1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alex41 [277]
2 years ago
15

243^0.2x=81^x+5Could you please help me with the steps to this problem?​

Mathematics
1 answer:
Natasha_Volkova [10]2 years ago
3 0

Answer:

-20/3

Step-by-step explanation:

First simplify the left side of the equation

243^(1/5x)= (243^1/5)^x

                =(\sqrt[5]{243} )^x

                = 3^x

Now that the left side is simplified,  let's move to the right side

81^(x+5)=( 3^{4})^(x+5) simplify 81 to base 3^4

             =x^{4(x+5) use the product of powers property to multiply the exponents together

             =x^{4x+20

With both sides simplified, let's rewrite the equation, this time in simplified terms

3^{x}=3^{4x+20}            

x=4x+20    because both the bases are same, their exponential value must also be equal

-3x=20 solve the algebraic equation for x

  x=-\frac{20}{3}

You might be interested in
Please Help, 35 Points.
Andrei [34K]

To answer this question, we have the start-up costs of $ 52,000

A monthly inflation of $ 0 is assumed

Operating costs  are $680

The daily gain  is $960

For the Part A.

The inequality that this situation represents

 960d-680d>52000

So:

d(960-680)>52000

Where d represents the number of days.

For the Part B.

To start earning, you must replace all the initial investment and cover the expenses per day. The time that must pass for this to happen is obtained by clearing "d" from the inequality.


 d>\frac{52000}{960-680}

d> 185.71 days

Then, the sum of the net profits will be greater than the initial investment after 186 days of starting the business.

4 0
2 years ago
According to the empirical (69-95-99.7) rule, if a random variable z has a standard normal distribution, then approximately 95%
Dmitry_Shevchenko [17]

Using z-scores, it is found that the value of z is z = 1.96.

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean \mu and standard deviation \sigma, is given by:  

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.
  • Each z-score has an associated p-value, which is the percentile.

  • The normal distribution is symmetric, which means that the middle 95% is between the <u>2.5th percentile and the 97.5th percentile</u>.
  • The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
  • The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
  • Thus, the value of Z is 1.96.

A similar problem is given at brainly.com/question/16965597

7 0
2 years ago
A manufacturer of bicycles has determined that 550 bikes per month will be sold at a price of $250. At a price of $150, it is es
iogann1982 [59]

750 bikes would be sold for $350

Let x represent the number of bikes sold per month and y represent the price.

550 bikes are sold at a price of $250, this can be represented by (550, 250). Also, 750 bikes is sold at a price of $150, hence it is represented by (750, 150)

A linear function is represented by:

y = mx + b

m is the slope, b is the y intercept.

Therefore the function is:

y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-250=\frac{150-250}{750-550}  (x-550)\\\\y=\frac{1}{2}x-25

The number of bikes sold for $350 is:

350 = (1/2)x - 25

x = 750

Therefore 750 bikes would be sold for $350

Find out more at: brainly.com/question/13911928

3 0
2 years ago
It's been a while since I've taken a math class and I'm stressed please help me out. The question is circled.
brilliants [131]
-3/2x

The rational expression would not be defined only when the denominator is divided by 0

That is:

2x =0

x = 0/2

x =0

Hence it would not be defined when x = 0.

Hope this helps.
8 0
3 years ago
Read 2 more answers
The number of views in a cat and a dog after they uploaded are represented by the following
alexandr1967 [171]

Answer:

i see nothin

Step-by-step explanation:

5 0
2 years ago
Other questions:
  • 10. A parasailor is attached to a boat with a rope 80 feet long. The angle of elevation
    11·1 answer
  • What is the sum of 536 and 232
    13·2 answers
  • 784,926 rounded by the 4
    5·1 answer
  • -4p+9=-5 what does p equal
    15·2 answers
  • Explain how to determine if the number is a solution to the equation. n + 6 = 33 for n = 27
    7·2 answers
  • The graphs below have the same shape. What is the equation of the blue<br> graph?
    7·1 answer
  • Answer choices are 9,-9,4,-4 for both spots PLEASE HELP FAST!!!
    14·1 answer
  • I need help with this
    6·1 answer
  • Solve <br>i)x²– X – 2 = 0<br>ii)3t-6&lt;10<br><br><br>​
    11·1 answer
  • 30 POINTS!!!!!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!