\frac { 3 ^ { p + 1 } - 3 ^ { p } } { 2 \times 3 ^ { p } } = 1​

Answers

Answer 1

Answer:

Given equation:

[tex](3^{p+1} - 3^p) /(2 *3^p) = 1[/tex]

Solving for p:

[tex]3^{p+1} - 3^p = 2 *3^p[/tex][tex]3*3^p - 3^p = 2 *3^p[/tex][tex]2 *3^p =2 *3^p[/tex]

p - any real number

We can state the initial expression is correct for any value of p.

Answer 2

Answer:

True for all p

Step-by-step explanation:

Given equation:

  [tex]\dfrac{3^{p+1}-3^{p}}{2 \times 3^{p}}=1[/tex]

Multiply both sides by [tex]2 \times 3^p[/tex]:

[tex]\implies 3^{p+1}-3^p=2 \times 3^p[/tex]

Add [tex]3^p[/tex] to both sides:

[tex]\implies 3^{p+1}-3^p+3^p=2 \times 3^p+3^p[/tex]

[tex]\implies 3^{p+1}=3 \times 3^p[/tex]

Rewrite 3 as 3¹:

[tex]\implies 3^{p+1}=3^1 \times 3^p[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 3^{p+1}=3^{1+p}[/tex]

[tex]\implies 3^{p+1}=3^{p+1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies p+1=p+1[/tex]

Subtract 1 from both sides:

[tex]\implies p+1-1=p+1-1[/tex]

[tex]\implies p=p[/tex]

Therefore as both sides are equal, true for all p.


Related Questions

Justin needs 9 pieces of rope that are
1 1/2 feet long each. He says he can cut the 9 pieces from a 12 3/4 foot long rope. Is Justin correct? Write an equation with a complex fraction to support your answer.​

Answers

Answer:

no.

Step-by-step explanation:

half of 9 ft is 4.5 ft, 9 + 4 and 1/2 is 13 1/2

Clyde bought a steak that weighs 1.4 pounds. The price is $4.50 per pound. how
much does the steak cost?

Answers

six dollars and 30 cents

Find the missing exponent. 7? x (75)4 = 734 Place only the missing exponnt value

Х

Answers

Answer:14

Step-by-step explanation:took the test

What is the mass of an object with a density of 3 g/mL and a volume of 112.5 mL? Show all work.

Answers

Answer:

337.5

Step-by-step explanation:

Based on the given conditions, formulate 3 112.5

Calculate the product or quotient: 337.5

Find the quotient of 902÷27
(It has a remainder)

Answers

Answer:

The quotient of 902 divided by 27 equals 33 and the remainder is 11.

simply the following expression

Answers

Answer:

C.

x^8 / y^28 z^20

Step-by-step explanation:

Answer: c

Step-by-step explanation:

= [tex](\frac{y^{7} z^{5} }{x^{2} } )^{-4}[/tex]

[tex]= (\frac{x^{2} }{y^{7} z^{5} } )^{4}[/tex]

[tex]= \frac{x^{8} }{y^{28} z^{20} }[/tex]

please give me a brainliest answer

Please help me this question

Answers

5x-147=2x
3x=147
X=49
Smallest angle is 49*2=98

Answer:

Angle C = 48°

Step-by-step explanation:

Kites have one pair of congruent angles.

In this case it is B and D:

m∠B = m∠D5x - 147 = 2x5x - 2x = 1473x = 147x = 49

Find the measure of B and D:

m∠B = 2*49 = 98°

Find the measure of angle C:

m∠C = 360 - 2*98 - 116 = 48°

The smallest angle is C

10 points
Jason is pulling a box across the room. He is pulling with a force of 15 newtons and his arm is making a 66 angle with the horizontal, what is the vertical component of the force he
is pulling with
Type your answer...

Answers

9514 1404 393

Answer:

  13.7 N

Step-by-step explanation:

The vertical component of the force is ...

  (15 N)sin(66°) ≈ 13.7 N

the value of x - y is

Answers

Answer:

Yes, in a Cartesian Coordinate system each point is given by two numbers. If the question is "where" the function has a max or min value, that's "x", the first number in pair. If the question is "what" is that max or min function value, thats "y", the second number in the pair

Amy contributes $50 per month into the Lincoln National Bond Fund that earns 7.26% annual interest.What is the value of Amy’s investment after 25 years?

Answers

Answer:

Inc Interest : $16,089

Step-by-step explanation:

1. Let's turn $50 a month into a year, so 50 * 12 = $600

2. Including the annual interest, which is $43.56 out of the $600

3. Add them together, which will be 43.56 + 600 = 643.56

4. Multiply it by 25 to get the full 25 years and you're done!

The value of Amy's investment after 25 years will be $140.75.

What is simple interest?

Simple interest is calculated just on the loan's principal amount, whereas compound interest is calculated on both the principal and the cumulative interest. The straightforward crediting of cash flows related to an investment or deposit is referred to as "simple" interest.

Given that, Amy contributes $50 per month to the Lincoln National Bond Fund which earns 7.26% annual interest.

The investment after 25 years will be calculated as,

SI = ( P x R x T)/100

SI = ( 50 x 7.26 x 25 ) / 100

SI = $90.75

The total investment will be calculated as,

A = $90.75 = $50

A = $140.75

Therefore, the value of Amy's investment after 25 years will be $140.75.

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1 4 cm 4 cm 5 cm 3 cm Perimeter: Area:​

Answers

Answer:

Step-by-step explanation:

840

which value of n makes the value of the expression 4n + 3 a composite number

Answers

Answer:

3

Step-by-step explanation:

Given expression :-

4n + 3

It will be composite if it will has more than 2 factors ( other than 1 and itself )

If n = 1 :-

4*1 + 3 4+ 3 7 ( prime )

If n = 2 :-

4*2 + 3 8 + 3 11 ( prime )

If n = 3 :-

4*3+312+3 15 ( composite )

Which of these functions have a domain of all real numbers?​

Answers

Answer:

I think it's A. I may be wrong tho.

Answer: A. Functions f, g, and h

Step-by-step explanation: Plato answer

30. You can work at most 25 hours next week. You need to earn at least $85 to cover your gas and food
expenses. Your babysitting job pays $7.50 per hour and your math tutoring job pays $6 per hour.
a) Define your variables.
b) Write two inequalities that represent the constraints of the scenario.

Answers

The answer is B. That’s the answer

Eight chocolate bars have 96 total squares. How many squares are there in each chocolate bar?

Answers

Answer: 12.

Step-by-step explanation: 96 divided by 8 is 12.

Answer: 12

Step-by-step explanation:

If there are 96 square and 8 chocolate bars, then we:

96 divided by 8 = 12

Can somebody help me find the volume?

You have a beaker of 20 mL of water. You place a rock in this beaker and the water rises to 30 mL. What is the volume of the rock?

thx if u can help. I don't fully understand this

Answers

Answer:

Hi, I believe the volume of the rock would be 10 mL.

If the beaker originally had 20 mL of water and then the rock turned it to 30 mL, subtract 20 from 30 and you get 10mL

Hope this helps!!!

The volume of the rock is 10 mL as per the concept of subtraction.

To find the volume of the rock, we can use the principle of displacement. When the rock is placed in the beaker, it displaces a certain volume of water equal to its own volume.

The increase in water level from 20 mL to 30 mL represents the volume of the rock.

The volume of the rock = Final volume of water - Initial volume of water

Volume of the rock = 30 mL - 20 mL = 10 mL

Therefore, the volume of the rock is 10 mL. The rock occupies an additional 10 mL of space in the beaker when submerged in the water.

This principle of displacement is based on the fact that the total volume of water and the rock combined remains the same as the initial volume of water in the beaker. By measuring the difference in water levels before and after adding the rock, we can determine the volume of the rock.

To learn more about subtraction;

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PLEASE HELP ASAP!!!!!

Answers

Answer: -8/7

Step-by-step explanation: (-2)(4)/7

expand and simpifly 2(x+7) + 3(x+1)

Answers

Answer: 5x+17

Step-by-step explanation:

2(x+7) + 3(x+1)

2x+14 + 3x+3

5x+17

Answer:

5x+17

Step-by-step explanation:

expanded:

2x+14 + 3x+3

simplified:

-collect like terms-

2x+3x=5x

14+3=17

How do I convert 1 5/6 into a decimal??????

Answers

Answer:

1.8(3) (three is a repeating number)

Step-by-step explanation:

Divide the numerator from the denominator. Add the value of the integer part.

Answer:1.83

Step-by-step explanation:

so the  1 that's a whole number and 5 out of 6 should be around 82-85 but for real its 1.83 but its a repeating decimal so its like 1.83333

Write the equation of the line in fully simplified slope-intercept form.

Answers

Answer:

y= [tex]\frac{5}{6} x[/tex] + 4

Step-by-step explanation:

Pick two points: (-6,-10) and (0,4)

Then solve for m (slope): I picked (0,4)

[tex]m= \frac{4-(-1)}{0-(-6)} =\frac{5}{6}[/tex]

Then put in slope intercept form:

4= [tex]\frac{5}{6} (0)[/tex] + b

4=b

Then put in final form:

y= [tex]\frac{5}{6} x[/tex] + 4

Hope this helps!

Answer:

y=5/6x+4

Step-by-step explanation:

Anyone pls answer this question.

Answers

If we start by 406.5 amount in 25/10/2017

And we have to pay car loan in 26/10/2017 equals 223.65
Then the balance will be 406.5-223.65= 182.85

Then we have the salary in 27/10/2017,
So the balance will become 182.85+ 1325.31= 1508.16

So the blanks are 182.85, 1508.16

Solve y for 4(3y - 1) - 5y - 6 = 18

Answers

Answer:

y=4

Step-by-step explanation:

find the slope of the line through the given points (1,1) (4,-1)

Answers

Answer:

hope it helps

.............

Find the slope of each line.

Answers

Answer:

Slope: - 5/2

Step-by-step explanation:

NEED MORE HELP DUE TOMMOROW ONLY HAVE 15 POINTS SO ITS GOTTA BE 10 CUZ I GOT OTHER QUESTIONS THAT NEED ANSWERING

Answers

Answer:

a: 00:45

b: 7:30 PM

Step-by-step explanation:

Hope this is right

Charlie deposited $115 in a savings account. Each week thereafter he deposits $35 into the account. How much total money has Charlie deposited after 30 weeks?

Answers

Answer:

$1165

Step-by-step explanation:

30x35 = 1050

1050+115=1165

Equation: 115+35x

Plug 30 in for x
115+35(30)
115 + 1050
= $1165

Old solve
(x ÷ 5)(x÷5)(x÷5)

Answers

Answer:

1/125(x^3)

Step-by-step explanation:

Let's simplify this expression.

[tex]\frac{x}{5} * \frac{x}{5} * \frac{x}{5}[/tex] [tex]\frac{xxx}{5*5*5}[/tex] [tex]\frac{x^3}{5*5*5}[/tex] [tex]\frac{x^3}{125}[/tex] [tex]\frac{1}{125}x^3[/tex]

Therefore, the simplified answer is [tex]\frac{1}{125}x^3[/tex].

A number increased by 331 is equal to 761. Find the number.

Answers

Answer:

430

Step-by-step explanation:

761-331=430

Answer:

the answer would be 430 because you subtract 761-331=430

HELP ME AND ILL GIVE U BRAINLIST I PROMISE BUT ITS ONLY IF U GET IT RIGHT

Mother made a cake. the ratio of the flour is 2 cup to 1 cup. she used 4 cups of sugar how many cups of sugar did she use​

Answers

Answer:

if it says she used 4 cups of sugar then she used 4 cups of sugar?

but if she used 4 cups of flour then she used 2 cups of sugar

Step-by-step explanation:

Hope this helps! :)

A company’s stock was selling at $20 a share. A month later, it was selling at $26 a share. What is the percent gain

Answers

Answer:

The percent gain would be 77952515`0%

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