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

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.


Related Questions

similfy the following ratio 1) 20:45 2) 12:32:20 3) 5m:350cm​

Answers

Answer:

1) 20/45= 4/9=4:9

2) 3:8:5

3) 10:7

Factor
x
3
+
6
x
2
+
2
x
+
12

Answers

Answer:

♿⚠️⛔☢☣⬆️↗️➡️↘️⬇️↙️⤵️⤴️↪↩↔️↕️↖️⬅️

A bakery uses 6 cups of flour for each batch of bread and spread another cup of flour on the counter write an algebraic expression using C to represent the cups of flour that are used.

Answers

Answer:

6c = b

Step-by-step explanation:

6 cups of flour for each batch of bread, so 6c;

b is the batch of bread.

So basically,

6c = b

Sally went to the video game store and bought 2 used video games for $22.50 each, one new game for $55, and a gaming magazine for $12.95. There was 6.5% tax on the purchase. What was the total purchase price after tax?

Answers

Answer:

$120.29

Step-by-step explanation:

first you add the normal prices of what sally bought, then add 6.5% of the price she paid.

22.5(2) + 55 + 12.95 = 112.95

6.5          x

-----  =    -----

100     112.95

6.5(112.95)  = 100x

734.175/100 = 100x/100

7.35 ≅ x

112.95 + 7.35 = 120.30

I think that's it! Let me know if it is! If so, please maybe consider giving me Brainliest! It would really help me out!

Help! What is the answer. Please, help ASAP.

Answers

I really don’t know but I got 66.30909

One serving of Mike’s crackers has 150 calories and a mass of 30 grams.

How many calories are in 6 grams of the crackers?

Answers

Step-by-step explanation:

You need to times it, so 150 x 30, and then whatever it is, thata the answer

x<-7 on a number line

Answers

Answer:

mark -7 on the line then draw a line to the left of it

hello please help i’ll give brainliest

Answers

10. 1

11. 0

12. 0

13. 0

14. 1

15. 2

16. 1

17. 3

18. 1

19. 0

20. 1

Can someone please help me!

Answers

Answer:

A)

Step-by-step explanation:

it is clearly reduced so you can eliminate the middle two options as answers;

reduction is always going to be a value less than 1 because a value greater than 1 would not be a reduction

What is the volume of this retangular prism

Answers

Answer:

27

Step-by-step explanation:

3 times 3 times 3

length times width times height

I hope this helped!

Answer:

27

Step-by-step explanation:

Can anyone help on this i don't understand it
the chooses for the choose is
15
12
10
14
11
13
9

Answers

median means the middle number and mode means which number appears the most

PLSSS HELP GIVING BRAINLIEST
Richard has a bag of blocks. Without looking in the bag, he selects a block, records its color, and puts it back in the bag. All blocks are equally likely to be chosen. He performs the process 50 times. In the 50 trials, he records the following colors of blocks from the bag. Number of times a yellow block was chosen 12 Number of times a red block was chosen 11 Number of times a green block was chosen 16 Number of times a blue block was chosen 5 Number of times a orange block was chosen 6 Based on the data Richard collected, what is the estimated probability, in simplest form, of choosing a green block from the bag? 8 25 O B. 16 100 C. 25 D. 8 100​

Answers

Answer:

C.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is c 16/100

50 POINTS!!! HELP ME PLEASE!!!!

Answers

Step-by-step explanation:

1. 3.6 x 10^-1

2. 3.1 x 10^6

3. 5.3 x 10^-6

4. 4.2 x 10^-1

algebra help pls answer

Answers

It’s the 3rd one I believe

Find the surface area of the composite figure.

Answers

Answer:

470

Step-by-step explanation:

there are several surface areas.

1. the 4 side walls of the big block = 4*12*7 = 336

2. top and bottom of the big block = 2* 7*7 = 98

3. subtract the small rectangular area from the top area covered by the small block = 2*7 = 14

4. the 3 (visible) side walls of the small block on top =

3* 2*7 = 42

5. the small top and bottom areas of the small block =

2* 2*2 = 8

so, 1.+2.-3.+4.+5. = 470

Find the surface area of the pyramid below. You do not need to include units. 8 cm 5 cm

Answers

Answer:

A=lw+l(w

2)2+h2+w(l

2)2+h2Step-by-step explanation:

Answer:

40

Step-by-step explanation:

well I need the 3rd number but right now the answer is 40

h+6.9+11.4
a
4.0
b
4.5
c
5.0
d
5.5

Answers

Could you please express this question better, I don't seem to understand the objective.

Every 3 months, homeowners in boise pay $46.00 for services provided by the city. How much do homeowners pay in one year? (1 year = 12 months)

Answers

Answer: 184.00

Step-by-step explanation: you have to see how many times are there 3 months in one year you divide 12 divided by 3 which equals 4 and 46 times 4

Answer: $184,00

Step-by-step explanation

Find the length side of W

Answers

Answer:

17.99

Step-by-step explanation:

Trig Ratios:

Sin = Opposite over Hypotenuse

Cos = Adjacent over Hypotenuse

Tan = Opposite over Tangent

We can use trig ratio sine as we are given an angle ( 40° )and the hypotenuse (28) and we need to find its opposite side (w)

Recall that sin = opposite over hypotenuse

That being said we want to create an equation to solve for w

[tex]sin(40)=\frac{w}{28}[/tex]

Now we solve for w

Step 1 multiply each side by 28

[tex]\frac{w}{28} *28=w\\sin(40)*28=28sin(20) = 17.99[/tex]

we're left with w = 17.99

Solve the following system. y = 2x2 - 3x - 4 and y + x = 8. Enter the solution with the smaller x value first. The solutions are ( , ) and ( , )

Answers

The solutions of the nonlinear system of equations are the points (x₁, y₁) = (- 2, 10) and (x₂, y₂) = (3, 5).

How to solve a system of algebraic equations

We find in this place a non-linear system formed by a quadratic equation and a linear equation, which can be solved by algebra properties. The complete procedure is shown below:

y = 2 · x² - 3 · x - 4     (1)

y + x = 8                     (2)

By (2) in (1):

2 · x² - 3 · x - 4 + x = 8

2 · x² - 2 · x - 12 = 0

2 · (x² - x - 6) = 0

2 · (x - 3) · (x + 2) = 0

x = 3 ∨ x = - 2

y = 8 - 3 ∨ y = 8 - (- 2)

y = 5 ∨ y = 10

The solutions of the nonlinear system of equations are the points (x₁, y₁) = (- 2, 10) and (x₂, y₂) = (3, 5).

To learn more on quadratic equations: https://brainly.com/question/17177510

#SPJ1

Nell writes the expression (3.6x +6)-4. She rewrites the expression using the associative property. Which expression could Nell have written using the associative property?

A.) 5.6x
B.) 9.6x-4
C.) 3.6+(6-4)
D.) 3.6(x+6)-4

Answers

Answer:

C.)  3.6 + (6 - 4)

Step-by-step explanation:

Find the length of the missing side. Round to the nearest hundredth if necessary
a=6
b=3
what is c

Answers

Answer:

6.71

Step-by-step explanation:

Pythagorean theorem

a^2+b^2=c^2

6^2+3^2=c^2

36+9=c^2

45=c^2

6.71=c

Determine the period.

Answers

Answer:

the period is the to top points of the highest points on top of the crests

The period of function is,

P = 5

Since, In order to find the period of a graph in general, first, find the period of the parent function, and divide that by the absolute value of the coefficient of the independent variable.

Here, Graph of function is shown.

Hence, The period of function is,

P = 10/2

P = 5

Because there is two wave are shown.

Therefore, The period of function is,

P = 5

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ7

HELP I WILL MARK BRAINLIEST

Answers

Answer:

#5 - C

#7 - A

Step-by-step explanation:

If two items are similar, it means that the angles and figure itself have not changed, just the size. The two objects are prototional to each other.

In order to find the length of one side, we have to find what the size difference is, if that makes sense. We have to figure out the number that the smaller size is multiplied by in order to get the bigger number (or the other way around).

#5:

Side LK and side DE are preportional. We can divide 35 by 10 to figure out the proportion size. 35/10=3.5. Then we can take that and use it to find the other side. MK and FD are proportional. We can now take 22 and multiply it by 3.5 to get the new side length. 22x3.5=77

#7:

Same thing. 12/8=1.5, which is the proportional size change. We can now take the already exisiting number and multiply it. 5x1.5=7.5

IM BEING TIMES HELPPPPPPPP THANK YOUUUUUUU

Answers

Answer:

1. make both equal, so...

-14/24 + 9/24

=-5/24

Step-by-step explanation:

(No links) HELP ME THIS IS THE LAST QUESTION

Answers

Part 1

Answer:  (x+5)(x+10) - 50 = 126

Other answers are possible.

-------------

Explanation:

The old width was 5, but then it increases to x+5. The old length was 10, but now it's x+10.

The area of any rectangle is length times width.

So the area of the larger rectangle is (x+5)(x+10). Subtract off the old area of 5*10 = 50 and we get (x+5)(x+10) - 50 as the area of the L shape. Set this equal to 126 to finish setting up the equation. This is one possible answer out of many others. This is because we could expand out the (x+5)(x+10) into x^2+10x+5x+50 or simplify that to x^2+15x+50, as two possible options.

==========================================================

Part 2

Answer:  x = 6

-------------

Explanation:

Solve the equation we set up in the previous part

(x+5)(x+10) - 50 = 126

x^2+10x+5x+50-50 = 126

x^2+15x = 126

x^2+15x-126 = 0

Apply the quadratic formula from here

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(15)\pm\sqrt{(15)^2-4(1)(-126)}}{2(1)}\\\\x = \frac{-15\pm\sqrt{729}}{2}\\\\x = \frac{-15\pm27}{2}\\\\x = \frac{-15+27}{2} \ \text{ or } \ x = \frac{-15-27}{2}\\\\x = \frac{12}{2} \ \text{ or } \ x = \frac{-42}{2}\\\\x = 6 \ \text{ or } \ x = -21\\\\[/tex]

Another method you could use is factoring, so you could say:

x^2+15x-126 = 0

(x-6)(x+21) = 0

x-6 = 0 or x+21 = 0

x = 6 or x = -21

The issue with this is that it may take a while to do this trial and error approach.

Whichever method you used, you'll end up with two solutions. One of those solutions doesn't make sense though. We can't have a negative length or distance value, so we ignore x = -21.

The only practical solution is x = 6

If x = 6, then the old height goes from 5 to x+5 = 6+5 = 11

If x = 6, then the old length goes from 10 to x+10 = 6+10 = 16

The new larger rectangle is 11*16 = 176 sq ft, in which we subtract off the 50 sq ft to get 176-50 = 126 sq ft, and this matches with the 126 given to us. Therefore, the answer is confirmed.

If a card is drawn at random from a standard 52-card deck, what is the probability that
the card drawn is:
Note: Give your answer as a fraction in simplest form or as a decimal rounded to the
nearest thousandths place.
a) a face card?
b) a red card?
c) a queen?
d) a club?
e) an Ace or 10?

Answers

Answer:

a) 12/52 = 3/14

b) 26/52 = 1/2

c) 4/52 = 1/13

d) 13/52 = 1/4

e) 8/52 = 2/13

Step-by-step explanation:

a) there are 12 face cards and 52 in the deck

b) half the cards are red, the other half black

c) one queen in each of four suits

d) the deck is broken up into 4 equal suits (hearts, diamonds, spades, clubs) so there are 13 of each.

e) like the answer in part C, there is one of each card in each of the four suits. that gives us four aces and four tens.

True or False:
A cube root is when you think about what number multiplies by itself 4 times to give us that number.

Answers

Answer:

False. It's 3 times.

Step-by-step explanation:

ASAP! Which number is a factor of the prime factorization of 60?

Answers

Answer:

So the prime factorization of 60 is 2 × 2 × 3 × 5, which can be written as 2 2 × 3 × 5. The actual prime factors of 60 are 2, 3, and 5.

Answer:

The Prime Factorization is:

2 x 2 x 3 x 5

In Exponential Form:

2^2 x 3^1 x 5^1

Select the correct answer.
Find the value of g(7) for the function below.
g(x) = zur

Answers

Answer:

B

Step-by-step explanation:

To evaluate g(7) substitute x = 7 into g(x) , that is

g(7) = [tex]\frac{7}{8}[/tex] × 7 - [tex]\frac{1}{2}[/tex]

      = [tex]\frac{49}{8}[/tex] - [tex]\frac{4}{8}[/tex]

      = [tex]\frac{45}{8}[/tex] → B

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