If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x) = log_b(x),[/tex] where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x) = log_b(x)[/tex] is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x)=log_b(x)[/tex]. where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x)=log_b(x)[/tex]. is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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Making connections between arithmetic sequences and linear function
Use the graph or the formula to write the equation of the line in a slope intercept form
on solving the provided question, we can say that - the graphs which is shown as the straight line graph.
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
here,
then line which is drawn is straright,
so the graph is straight .
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The table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than
27 kg
b) Work out the maximum number of dogs that could have a mass of more than
27 kg
a) The minimum number of dogs that could have a mass of more than 27 kg is 6.
b) The maximum number of dogs that could have a mass of more than 27 kg is 18.
We have a table which shows information about the masses of some dogs.
Now , we need to determine the minimum number of dogs could have a mass more than 27 kg . Let us see dogs with mass of more than 27 kg present in the following intervals , 20≤x<30 and 30≤x<40 with 12 and 6 respectively.
But we wants minimum of 12 and 6 is 6 .
so, the minimum number of dogs with mass more than 27 kg is 6.
b) We need to determine maximum number of dogs with mass more than 27 kg ,so Maximum is equals to sum of number of dogs present in interval 20≤x<30 and in interval 30≤x<40 = 12+6 = 18. So, required maximum number of dogs are 18.
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Complete question:
The above table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than 27 kg
b) Work out the maximum number of dogs that could have a mass of more than 27 kg
4/3 divided by 12= simplified and fraction form!
Answer:
[tex]{\huge\pink{\fbox{{࿐αɴѕωєя࿐}}}}[/tex]
[tex] \frac{4}{3} \div 12 \\ = \frac{4}{3} \times \frac{1}{12} \\ = \frac{4}{3 \times 12} \\ = \frac{4}{36} \\ = \frac{1}{9 } \\ = 0.11[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex] \huge\red{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]
Answer:
1/9 is the answer
4/3 x 1/12 just multiply but the reciprocal
hope this helps
have a good day :)
Step-by-step explanation:
Which of the following numbers is 90 divisible by?
2, 3, 4, 5, 6, 9, and 10 only
A. 2, 3, 4, 5, 6, 9, and 10 only B. 2, 3, 5, 6, 9 and 10 only
C. 2, 3, 6, 9, and 10 only D. 2, 5, 9, and 10 only
Answer:
B
Step-by-step explanation:
90/2= 45
90/3= 30
90/5= 18
90/6= 15
90/9= 10
90/10= 9
90/4= 22.5
What is the circumference of the circle? Assume pi = 3.14
Answer:
5 x 2 x 3.14 = 31.4
Formula of circumference:
radius(half of your diameter or given radius) x pi(3.14 or 22/7 depending on what they tell you to use for pi) x 2(just always there when finding circumference)
Answer:
Circumference : 31.4 cm
Step-by-step explanation:
Circumference = 2× 3.14 × 5 cm
= 10× 3.14 cm
= 31.4 cm
Graph the line y=-2x-1
Answer:2024
Step-by-step explanation:
11 in.
9 in.
4
8 in.
What is the volume of the figure above?
Answer:
Mizuki is here to help you! The volume of the figure above is 176[tex]in^2[/tex], but since you can only put numbers you need to put in 176.
Step-by-step explanation:
11 x 4 x 8 ÷ 2 =
44 x 8 ÷ 2 =
352 ÷ 2 =
176
ILL BRAINLIEST YOU PLEASE HELP ME
Answer:
L = 40 The length is AC
W = 20 The width is AB
Step-by-step explanation:
Givens
P = 120
AB = 1/2 AC
Solution
P = L + L + W + W
W = 1/2 L
P = L + L + 1/2L + 1/2L Combine like terms
P = 3L
120 = 3L Divide by 3
3L/3 = 120/3
L = 40
W = 1/2 L
W = 1/2 * 40
W = 20
Triangle EFG is dilated by a scale factor of 2/3 to form a triangle E'F'G'. What is the measure of side E'F'?
By using scale factor formula we can evaluate the measure of side EF.
What happens when we dilate a triangle?When a triangle is dilated by scale factors.The base and height change by the scale factor s while the area changes by a factor of s^2. While the scale distances between points dilations do not change angles.Dilation is used to make the objects larger or smaller.
How do you find scale factor?The scale factor can be calculated when the new dimensions and the original dimensions are given. The basic formula to find the scale factor of a figure is Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
From the question ΔE'F'G' is the image formed by the dilation of preimage ΔEFG.
Therefore,
2/3 =[tex]E_{1}[/tex][tex]F_{1}[/tex]/EF
EF=3/2[tex]E_{1}[/tex][tex]F_{1}[/tex]
By substituting any value of F'G' given in the equation we can evaluate the measure of side FG.
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Wanda has 5 different fish in a small, crowded tank. She decides to randomly scoop up individual fish and transfer them to a new tank until a total of 4 fish have been moved. How many sequences of 4 fish are possible?
Answer:
64 sequences of 4 fish are possible.
Mike has $25 in his savings account. He earns $8 for every lawn he mows, and he plans to put it all in savings. Write and solve an inequality to find how many lawns would he have to mow to earn at least $65 1. Define the wariable: 2. Write the inequality and solve: 3. Answer the problem:
HELPPPP!!! PLEASEEE!!! THANK U:)
Answer:
1st, 2nd, and 3rd options
Step-by-step explanation:
Some of the main properties of a kite:
It has no parallel sides
It has two pairs of congruent sides
It has two pairs of congruent angles
the diagonals are perpendicular
the longer diagonal bisects the other diagonal
opposite sides are not congruent
Answer:
hope this helps you bye..
A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 224 cars owned by students had an average age of 5.06 years. A sample of 233 cars owned by faculty had an average age of 7.19 years. Assume that the population standard deviation for cars owned by students is 3.42 years, while the population standard deviation for cars owned by faculty is 2.81 years. Determine the 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.
The difference between the population means - 3.4 and -1.84 when calculated is found to be -2.62 years.
The 95% confidence interval for the difference in true mean ages of cars owned by students and faculty is between -3.4 and -1.84 years.
We know that the sample of 138 cars which belongs to the students have an average age of 5.13 years. The standard deviation = 3.45 years.
Then again,
A sample of 111 cars which belongs to the faculty have an average age of 7.75 years. The standard deviation= 2.08 years.
So the difference between them will be , s - f
= 3.45 - 2.08 = 1. 37
and the mean will be , mean of students - mean of faculty =
-2.62.
This is the point of difference between their means.
The SD is found to be as 0.3961.
and MOE is 0.78
with these details now we will calculate the required intervals,
The lower end is found to be as -2.62 - 0.78 = -3.4
The upper end is found to be as -2.62 + 0.78 = -1.84
Therefore, the mean difference between the cars is - 3.4 and -1.84.
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NO LINKS Consider the isosceles trapezoid.
What is the value of y?
Answer:
y = 9 x= -11
Step-by-step explanation:
opposite angles of a trapezoid are supplementary.
The two angles of the same base in an isosceles triangle are congruent.
-6x-16 = 50
-6x = 66
x= -11
The supplementary of 50 is 130
3x+16y+19 = 130
-33 +16y +19 = 130
16y = 144
y = 9
The sum of all 4 angles is 360 degrees
During a sale, a store offered a 20% discount on a tablet computer that originally sold for $490. After the sale, the discounted price of the tablet computer was marked up by 20%. What was the price of the tablet computer after the markup? Round to the nearest cent.
Step-by-step explanation:
I think you have to change 20% to a fraction
3) Breanna thought of a number, subtracted 4 from it, and then multiplied her answer by 3. She got
a final number of 24. What was her starting number?
HELP DUE IN 15 MINS!
The opposite angles of a parallelogram are congruent.
True
False
Answer:
True
Step-by-step explanation:
A rectangle is a parallelogram with four right angles, opposite sides parallel, opposite sides congruent, opposite angles congruent, consecutive angles are supplementary, and the diagonals bisect each other.
Hope it is helpful....What are the opposites of 8, −3.5, 1.15, and 7/1/4
David launches a rock straight up over the edge of a 60-foot cliff and into the ocean. after 4 seconds, the rock reaches a maximum height of 108 feet. Six seconds later, the rock enters the ocean.
A) Write a function to model the scenario
B) Create a table of at least five values to represent the scenario
C) Identify how you see the X- and Y- intercepts in the table, graph, and equation.
Answer:
David launches a rock straight up over the edge of a 60-foot cliff and into the ocean. After 4 seconds, the rock reaches a maximum height of 108 feet. Six seconds later, the rock enters the ocean. . Create a graph to represent the scenario. The graph should include at least the x- and y-intercepts and the vertex. (A complete graph consists of axis labels and appropriate scales, ordered pairs for each identified point, the function, and appropriate domain/range.) . Write a function to model the scenario. Part C. Create a table of values to represent the scenario. Be sure to include at least five values. Values should include at least the x- and y-intercepts and the vertex. Part D. Identify how you see the x- and y-intercepts and vertex in the table, graph, and equation. (Hint: You may want to rewrite the equation in equivalent forms.)
Step-by-step explanation:
Solve the system by graphing
2x-3y=-6
7x-3y=9
Following is the graph of two given equations.
The mapping of functions of two variables onto a Cartesian coordinate system, which is made up of a horizontal x-axis, or abscissa, and a vertical y-axis, or ordinate, is done analytically through the use of graphs. The intersection of each axis, which is a real number line, at its zero point is known as the origin.
On solving the two equations,
2x-3y=-6 ....(1)
7x-3y=9 .....(2)
Firstly we will find common points by elimination -
The common points are - (3,4)
Then We can find all the values of equation (1)
2x-3y=-6
x 0 3 -3
y 2 4 0
7x-3y=9
x 0 3 10
y -3 4 20.33
The respective graph is attached below
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A spinner with equal sections numbered from 1 to 5 is spun twice. Raul is finding the probability that both spins will result in an even number. Find his mistake and explain what he should have done instead.
(2/5) x (1/4) =(2/10)
please help im really just about to cry myself to sleep and call it a day bcs im off the edge rn and i have to deal with school at the same time T_T
Answer:
his mistake is that he didn't need to remove one even number on the spinner so we just need to take 2/5x1/5equals2/25
Help ASAP plz need answer:)
In a rhombus MNLP, diagonals intersect each other at point O. If m∠MNL is 120° and the length of the side is 8 in, find m∠MNO, m∠MON, and NP. A (5pts) Find m∠MNO. Answer
In a rhombus, all sides are equal and the diagonals intersect each other at a 90 degree angle and bisect each other.
Diagonal of a rhombus bisects the angles of the rhombus at the vertex.
So as m∠MNL is 120°,
∠MNO = ∠LNO = 120/2 = 60°
The diagonals intersect each other at a 90 degree angle, therefore
m∠MON = 90°
Considering ΔMNO, right angled at O.
cos(∠MNO) = NO/ MN
cos(60) = NO/ 8
NO = 0.5×8 = 4
NP = NO + OP
NP = 2NO
NP = 2×4
NP = 8 in
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Solve 12 (10x + 3 -8y)
Answer:
120x - 96y + 32
Step-by-step explanation:
12 (10x + 3 -8y)
We use the distributive property to solve
120x - 96y + 32
One of the most important when writing the order of an equation is always written the number with the variable first; that is why the answer is
120x - 96y + 32
5. Suppose you went on vacation but forgot your smart phone
charging cable. Your phone battery died after two full days
(48 hours) of use. This situation is modeled by the equation
f(h) = 48, where h is the hours of cell phone use and
f(h)is the percentage of battery life left.
What is the upper bound of the parameter h?
hrs
What is the lower bound of the parameter h? •
hrs
The upper and lower bounds of the parameter h is found to be 0 and 1 respectively.
What is upper and lower bound of a function?
A number U serves as an upper bound for a function f, meaning that for any x, f(x) ≤ U. A number L serves as a function's lower bound, ensuring that for all x, f(x) ≥ L.
Given,
[tex]f(h) = \frac{48-h}{48}[/tex]
where f(h) = Percentage of battery left
h = Hours of cell phone use
Lower Bound of parameter h,
h = 0 ( When percentage is 100%)
f(h) = [tex]\frac{48 - 0}{48}[/tex] = 1
Upper bound of parameter h,
h = 48 (When percentage is 0%)
f(h) = [tex]\frac{48-48}{48}[/tex] = 0
Therefore the upper bound of h is 0 and lower bound of h is 1.
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PLEASE HELP ILL BRAINLIEST YOU
Answer:
let's take AC as x
AB is half of AC making it ½x
½x+½x+x+x=120
3x=120
[tex] \frac{3x}{3} = \frac{120}{3} [/tex]
x =120÷3
x=40
therefore AC is 40 while AB is 20
Answer:
AB = 20 ft
AC = 40 ft
Step-by-step explanation:
Perimeter of a rectangle = 2(l+b)
Perimeter (given) = 120 ft.
AB = ½ of AC
AC = 2 AB
Let x be the length of AB.
Then, AC = 2x
Now,
2(2x+x) = 120
2×(3x) = 120
6x = 120
x = 120/6 = 20 ft.
2x = 2×20 = 40 ft.
AB = 20 ft.
AC = 40 ft
Answer ALL of the questions. LOOK AT ALL THE PICTUERS .Show your work. if you can show me a picture of your work and the step you did to complete it. HELP ME PLZZ.
BRAINLEST TO I GIVE BRAINLIEST
What will the width of the paper need to be ?
I don't get this question can some one please help me solve it
Answer:
3, 2
Step-by-step explanation:
In order for the equation to be equal to zero, the following must be true:
x-3 = 0 or,
x-2 = 0
Therefore the 2 solutions are x=3, x=2
2x × 3y(4 - 8) + 8(4y - 2x)
Answer:
5.3
Step-by-step explanation: