A logarithmic function is a type of inverse function.
A logarithmic function is a type of inverse function that is commonly used in mathematics and science. It is typically written in the form of y = log base b (x), where b is the base of the logarithm, and x is the input value. The most common bases for logarithms are 10 (common logarithm) and e (natural logarithm).
The logarithmic function is the inverse of the exponential function with base b. This means that if y = log base b (x) then x = b^y
One way to describe a logarithmic function is to say that it represents the exponent to which the base number must be raised in order to produce the input value x. For example, log base 10 of 100 is 2, because 10^2 = 100.
Another way to describe a logarithmic function is to say that it is a way of expressing very large or small numbers in a more manageable form. For example, instead of expressing a number like 10^9 as 1 billion, it can be expressed as 9 using a logarithm to base 10.
It is also important to note that logarithmic function have some key characteristics such as:
The domain of a logarithmic function is x>0, since the logarithm of a non-positive number is undefined.
The range of a logarithmic function is all real numbers.
The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.
A logarithmic function is increasing over its domain and concave down.
The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.
Overall, logarithmic functions are mathematical tools that allow us to simplify the representation and manipulation of very large and small numbers, and are used in many areas of science and engineering.
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In 2010, the population of a city was 59,000. From 2010 to 2015, the population grew by 7.3%. From 2015 to 2020, it fell by 5.3%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
To the nearest percent, the percent by which the population grew from 2010 to 2020 is; 2%
How to find the percentage growth?Percentage increase is defined as the difference between the final value and the initial value, expressed in the form of a percentage.
Now, we are told that;
Initial Population in 2010 = 59000
From 2010 to 2015, the population grew by 7.3%. Thus;
Population in 2015 = 1.073 * 59000 = 63307
Now, we are told that from 2015 to 2020, it fell by 5.3%. Thus;
Population in 2020 = 63307 * (100% - 5.3%)
= 59952
Thus, percentage increase from 2010 to 2020 = (59952 - 59000)/59000) * 100% = 1.61% ≈ 2%
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Translate the sentence into an equation.
Five more than the product of a number and 6 equals 4.
Use the variable w for the unknown number.
Answer:
The to your question is 5w+6=4
Answer:
Below,
Step-by-step explanation:
Produce of w and 5 = 6w
Adding 5 gives 6w + 5 so the equation is:
6w + 5 = 4.
if u answer this u are a god at math
Answer:
its 90
hope this helped
Step-by-step explanation:
Answer:90
Step-by-step explanation:
Which expression has the greatest value?
Answer:
the answer is 16^3/2
Step-by-step explanation:
I took the Iready test too ;)
options:
Reflection across the y-axis
Translation to the left
Reflection across the x-axis
90° counter clockwise Rotation
Answer: Translation to the left
Step-by-step explanation: Although it may appear at first that this graph represents a reflection across the y-axis, it actually represents a translation 7 units to the left. Every point in the object is moved in the same direction and the same distance to form the new image. If you count the number of units between A and A' or B and B' (and so on), you will find that each point has been shifted to the left 7 times.
If m<1 = 98º and m< 2 = 19°, what is m 3?
mz3 =
Answer:
umm... i cant find the answer sorry
Step-by-step explanation:
Jason took his Siberian Husky dog to the veterinarian. The dog was put on a scale and found to weigh 52 lb. Assume that the population mean weight of Siberian Huskies is 49 lb. with a standard deviation of 7. The weights of Huskies are normally distributed.
What is the approximate percentage of Huskies that weigh less than Jason's dog?
a) 67%
b) 40%
c) 33%
d) 60%
Answer:
im kinda not smart but i think its B
Step-by-step explanation:
A straight line is shown on the coordinate grid below. a) What is the y-intercept of this line? b) What is the gradient of this line? Give each of your answers as an integer or as a fraction in its simplest form. Y 8- 7- 6- 5- 4- 3- 2- 1- ܝ ܚ ܚ ܢ ܗ ܘ ܙܢ ܣ -8-7-6-5 -4 -32 -1.0 -2+ -3. -4- -8- 12 4 X
Answer:
a. 4
b. -2
Step-by-step explanation:
coordinate: (2,0), (0,4)
gradient = 4 - 0 / 0 - 2
= -2
5. The hourly garage at BWI Airport costs $4 an hour with a maximum cost of $22 a day. The equation (ℎ)= { 4 , 0<ℎ≤1 8 , 1<ℎ≤2 12 , 2<ℎ≤3 16 , 3<ℎ≤4 20 , 4<ℎ≤5 22 , 5<ℎ≤24 represents the cost of parking for ℎ hours. a. How much does it cost to park for 45 minutes? b. How much does it cost to park for 2 hours? c. How long could you have parked if it cost you $16? d. List the domain and range for this situation.
It will cost $4 for 45 minutes and for 2 hours it will cost $8. If parked for 3 to 4 hours it will cost $16 for garage at BWI Airport.
What is the scope and domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
How are range and domain determined?Graphs can be used to determine the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis because the term "domain" refers to the set of potential input values. The possible output values that make up the range are shown on y-axis.
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i really need help with this one.
Solve by factorising:
x^2+10x+21=0
Answer:
[tex]x = -7\\x = -3[/tex]
Step-by-step explanation:
The steps are in the image attached to this response.
the scale on a map is 1:5000000
two towns are 7cm apart on the map
work out the actual distance between the towns
Answer:
Step-by-step explanation:
scale,= 1 : 5000000
it means 1 cm depicts 5000000cm
or 50000m else 50km
the distance between two towns in map = 7cm
so the distance between two towns = 7 *50
= 350km
What is an equation of the line that passes through the points (-3, 8) and (4, 1)?
Answer:
y=mx+c
m=(8-1)÷(-3-4)
=7÷-7
=-7
8=-7(-3)+c
8=21+c
c=-13
y=-7x+c
i hope it is correct :)
if g varies inversely as the square root of h, and g = 9 when h = 121, find g when h = 81.
If g varies inversely as the square root of h, this means that the product of g and the square root of h is constant. We can represent this relationship using the equation g*sqrt(h) = k, where k is the constant value.
We are given that g = 9 when h = 121, so we can substitute these values into the equation to find the constant:
9sqrt(121) = k
Simplifying this expression gives us:
k = 911 = 99
Now that we know the value of the constant, we can use the equation to find g when h = 81:
g*sqrt(81) = 99
Solving for g gives us:
g = 99/sqrt(81) = 99/9 = 11
Therefore, when h = 81, g = 11.
B. find the value of the unknown variables and sides using parallelogram SAFE,given:
Answer:
answer below
Step-by-step explanation:
x=4
y=8
AE line equals 16
sf line equals 20
st line equals 10
Could someone help me
[tex]\cfrac{6a^2 + 21a}{3a^2}\implies \cfrac{6a^2 }{3a^2}+\cfrac{21a}{3a^2}\implies 2+\cfrac{7}{a}[/tex]
Find the inverse of each function. Then graph the function and its inverse. f(x)=-1-1/5x
The inverse of the given function is y = -1/5(x + 1).
The graph the function and its inverse is shown in the image attached below.
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of this function f(x) = -1 - 1/5x, we would interchange both the input value (x) and output value (y) as follows:
y = -1 - 1/5x
x = -1 - 1/5y
Adding 1 to both sides of the function, we have:
x + 1 = -1/5y
Multiplying both sides of the function by -1/5, we have:
y = -1/5(x + 1)
The cost of hiring a plumber is shown by the equation � = 100� + 75, where n is the number of hours
worked, and C is the total cost to hire the plumber. The plumber wants to earn at least $200 per job,
and will work for a maximum of 6 hours for each job.
(a) What is the minimum and maximum number of hours that the plumber will work?
Answer:
The minimum number of hours the plumer can work is 1 hour and 15 minutes and the maximum number of hours is 6.
Step-by-step explanation:
What is the length of the diagonal of a poster board with dimensions 22 inches by 28 inches? round to the nearest tenth
A. 24.8 in.
B. 28.4 in
C. 35.6 in
D. 50 in
Answer:
answer is c
Step-by-step explanation:
Enter the length ,X of the ramp in inches (no links need answers ASAP)
Answer:
53 inches
Step-by-step explanation:
use the Pythagorean Theorem
c^2 = a^2 + b^2
x^2 = 28^2 + 45^2
x^2 = 784 + 2025
x^2 = 2809
Take the square root of both sides
x = 53
is 9.2 rational or irrational?
Answer:
Rational number
Step-by-step explanation:
it's a decimal
Sophia wants to take out a loan of $6,000 with interest that compounds monthly. Use the formula A = P(1 + rn)n∗t to find which of these loan terms will have the lowest total cost. A) 2 years at 4% interest B) 3 years at 3% interest C) 4 years at 1% interest D) 5 years at 2% interest
Answer:
d
Step-by-step explanation:
FV = P (1 + r/m)^mn
FV = Future value
P = Present value
R = interest rate
N = number of years
m = number of compounding
a. 6000x (1 + 0.04/12)^24 = 6498.86
b. . 6000x (1 + 0.03/12)^36 =6564.31
c. . 6000x (1 + 0.01/12)^48 = 6244.76
d. . 6000x (1 + 0.05/12)^60 =6630.47
What is the equation to this graph above
Answer:
y = -5/2x + 1
Step-by-step explanation:
y=mx+b
m is slope
b is y intercept
Answer:
(-2, 6)
(0,1)
(2,-4)
Step-by-step explanation:
It where the line meets the graph but like where the line meets equally together with other lines
formula (x,y)
A jar contains 3 blue cubes 3 blue spheres and 6 green cubes and 4 green spheres. If you select an object at random, what is the probability that the object is green or a cube?
Answer:
it would be around 62%
Step-by-step explanation:
since there are 10 chances for the object to be green or a cube and 16 objects in total, the fraction would be 10/16. 10/16 simplified is 10 divided by 16 = 0.62. when you turn that into a percent it would be about 62%
heyy! i’ll give brainliest please help
Answer:
Last one
Step-by-step explanation:
Molly needs to classify the triangle below based on angles. Which class is correct? 60° 50° 70° A. acute triangle О B. isosceles triangle C. equilateral triangle D. obtuse triangle
Answer:
A. Actute triangle
Step-by-step explanation:
Is A because an acute triangle is a triangle where all the angles are the same.
Can not be B. because isosceles triangles have two sides that are the same which doesn't relate to angles.
Can not be C. because equilatiral triangles are triangles with sides that are all the same.
Can not be D. because for a triangle to be obtuse one of the angles needs to be greater that 90 degrees.
So it has to be A.
My favorite recipe for lemonade calls for 4 cups of water to 3/4 cups sugar. How
much sugar would I need for 6 cups of water?
Hint: One way to solve this would be to find the unit rate for 1 cup of water, then
use a proportion to find 6 cups of water.
Answer and Step-by-step explanation:
To find the unit rate, divide the 4 cups of water and the [tex]\frac{3}{4}[/tex] cups sugar by 4 to get a unite rate for 1 cut of water.
4 divided by 4 equals 1.
[tex]\frac{3}{4}[/tex] divided by 4 equals [tex]\frac{3}{16}[/tex].
Now, we multiply [tex]\frac{3}{16}[/tex] by 6.
[tex]\frac{9}{8}[/tex] is how many cups of sugar that needs to be measured for 6 cups of water.
#teamtrees #PAW (Plant And Water)
Elena made two batches of food to put in a bird feeder. She uses 1/8 cups of cracked corn, 3/4 cups of sunflower seeds, and 1/4 of dried cranberries for each batch. What is the best estimate of the total amount of bird food she made?
Elena made 2 batches of bird food, each with 1/8 cup cracked corn, 3/4 cups sunflower seeds, and 1/4 cup dried cranberries, for a total of 1.75 cups of bird food.
Elena made two batches of bird food using a combination of cracked corn, sunflower seeds, and dried cranberries. Each batch uses 1/8 cup of cracked corn, 3/4 cup of sunflower seeds, and 1/4 cup of dried cranberries.
To find the total amount of bird food she made, we need to add the ingredients of the two batches together.
Since she made two batches and each batch contains 1/8 cup of cracked corn + 3/4 cup of sunflower seeds + 1/4 of dried cranberries, the total amount of bird food is 2 × (1/8+3/4+1/4) = 2 × (7/8) = 7/4 = 1.75 cups.
This is the best estimate of the total amount of bird food made by Elena. It's important to note that this estimate is based on the assumption that the proportion of ingredients in each batch is the same, and that the ingredients are measured accurately.
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tina worked out the median of the number of points scored to be 5
a) explain why it's not possible for the median to be 5?
number of points - frequency
0 1
1 3
2 5
3 4
4 3
Answer:
Could you explain this more nicley, this is quite hard to read
Step-by-step explanation:
The cosine of 55 1/2 degrees is approximately 0.566. What angle, in degrees, has a sine of approximately 0.566?
Given:
[tex]\cos (55\dfrac{1}{2})^\circ\approx 0.566[/tex]
To find:
The angle, in degrees, that has a sine of approximately 0.566.
Solution:
We know that,
[tex]\sin(90^\circ-x)=\cos x[/tex]
We have,
[tex]\cos (55\dfrac{1}{2})^\circ\approx 0.566[/tex]
Using the above trigonometric identity, it can be written as:
[tex]\sin (90-55\dfrac{1}{2})^\circ\approx 0.566[/tex]
[tex]\sin (90-\dfrac{110+1}{2})^\circ\approx 0.566[/tex]
[tex]\sin (90-\dfrac{111}{2})^\circ\approx 0.566[/tex]
Taking LCM, we get
[tex]\sin (\dfrac{180-111}{2})^\circ\approx 0.566[/tex]
[tex]\sin (\dfrac{69}{2})^\circ\approx 0.566[/tex]
[tex]\sin (34\dfrac{1}{2})^\circ\approx 0.566[/tex]
Therefore, the angle [tex]34\dfrac{1}{2}[/tex] degrees has a sine of approximately 0.566.