane and wind, respectively.

Traveling with the wind, the plane moves p+w miles per hour.

p+w = (1092 miles)/(6 hours) = (182 miles)/hour

Traveling against the wind, the plane moves p-w miles per hour.

p-w = (1092 miles)/(7 hours) = (156 miles)/hour

Add the equations together

p+w = 182

p-w = 156

—————-

2p = 338

p = 169 miles per hour

w = p-156 = 13 miles per hour

solve for the variable, please show work.

correct answer = brainliest !!!!

3√(c) + 1 = 1

Answers

The answer is c = 0

Explanation, see the picture

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