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
Tems11 [23]
3 years ago
14

Give the domain on which the equation is defined. In particular, describe the set of x for which the equation is defined, using

interval notation.
Solve for the unknown variable. Show all your work.
e^(x-5)*e^(3x+8)=19
Mathematics
1 answer:
Anestetic [448]3 years ago
7 0


law's of exponents

e^(x-5)*e^(3x+8) = 19
e^(x-5+3x+8) = 19
e^(4x+3) = 19

take the natural log, which is base "e" of both sides.

ln[e^(4x+3)] = ln[19]
4x +3 = ln[19]
4x = ln[19] - 3
x = (ln[19] - 3) / 4
x = -0.0139
You might be interested in
Which is 2logx-6log(x-9) written as a single logarithm
Elena-2011 [213]

Answer: option c.

Step-by-step explanation:

 To solve the given exercise and write the expression as a single logarithm, you must keep on mind the following properties:

m*log(a)=log(a)^m

log(a)-log(b)=log(\frac{a}{b})

Therefore, by applying the properties shown above, you can rewrite the expression given, as following:

2logx-6log(x-9)=logx^2-log(x-9)^6=log(\frac{x^2}{(x-9)^6})

Then as you can see, the answer is the option c.

3 0
3 years ago
Find the constant of proportionality r in the equation y = rx
Zepler [3.9K]

The constant of proportionality is 1/5

Also flexing on us with that 5G

5 0
3 years ago
Read 2 more answers
The graph shows a probability distribution. What is P(2.5≤X≤4)?
jeka57 [31]

Answer:

P(2.5≤X≤4) = 0,3125‬

Step-by-step explanation:

We know that the area under the curve of ANY probability distribution should not be greater than 1.

In this case, we now that 4P = 1, therefore, P=1/4. Where 'P' represents the height of the rectangle that represents the probability distribution.

The probability of P(2.5≤X≤4) will be given by the area of the following rectangle:

(4 - 2.5) × 1,5 = 0,3125‬

Therefore, P(2.5≤X≤4) = 0,3125‬

5 0
4 years ago
Read 2 more answers
A student has a monthly budget of $800. She can spend her budget on two items, X and Y. Each unit of X costs $20 and each unit o
Aleonysh [2.5K]

Answer:

Check the explanation

Step-by-step explanation:

Total utility is the overall satisfaction that a particular consumer received from consuming a given overall quantity of a good or service, To calculate the value of total utility economists utilize the following basic total utility formula: TU = U1 + MU2 + MU3

Kindly check the attached image below to see the step by step explanation to the question above.

3 0
4 years ago
Factor completely. 4p² + 36p + 81 Express the answer in the form (ap+b)2 . Enter your answer in the box.
Scrat [10]
We can factor this polynomial using grouping. What we do is split the 36p into into parts so that we can factor the polynomial one half at a time.

To do so, we first multiply the leading coeffient by the constant. In other words, a times c where ap^2+bp+c. After multiplying 4 and 81, we get 324. Now we need to find two numbers that multiply to be 324 and add to be 36.

The factors of 324 are: 1, 2, 3, 4, 6, 9, 12,18, 27, 36, 54, 81, 108, 162, and 324.

The pair of numbers that works in this case are 18 and 18 since 324 is a perfect square.

Now we split the 36p:

(4p^2+18p)+(18p+81)

Now factor both halves.

2p(2p+9)+9(2p+9)

We have a common binomial of 2p+9 that can be factored out it get

(2p+9)(2p+9)

or

(2p+9)^2


5 0
4 years ago
Other questions:
  • HELP <br>Which equations represent hyperbolas?
    15·2 answers
  • Express vector f⃗ in the form of fx, fy, fz, where the x, y, and z components are separated by commas. f⃗ = n
    13·1 answer
  • What is the range of g(x)=-4^x+2
    10·1 answer
  • iTunes charges a one time fee of $10 and $ 1 per song . Spotify charges a one time fee of $20 and $0.50 per song. After how many
    12·1 answer
  • Mane who be shaking dice?
    8·2 answers
  • PLEASE HELP PLEASe!!!!
    11·2 answers
  • Please do correctly! I will mark you Brainliest!
    7·1 answer
  • 5. Evaluate the following expression when a = -4
    7·1 answer
  • A 10% increase in cigarette prices has been found to result in a _____ decrease of smokers. a. 2% b. 4% c. 10% d. 20% please sel
    8·2 answers
  • HELPP!!!!! PLSSSS!!!!
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!