Answer:
The inverse function of the exponential function f(x) = a^x is the logarithmic function with base a.
The inverse function of a function f is a function that "undoes" the original function, meaning that it reverses the transformation applied by the original function. In the case of the exponential function, the inverse function is the logarithmic function, which "undoes" the transformation applied by the exponential function.
For example, suppose we have the exponential function f(x) = 2^x. The inverse function of this function is the logarithmic function with base 2, which is written as y = log_2 x. If we apply the inverse function to 2^x, we get:
y = log_2 (2^x)
Solving for x gives:
x = 2^y
This means that the inverse function of the exponential function f(x) = a^x is the logarithmic function with base a, which is written as y = log_a x.
The other options (a. transcendental, c. rational, d. polynomial, e. algebraic) are not correct, since they do not describe the inverse function of the exponential function.
Answer:
b. logarithmic
Step-by-step explanation:
Given exponential function:
[tex]f(x)=a^x[/tex]
The inverse of the given function is the logarithmic function with base a.
To find the inverse of a function, replace f(x) with y:
[tex]\implies y=a^x[/tex]
Swap the x and y:
[tex]\implies x=a^y[/tex]
Take logs with base a of both sides of the equation:
[tex]\implies \log_ax=\log_aa^y[/tex]
Apply the log power law: logₐ xⁿ = n logₐ x
[tex]\implies \log_ax=y\log_aa[/tex]
Apply the log law: logₐ a = 1
[tex]\implies \log_ax=y[/tex]
[tex]\implies y=\log_ax[/tex]
Replace y with f⁻¹(x):
[tex]\implies f^{-1}(x)=\log_ax[/tex]
Thus proving that the inverse of the exponential function f(x) = aˣ is the logarithmic function with base a.
1. Given: f(x)= x* - 6x² + 7x-6
(a) Using correct limit notation, describe the end behavior of f(x).
x/-7 +14 >/ 16
show your work
include a number line
9514 1404 393
Answer:
x ≤ -14
Step-by-step explanation:
We assume you want to solve ...
x/(-7) +14 ≥ 16
Subtract 14, then multiply by -7.
x/(-7) ≥ 2 . . . . subtract 14
x ≤ -14 . . . . . . multiplying by a negative number reverses the inequality
The solution is shown on the number line below.
The base of an ice cream cone has a radius of 4cm and the cones height is 12cm
Answer:
V=201.06
Step-by-step explanation:
V=πr2h
3=π·42·12
3≈201.06193
Find the value of x
A. 7
B. 8
C. 10
D. 15
help please. 10 points yall.
Ardit left a 18% tip on a $60 restaurant bill. How much money did he leave for the tip?
Answer:
$10.80
Step-by-step explanation:
$60.00 x 0.18 = $10.80
Marcie baked several pies. She used 4 cups of flour for the dough. How many pints of flour did she use?
I have to turn this is Immediately please
Answer:
well if several means 3 then she used 12 pints.
Step-by-step explanation:
3X4=12
4X4=16
5X4=20 and so on.
The number of items sold over a four-month period are: month 1 2 3 4 sales 5100 5500 5400 5600 Calculate the forecasts for the 4th and 5th months using 3-month weighted moving average method with weights of 0.6 for the most recent month and 0.3 for the next to the most recent month. Further, suppose that the exponential smoothing constant α=0.5. Then calculate the forecasts for 3rd, 4th and 5th months, using exponential smoothing method. Under the 3-month weighted moving average method, what is the forecast for the fourth month?
Answer:
By using 3-month weighted moving average method -
Forecasts for the 4th month = 5400
Forecasts for the 5th month = 5530
By using Exponential smoothing method -
Forecasts for 3rd month = 5300
Forecast for 4th month = 5350
Forecast for 5th month = 5475
Step-by-step explanation:
To find - Calculate the forecasts for the 4th and 5th months using 3-month weighted moving average method.
Calculate the forecasts for 3rd, 4th and 5th months, using exponential smoothing method.
Proof -
Given that,
month 1 2 3 4
sales 5100 5500 5400 5600
F(4) = 0.6 A(3) + 0.3 A(2) + 0.1 A(1)
= 0.6 [ 5400] + 0.3 [ 5500] + 0.1 [ 5100]
= 3240 + 1650 + 510
= 5400
⇒forecasts for the 4th month = 5400
Now,
F(5) = 0.6 A(4) + 0.3 A(3) + 0.1 A(2)
= 0.6 [ 5600] + 0.3 [ 5400] + 0.1 [ 5500]
= 3360 + 1620 + 550
= 5530
⇒forecasts for the 5th month = 5530
Now,
Given that, the exponential smoothing constant α=0.5
Month Sales Forecast
1 5100 5100
2 5500 5100 + 0.5(5100 - 5100) = 5100
3 5400 5100 + 0.5(5500 - 5100) = 5300
4 5600 5300 + 0.5(5400 - 5300) = 5350
5 5350 + 0.5(5600 - 5350) = 5475
∴ we get
By using Exponential smoothing method -
Forecasts for 3rd month = 5300
Forecast for 4th month = 5350
Forecast for 5th month = 5475
Assume we have two lines which are parallel. If one line has a slope of -1/11
what is the slope of the other line? Enter your answer as an integer or fraction
in lowest terms
Is urgent no link please
if x is equal to –2, then find the value of 3x² + 5x
Answer:
2
Step-by-step explanation:
3*(-2)to power of 2 + 5*-2
= 3*4 + 5*-2
= 12 + -10 = 2
worries qui ouch Sunday each USCIS who what eeeei such Turkish what Umpqua snuggled han
Ms. Spencer has 15 students in her class. She asks each
student how many siblings they have. She wants to see
which number of siblings is the most common in the class.
Would a dot plot or a histogram be a more appropriate way to display the
data for this situation?
O A. A histogram, because Ms. Spencer wants to show how the data
fall into different intervals or ranges.
B. A histogram, because Ms. Spencer wants to show all of the
individual data values.
O C. A dot plot, because Ms. Spencer wants to show all of the
individual data values,
O D. A dot plot, because Ms. Spencer wants to show how the data fall
into different intervals or ranges.
PREVIOUS
Answer:
A dot plot, because Ms. Spencer wants to show all individual data values.
Step-by-step explanation:
ap3x approved
Jim got 46 out of 60 correct on a test. What is the best estimate of the percent Jim got correct ?
Answer-
77
Step-by-step explanation:
i rounded 76.67% (which was the exact percentage of 46 out of 60)
2- 77%
Answer:
About 76.5% (77%)
Step-by-step explanation:
well start with the simple fractions. 40/60 is 2/3 which is 66.66666 repeating.
If we know it increased at least 5 more that is 45/60 which is 3/4, since 15 * 4 = 60, so 15 * 3 = 45.
We could say without getting too specific that every point will have about a 1.5 or more % increase since if it was out of 100 points every 1 question is +1 % and 50 points every question is +2 %. Since this is 60 it will be roughly about 1.6%
Ok the point is, about 76.5% (77%)
cAlCulAtOrS ExiSt SkOoL Hw
Is (3,11) a solution to the equation y= 5x-4
You are having a wedding with 243 guests. If each
table holds 8 guests, what is the least number of tables
you must have to seat all of the guests?
19-3/4n in standard form
Answer:
So, if you need to convert the fraction into a decimal, 3/4=0.75. So, I think it's 19-0.75 I'm not sure if I'm correct.
Step-by-step explanation:
WILL MARK BRAINLIEST
Solve for x.
60
10
20
120
Answer:
x = 10
Step-by-step explanation:
Let's draw the center of the circle S and the segments SE and SD.
SE is perpendicular to EF (as EF is tangent to circle).
That means FED + DES = 90deg
We also know that DSE = 120deg
And because the SED is an isosceles triangle, we know that angle measures for DES and SDE are equal.
DES = (180deg - 120deg) / 2 = 30deg
FED = 90deg - DES = 90deg - 30deg = 60deg
7x - 10 = 60
7x = 70
x = 10
5. Casey's bank account offers him 2% interest every year, given by the equation
g(x)= 1.02. If Casey deposits $5,625 in his bank account, which equation
represents the amount of money that will be in his account after 2 years?
Answer:
Casey will have 5852.25 in his bank account after 2 years.
Step-by-Step Explaination:
2%=0.02
0.02*5625=112.5
112.5+5625=5737.5
0.02*5737.5=114.75
114.75+5737.5=5852.25
1) A store sells small and large TV sets in the ratio 2:3. The total stock is 70
sets.1) How many small and large sets are in stock? 2)If the number of large
sets is increased by 8,what is the new ratio of small to big*
Answer:
(a)
[tex]Small = 28[/tex]
[tex]Large = 42[/tex]
(b)
[tex]Ratio = 14 : 25[/tex]
Step-by-step explanation:
Given
[tex]L = Large\\ S = Small[/tex]
[tex]S : L = 2 : 3[/tex]
[tex]Total = 70[/tex]
Solving (a): Number of each set.
The small set is calculated as:
[tex]Small = \frac{S}{S + T} * Total[/tex]
[tex]Small = \frac{2}{2+3} * 70[/tex]
[tex]Small = \frac{2}{5} * 70[/tex]
[tex]Small = 0.4 * 70[/tex]
[tex]Small = 28[/tex]
Using complement rule.
[tex]Large = Total - Small[/tex]
[tex]Large = 70 - 28[/tex]
[tex]Large = 42[/tex]
Solving (b): Increase large by 8.
The ratio is then calculated as:
[tex]Ratio = Small : Large + 8[/tex]
[tex]Ratio = 28 : 42 + 8[/tex]
[tex]Ratio = 28 : 50[/tex]
Divide by 2
[tex]Ratio = 14 : 25[/tex]
) Which expression is equivalent to -24 - 12w?
6(4 - 2w)
-6(4 + 2w)
6(-4+ 2w)
-6(4 - 2w)
The length of a chord is 22 cm and that chord is 5 cm from the center of the circle. What is the length of the diameter ?
Answer:
The circle's diameter is approximately 24.2 cm
Step-by-step explanation:
You can use the Pythagorean theorem to solve this, my realising that the 5cm distance of the chord represends one side of a right triangle, half the chord's length is the other side, and the hypotenuse of the two is the circle's radius. With that we can say:
r = √(11² + 5²)
r = √(121 + 25)
r = √146
Now we can double that to get the diameter:
r = 2√146
r ≈ 24.2
Use the formula SA = 2(lw) + 2(wh) + 2(lh) to find the surface area for a rectangular prism with the L of 2.1 yd, a width w of 1.86 yd, and a high h of 6 yd.
Answer:
SA = 19.92 yd²
Step-by-step explanation:
SA = 2(2.1) + 2(1.86) + 2(6) = 19.92 yd²
HELP ME PLEASE I NEED HELP PLEASE
Answer:
From top to bottom:
35 - 7
-10 - -2
15 - 3
-20 - -4
25 - 5
Sorry If I am wrong
Simplify the following expression.
(3x−6)+(5x−5)
PLEASE I NEED HELP
Answer:
8x-11
Step-by-step explanation:
3x+5x=8x
-6+-5=-11
8x-11
Answer:
8x-11 hope nthisbelps sorry if im wrong
Step-by-step explanation:
An exam has 40 multiple-choice questions, each with 5 choices. Only 1 of the 5 choices for each
question is correct. If you used a table of random digits to randomly choose your answer on all
questions, about how many answers would you expect to get correct?
Select one:
O
a. 40
O
b. 0
0
C. 20
d. 8
e. 5
I will give a brilliant if the answer was correct
Please helppp
Answer:
D.8
Step-by-step explanation:
Since your chance of success is only 1 out of 5 or rather, 20%, so
40 divided by 5 equals 8, so the answer is D.
(Of course, this is just what SHOULD happen, not what CERTAINLY can happen.)
Expected number of answers to be correct = 8.
What is probability?Measure of the likelihood of an event happening is called Probability. Probability can be between 0 to 1. 0 means the event cannot happen, 1 indicates the specific event. The sum of the probabilities of all events in the sample space is 1.
Probability can be defined as the ratio between the number of favorable outcomes and the total number of outcomes of an event. For a trial with “n” number of results, the number of favorable outcomes can be denoted by x. The formula for calculating the probability of an event is as follows.
Probability (Event) = Favorable Outcome/Total Outcome = x/n
Given,
Number of questions = 40
One of 5 choices is correct
then, probability of getting correct option = 1/5
Number of correct answers = 40 × 1/5 = 8
Hence, 8 answers are expected to be correct.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ6
|y-x|,if y>x pls dont write in absolute value
Answer:
The answer is y-x
Step-by-step explanation:
Applying the rule that |y| = y when y>0, we can plug in the values of y-x instead of y.
So, |y-x| = y-x if y>0
Can anyone help me with this all i need is an explanation on how to do it?
Answer:
x = 24
Step-by-step explanation:
Ok so basically the angles shown are vertical angles
One of the properties of vertical angles is that they are congruent
That being said we would use this equation to solve for x
120 = 5x
then you would solve for x
*isolate the variable*
step 1 divide each side by 5
120/5=24
5x/5=x
we're left with x = 24
I hope this helps and if you have anymore questions feel free to ask! :)
What is 7÷10 in fraction form?
Answer:
7/10
Step-by-step explanation:
Answer:
7/10
Step-by-step explanation:
Jacob opened a money-market account. In the first month, he made an initial deposit of $500, and
he plans to contribute an additional $75 every month. The account does not pay any interest.
After how many months will he have a total of $1,475?
Answer:
after 13 months
Step-by-step explanation:
........ur welcome..........
1475-500=975
975÷75=13
so 13 months
Which ones supplementary?
Answer:
D)
Step-by-step explanation:
Choice A is vertical angle
Choice B is complementary
Choice C is corresponding angle
Which of the following variables is most likely to be used as quantitative?
Choose the correct answer below.
ZIP code
Country of birth
Flash drive capacity
Car manufacturer