I need Help with this question.
Please show workings.

Question:
[tex] {3}^{x} + {4}^{x} = {5}^{x} [/tex]

P.S : The answer is 2.
I just need the working.​

Answers

Answer 1

9514 1404 393

Answer:

  x = 2

Step-by-step explanation:

There are no algebraic methods for solving an equation like this.

The proof of Fermat's Last Theorem demonstrates that no integer x-value can possibly exist that is greater than 2. Trial and error (or your familiarity with Pythagorean triples) tells you that x=2 is a solution for this equation. Equations like this can be solved graphically, as in the attached.

I Need Help With This Question.Please Show Workings.Question:[tex] {3}^{x} + {4}^{x} = {5}^{x} [/tex]P.S
Answer 2

Answer:

[tex] x =2[/tex]

Step-by-step explanation:

Given :-

[tex]{3}^{x} + {4}^{x} = {5}^{x} [/tex]

And we need to find out the value of x. Well there is no specific method to solve the equation .This can be only done using the " Trial and error" Method.

We know that , 3 , 4 and 5 are Pythagorean triplets . So the sum of squares of two smallest numbers is equal to the square of the largest number . Henceforth ,

[tex]\implies {3}^{2} + {4}^{2} = {5}^{2} [/tex]

Verification :-

[tex]\implies {3}^{2} + 4^2 = 9+16=25=\boxed{5^2}[/tex]

So , the value of x is 2 . We can here prove that , x does not have other roots other than 2 . For that , divide the both sides of equation by [tex]5^x[/tex] , we have ,

[tex]\implies \dfrac{{3}^{x} + {4}^{x}}{5^x} = \dfrac{{5}^{x}}{5^x} [/tex]

[tex]\implies \bigg( \dfrac{3}{5}\bigg)^x+ \bigg( \dfrac{4}{5}\bigg)^x = 1 [/tex]

Now if we take the value of x greater than 2 or less than 2 , then the value 1 will not be satisfied for the values of x greater than or less than 2 .

That is ,

If x > 2

[tex]\implies \bigg( \dfrac{3}{5}\bigg)^x+\bigg( \dfrac{4}{5}\bigg)^x > \bigg( \dfrac{3}{5}\bigg)^2 +\bigg( \dfrac{4}{5}\bigg)^2 [/tex]

Subsequently :-

[tex]\implies \bigg( \dfrac{3}{5}\bigg)^x+\bigg( \dfrac{4}{5}\bigg)^x > 1 [/tex]

If x < 2

[tex]\implies \bigg( \dfrac{3}{5}\bigg)^x+\bigg( \dfrac{4}{5}\bigg)^x < \bigg( \dfrac{3}{5}\bigg)^2 +\bigg( \dfrac{4}{5}\bigg)^2 [/tex]

Subsequently :-

[tex]\implies \bigg( \dfrac{3}{5}\bigg)^x+\bigg( \dfrac{4}{5}\bigg)^x <1[/tex]

Thus there is no other value other than 2 for which the value of above expression becomes 1 .

Hence 2 is the root of the given equation.


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Answers

Answer:

840 megabytes

Step-by-step explanation:

hope this helps

The students in Mabel's class got to choose between pizza and burgers for the celebration on the last day of school. 12 students picked the pizza. If there are 40 students in all in Mabel's class, what percentage of the students picked the pizza?

Answers

Answer:

30%

Step-by-step explanation:

The percentage of something can be calculated by dividing that number by the total amount. In this scenario, you divide 12 by 40

12/40 = 0.3

Or, you could do it the way without doing the math and simplifying to make it easier

12/40 = 6/20 = 3/10 = 0.3 = 30%

Help please and thank you

Answers

Answer:

B is correct: 3x=40

Step-by-step explanation:

just cross multiply and mark brainliest if you feel like it :)

Answer:

3x =40

Step-by-step explanation:

3 will cross multiply with x then 4 will multiply 10

Hence 3x=40

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uhm .. do you want us to do the photo or name a pair?
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Answers

4+n symplify the equation 8+(n-4) and you will get 4+n

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Answers

Answer:

x = 16 units

Step-by-step explanation:

BC = 32√2 / √2 = 32

x = 32/2 = 16

Solve each problem and show the work for each one.

Solve by factoring.
1. 2x^2+9x+26=-4x+5

Solve by using the quadratic formula and round to the nearest hundredth.
2. 3x^2-6x-4=0​

Answers

Answer:

Solve by factoring.

1. 2x^2+9x+26=-4x+5

2x²+9x+4x+26-5=0

2x²+13x+21=0

doing middle term factorization

2x²+7x+6x+21=0

x(2x+7)+3(2x+7)=0

(2x+7)(x+3)=0

either

x=-7/2

or

x=-3.

2.

3x^2-6x-4=0

comparing above equation with ax²+bx+c=0

we get

a=3

b=-6

c=-4

By using quadratic equation

x=[tex] \frac{ - b±\sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

Substituting value

x=[tex] \frac{ 6±\sqrt{ {-6}^{2} - 4*3*-4 }}{2*-4} [/tex]

x=[tex] \frac{ 6±\sqrt{ {84}}}{-8} [/tex]

x=[tex] \frac{ 6±2\sqrt{ {21}}}{-8} [/tex]

-8x=6±2√21

taking positive

-8x=6+2√21

x=[tex] \frac{6+2√21}{-8} [/tex]

x=-[tex] \frac{3+√21}{4} [/tex]

taking negative

-8x=6-2√21

x=[tex] \frac{6-2√21}{-8} [/tex]

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four less than the sum of a number, x and nine is 35​

Answers

Step-by-step explanation:

(x+9)-4=35x+9-4=35x=35-5x=30

,stay safe healthy and happy..

Help me with the math

Answers

Answer:

See below

Step-by-step explanation:

[tex] m\angle 1 = 180\degree - (90+39)\degree = 51\degree [/tex]

[tex] m\angle 2= 90\degree -51\degree =39\degree [/tex]

[tex] m\angle 3= 90\degree[/tex]

[tex] m\angle 4 = 180\degree - (90+39)\degree = 51\degree [/tex]

[tex] m\angle 5 = 180\degree - (129+34)\degree = 17\degree [/tex]

[tex] m\angle 6 = 90\degree +39\degree = 129\degree [/tex]

Need help please!!!!

Answers

Answer:15

Step-by-step explanation:

Madison, Natalie, Isabella and Rebecca go shopping. Madison spent 4/5 of her money, Natalie spends 75% of her money,Isabella spends 0.68 of her money and Rebecca spends 17/20 of her money. Who has the largest percentage of their money left?

Answers

Answer:

you need common denominater so 10/10 - 9/10 =1/10 thats how much of her money she used.

Step-by-step explanation:

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

Answers

Answer:

It’s just a black screen I cant see the picture?

Answer:

1.

It has two solution because it is in quadratic form.

2.

(x-4)²-28=8

x²-8x+16-28-8=0

x²-8x-20=0

Doing middle term factorization

x²-(10-2)x-20=0

x²-10x+2x-20=0

x(x-10)+2(x-10)

(x-10)(x+2)=0

either

x=10

or

x=-2

:. x= 10 or -2

3.

2x²-5x-5=0

Comparing above equation with ax²+bx +c

we get

a=2

b=-5

c=-5

quadratic equation is

[tex]x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

Substituting value

[tex]x = \frac{ 5 ± \sqrt{ {-5}^{2} - 4×2×-5} }{2×-5} [/tex]

-10x=5±[tex] \sqrt{ {25+ 40}}[/tex]

taking + ve

-10x=5+[tex] \sqrt{ {65}}[/tex]

x=-½-[tex] \frac {\sqrt{ {65}}}{10}[/tex]

taking -ve

x=-½+[tex] \frac {\sqrt{ {65}}}{10}[/tex]

A new price of an item is $39.32. The percent increase was 16%. What was the original price?

Answers

Answer:

let x =the original price

then 116x/100=$39.32

116x=100×39.32

116x=3932

divide both sides by 116

116x/116=3932/116

x=33.89655

(2dp)

x=33.90

?? im conufsed please help

Answers

Answer:

B

Step-by-step explanation:

The sign means greater than or equal to and the car need to travel at least 570 miles.

Hope it helps, sorry if it's not right :>

Answer:

Step-by-step explanation:

b

how to solve fractagons​

Answers

Answer:

By using cross multiplication

Step-by-step explanation:

What are the values of Limit of g (x) as x approaches 33 minus and Limit of g (x) as x approaches 33 plus?

Answers

Answer:

D

Step-by-step explanation:

Darla washed 5/9 of the windows on a building, and Cindy washed 1/9 of them. How much greater was Darla's fraction of the windows than Cindy's

Answers

Answer:Darla's fraction of the windows was 4/9 greater than Cindy's.

Step-by-step explanation:

Fraction of the window washed by Darla =5/9

Fraction of the window washed by Cindy=1/9

To find How much greater  Darla's fraction of the windows was than Cindy's, we subtract ,

5/9-1/9=4/9

Thetrefore, Darla's fraction of the windows was 4/9 greater than Cindy's.

Answer:

4/9

Step-by-step explanation:


[tex]6 - 2x - 4(2x + 1)[/tex]

I need help with this problem.​

Answers

you should use photo math it helps a lot

Answer:

2 - 10x

Step-by-step explanation:

Given

6 - 2x - 4 (2x + 1) ← distribute parenthesis by - 4

= 6 - 2x - 8x - 4 ← collect like terms

= 2 - 10x

The cumulative frequency table shows the heights (inches) of every student in Mrs. Torjman’s math class. What number should be written in the red box?

Answers

Answer:

The number 28 should be written in the red box.

Solve the equation for x

Answers

Answer:

B.   x = -4

Step-by-step explanation:

- 7x - 35 = -7

add 35 to both sides

-7x = 28

Divde both sides by -7

x = -4

Answer: X = -4

Step-by-step explanation:

-7x - 35 = -7

-7x = -7 + 35

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thank u!

Answers

Answer:

The Slope Equation = y2 -y1 over X2 - X1

Step-by-step explanation:

1.) Pick every graph

2.) Pick any 2 point in the graph

3.) do the slope equation

4.) the answers must be equal  

3x+5(2+x)=4x-7 help me out here?

Answers

Answer:

x = -17/4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Distributive Property

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

3x + 5(2 + x) = 4x - 7

Step 2: Solve for x

[Distributive Property] Distribute 5:                                                                 3x + 10 + 5x = 4x - 7[Addition] Combine like terms:                                                                        8x + 10 = 4x - 7[Subtraction Property of Equality] Subtract 4x on both sides:                      4x + 10 = -7[Subtraction Property of Equality] Subtract 10 on both sides:                       4x = -17[Division Property of Equality] Divide 4 on both sides:                                  x = -17/4

Answer:

x=[tex]\frac{-17}{4}[/tex]

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3x+5(2+x)=4x−7

3x+(5)(2)+(5)(x)=4x+−7(Distribute)

3x+10+5x=4x+−7

(3x+5x)+(10)=4x−7(Combine Like Terms)

8x+10=4x−7

8x+10=4x−7

Step 2: Subtract 4x from both sides.

8x+10−4x=4x−7−4x

4x+10=−7

Step 3: Subtract 10 from both sides.

4x+10−10=−7−10

4x=−17

Step 4: Divide both sides by 4.

[tex]\frac{4x}{4}[/tex]=[tex]\frac{-17}{4}[/tex]

x=[tex]\frac{-17}{4}[/tex]

Multiply 5730 x (1/2)4

Answers

Answer:

no  its 5_8)8_9

Step-by-step explanation:

Answer:

The answer is 11460

Hope this helps!

1. Calculate exactly;
(b) 3/4 + 2/3 + 4/5

Answers

2.2166666666 this is what I got man

74.55 divided by 5
I’m not sure of the answer I need some help

Answers

Answer:

14.91

Step-by-step explanation:

Have a good day :)

Answer:

The answer is 14.91

Step-by-step explanation:

To find the answer we must first see how many times 5 can go into 74.55.  Since 5 x 14.91 = 74.55, then it means that our answer is 14.91.  

9. In the diagram below, Angle A is 50 degrees. What is angle B?

Answers

Answer:

130

Step-by-step explanation:

Angle B = 180 - Angle A

180 - 50 = 130

Answer:

The answer is 130 degrees.

Step-by-step explanation:

A+B should be 180, so with A being 50; B has to be 130.

PLEASE HELP ME!!!

Boyle's law is :
p1 v1 = p2 v2

what happens to the pressure of a container if the volume is doubled and the temperature is kept the same?

- impossible to determine with the info provided

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Answers

Answer:

- the pressure will decrease

(volume is doubled ,the pressure reduced by half).

Step-by-step explanation:

P_1 V_1=P_2 V_2

This equation shows that, as volume increases, the pressure of the gas decreases in proportion.

Similarly, as volume decreases, the pressure of the gas increases.

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Answers

Answer:

I belive the answer will be 28,350

Find the exact value of sin v/2, given tanv=12/5 and pi

Answers

The correct way of getting this answer with proof of simplifying the top to the multiplied amount and then subtracts that then simplify to double check

I need help asap

Which expression represents the volume of a cube with a side length of 6x?
a)6x^2
b)36x^2
c)36x^3
d)216x^3

Answers

Answer:

Option 4

Step-by-step explanation:

So formula of voulme of the cube is a³

We have the side length is 6x

So sub the value in formula we get 216x³

Answer(D216x^3
Explanation
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