The inverse function of the function f(x) = log₂(3x + 4) − 5 is y = [2^(x + 5) - 4]/3
How to determine the inverse of the function?From the question, we have the following equation that can be used in our computation:
f(x) = log2(3x + 4) − 5.
Rewrite as
f(x) = log₂(3x + 4) − 5.
Express f(x) as y
This gives
y = log₂(3x + 4) − 5.
Swap the positions of x and y
So, we have the following representation
x = log₂(3y + 4) − 5.
Add 5 to both sides
log₂(3y + 4) = x + 5
So, we have
3y + 4 = 2^(x + 5)
Subtract 4 from both sides
3y = 2^(x + 5) - 4
Divide b y3
y = [2^(x + 5) - 4]/3
Hence, the inverse function is y = [2^(x + 5) - 4]/3
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Grandma received 0.25 liters of medicine from her doctor. The directions asked her to take one teaspoonful 3 times daily until it is finished. A full teaspoon has a capacity of 4 ml. Grandma started taking her medicine on November 20th. What date should the medicine finish?
Answer:
Dec 10
Step-by-step explanation:
0.25 liter = 250 ml
4 ml * 3 = 12 ml
250/12 = 20.83 days
Nov 20 - Nov 30: 11 days
Dec 1 - Dec 9: 9 days
On December 9, she can still take her 3 doses.
By December 9, she will have taken 12 ml per day for 20 days for a total of 240 ml. She has 10 ml left for Dec 10th.
On Dec 10, she will take 2 doses of 4 ml and 1 dose of 2 ml, and she will finish the medicine.
At her new job, Laura is getting paid $18.35 per hour. If she is scheduled to work 12 hours on Saturday, how much will she earn?
Answer:
$220.2
Step-by-step explanation:
Multiply 18.35 to 12
Write the proportion.
8.5 hours is to 3.4 hours as
7.0 hours is to 2.8 hours?
Find the average number of people in these cities: New York, Philadelphia, Chicago and Detroit a. 3.35 million b. 40 million. C. 4.0 million d. 33.million
Answer:
The answer is maybe going to be D which is 33 million
Step-by-step explanation:
New york is a big city
He measured the pool’s dimensions to be 15 feet long by 35 feet wide. The actual dimensions of the pool are 14.5 feet by 34.75 feet. Find Jack’s percent error to the nearest percent.
Answer:
Percent error = -4.02 (Approx.)
Step-by-step explanation:
Given:
Estimated pool dimension = 15 ft long and 35 ft wide
Actual pool dimension = 14.5 ft long and 34.75 ft wide
Find:
Percent error
Computation:
Area of Estimated pool = 15 x 35
Area of Estimated pool = 525 ft²
Area of Actual pool = 14.5 x 34.75
Area of Actual pool = 508.875 ft²
Percent error = [(Actual - Estimated) / Estimated]100
Percent error = [(508.875 - 525) / 525]100
Percent error = [(-21.125) / 525]100
Percent error = -4.02 (Approx.)
Help last assignment for the semester
Answer:
b=2sqrt14
A=33.7°(rounded to nearest tenth)
B=56.3°
Step-by-step explanation:
Pythagorean theorem= sqrt(c^2-a^2)=sqrt(9^2-5^2)=2sqrt14
angleA= sin^-1(5/9)=33.7°
angleB=90°-33.7°= 56.7°
Hopefully that makes sense
Your round-trip drive to work is 4 1. miles. How many miles do you drive to and from
work in 3 days?
7 3/10
12 3/10
12 9/10
8 3/5
what type of function is shown on the table below
Answer:
x-fx-x*x
Step-by-step explanation:
Write an expression showing 5 less than the number K
Answer:
K-5
Step-by-step explanation:
Five less than K would be K-5.
Help please will mark brainliest!!!
Answer:
18
Step-by-step explanation:
(a) select all the describe bd
Answer:
First - Perpendicular Bisector
Second - Angle Bisector
Fourth - Altitude
Step-by-step explanation:
It is not the median because it does not touch the base in the middle.
What are the ordered pairs of the
solutions for this system of equations?
f(x) = x2 – 2x + 3; f(x) = –6x
(-3, [?]); ([ ]), ([ ])
Answer:
[tex] {x}^{2} - 2x + 3 = - 6x \\ = {x}^{2} - 2x + 6x + 3 = 0 \\ \\ = {x}^{2} + 4x + 3 = 0 \\ = (x + 1)(x + 3) \\ = x = - 1and \: x = - 3[/tex]
4) What is the perimeter of a square that has an area of 262.44 feet?
Answer:
64.8 ft
Step-by-step explanation:
A square has all its sides equal
Therefore to get one side from its area is simply finding the square root of its area
√262.44=16.2ft
Having the one side then perimeter= to the four equal sides × the dimensions of one side
=4×16.2
=64.8 ft
Point B is located at _____.
(-3, 0) (3, 0) (0, 3) (0, -3)
Answer:
3, 0
Step-by-step explanation:
first number is on the horizontal line and the second number on the vertical line
Answer: (3, 0)
Step-by-step explanation: To get to point B from the origin, we move 3 units to the right and 0 units up or down so our point has the coordinates (3, 0).
Remember to always go left or right first, which represents x,
then up or down, which represents y.
A 3-column table with 4 rows titled 90-Day Forecast. Column 1 is labeled Weather Type with entries wind, rain, clouds, sunshine. Column 2 is labeled Predicted frequency with entries 9, 18, 27, 36. Column 3 is labeled Observed frequency with entries 12, 15, 33, 30.
The table shows the results of the experiment to determine the 90-day weather forecast. How does the experimental probability compare to the theoretical probability?
The theoretical probability for rain is 1/5. The experimental probability for rain is
.
The actual weather is
the theoretical probability.
1/6
approximately the same as
Answer:
✔1/6
✔ approximately the same as
Step-by-step explanation:
Here's proof
what is the givien x-value that can used to make the prediction
Answer:
haha there is no question
Step-by-step explanation:
aww please check if there are more expect around to answer
Identify the following parts of an introductory paragraph in the order that they should appear.
First:
Second:
Third:
Answer Choises
hook, context, thesis
Have a nice day!
Answer:
1st-Hook
2nd- Thesis statement
3rd-context
Step-by-step explanation:
1- hook is to attract the reader, like a line to a song that is catchy! you want to draw the reader in!
2- Thesis statment
3- give context on the thesis statement! to further prove.
good luck
50+12÷3×5−2 do this for 25 points fast please (use PEMDAS)
Answer:
68
Step-by-step explanation:
Using traditional methods it takes 101 hours to receive an advanced driving license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher believes the new technique may reduce training time and decides to perform a hypothesis test. After performing the test on 280 students, the researcher decides to reject the null hypothesis at a 0.05 level of significance.
What is the conclusion?
a. There is sufficient evidence at the 0.02level of significance that the new technique reduces training time.
b. There is not sufficient evidence at the 0.02 level of significance that the new technique reduces training time.
Find the value of x.
log 3 X= 4
OA. 7
OB.
12
Oc.
27
OD
81
Answer:
OB
Step-by-step explanation:
when we multiple 4 by 3 because they are like terms they give us 12
sorry for the bad picture. I’m confused on how to solve this as it feels like I don’t have all the information needed.
What is the area of △STU rounded to the nearest tenth?
Answer:
38.7 units²
Step-by-step explanation:
4.6/SV = SV/8.1
SV² = 37.26
SV = 6.1
area = 1/2(8.1)(6.1) + 1/2(4.6)(6.1) = 38.7 units²
Roller skates that usually sells for $125 is on sale for 35% off. Find the sale price.
Answer:
$81.25
Step-by-step explanation:
First find 35% of 125 which is 43.75
Next subtract 43.75 from 125
Your answer is $81.25
At a school carnival, 51 out of 68 tickets sold were early-admission tickets. What percentage of the tickets were early-admission tickets?
What is the arc measure of major arc \stackrel{\large{\frown}}{ACB}
ACB
⌢
A, C, B, start superscript, \frown, end superscript on circle PPP in degrees?
Answer:
286°
Step-by-step explanation:
A circle is the locus of a point such that its distance from a fixed point (known as the center) is always constant. This distance is known as the radius of the circle.
A major arc is an arc larger than a semicircle, therefore its measure is greater than 180°. A minor arc is an arc smaller than a semicircle, therefore its measure is less than 180°.
The arc measure of [tex]\stackrel{\large{\frown}}{ACB}=angle\ about\ a\ point-\stackrel{\large{\frown}}{AB}[/tex]
The arc measure of [tex]\stackrel{\large{\frown}}{ACB}=360-74=286^o\\[/tex]
Square 1 has a area of 24 square units if square 2 is half the size what is the ratio of the area of square one to square two?
Answer:
Step-by-step explanation:
I'm going to guess that 1/2 the size means the sides are 1/2 the size.
Square 1 has an area of 24. The sides are s, so the area is found by using s^2
The second square is made from sides that are 1/2 s
Area = 1/2 s * 1/2 s
Area = 1/4 s^2
Area 1 / area 2 = 24 / x^2 = s^2 / 1/4 s^2 = 1/0.25
Find a formula for the exponential function passing through the points
4
3,
and (1,20)
125
f(x) -
Answer:
[tex]y = 4*5^x[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-3,\frac{4}{125})[/tex]
[tex](x_2,y_2) = (1,20)[/tex]
Required
Determine the exponential equation
An exponential equation is of the form: [tex]y = ab^x[/tex]
In: [tex](x_2,y_2) = (1,20)[/tex]
[tex]20 = ab^1[/tex]
[tex]20 = ab[/tex] ---- (1)
In: [tex](x_1,y_1) = (-3,\frac{4}{125})[/tex]
[tex]\frac{4}{125} = ab^{-3}[/tex] --- (2)
Divide (1) by (2)
[tex]20/\frac{4}{125} = \frac{ab}{ab^{-3}}[/tex]
[tex]20/\frac{4}{125} = b^4[/tex]
[tex]20*\frac{125}{4} = b^4[/tex]
[tex]5*125 = b^4[/tex]
[tex]625 = b^4[/tex]
Take 4th roots of both sides
[tex]\sqrt[4]{625} = b[/tex]
[tex]5 = b[/tex]
[tex]b = 5[/tex]
Substitute [tex]b = 5[/tex] in [tex]20 = ab[/tex]
[tex]20 = a * 5[/tex]
Solve for a
[tex]a = 20/5[/tex]
[tex]a = 4[/tex]
Hence, the equation is:
[tex]y = 4*5^x[/tex]
There are two ways to go from Fujairah to Sharjah , and four ways to go from Sharjah to Dubai. How many different ways are there to go from Fujairah to Dubai, passing through Sharjah?
6
8
16
12
Answer:
8
Step-by-step explanation:
a group of students collected old newspapers for a recycling project. the data shows the mass, in kilograms, of old newspapers collected by each student.
23, 35, 87, 64, 101, 90, 45, 76, 105, 60, 55
98, 122, 49, 15, 57, 75, 120, 56, 88, 45, 100.
A.) Find the range of the mass of the newspapers collected.
B.) Find the interquartile range.
Answer:
A. 107 kg
B. 49 kg
Step-by-step explanation:
Graph this function.
F(x)= -1/3x + 8
I need help ASAP! The -1/3x is a fraction. Can anyone help?
Step-by-step explanation:
Rewrite the function as an equation.
[tex]y = - \frac{x}{3} + 8[/tex]
Rewrite in slope-intercept form.
[tex]y = - \frac{1}{3} x + 8[/tex]
Use the slope-intercept form to find the slope and y-intercept.
Slope : - 1/3
y-intercept: (0,8)
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
Graph the line using the slope and the y-intercept, or the points.