The inverse of the logarithmic function f(x) = log9x is f^-1(x) = 9^x.
The inverse of a function is a new function that "undoes" the original function. For a logarithmic function, such as f(x) = log9x, the inverse is an exponential function.
To find the inverse of f(x) = log9x, you can follow these steps:
Switch the roles of x and y in the original function to make y the subject of the formula.
log9x = y
Replace the logarithm function with its inverse function, the exponential function.
9^y = x
Switch x and y back to their original roles in the equation.
x = 9^y
It's worth noting that for this logarithmic function, the domain of the function is x > 0 and the range is y > 0, and the inverse function will have its domain as y > 0 and range as x > 0. Also, the base of the logarithm 9, is a positive real number, different than 1, this ensures that the logarithm function is defined for all x > 0, for b = 1 it would not be defined for x = 1.
So the inverse of the logarithmic function f(x) = log9x is f^-1(x) = 9^x
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What are the 7 laws of logarithms?.
7 laws of logarithms are,
1- Product rule
2- Division rule
3- Power rule/Exponential Rule
4- Change of base rule
5- Base switch rule
6- Derivative of log
7- Integral of log
logarithms
it is the exponent or power to which a base must be raised to yield a given number.
For example,
23 = 8,
therefore,
3 is the logarithm of 8 to base 2, or 3 = log2 8.
A logarithm is defined as the power to which a number must be raised to get some other values.
Logs are the other way of writing exponent. The formula for conversion between exponential and log forms is: bx = a ⇔ log b a = x. Logarithms are very useful in solving equations involving exponents.
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Which model shows 2 + 0.4?
(use photo)
Answer:
B
Step-by-step explanation:
2 ÷ 0.4 = 5
----------------
An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. Another side is 12 more than four times the length of the bottom of the triangle. The last side is 10 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.
I need help filling in the missing blanks.
The degree measure of each angle in the triangle are:
m angle l = 18.4
m angle J = 57.6
m angle K = 93
What is the Degree Measure?
The degree measure, also known as an angle measure, is a way to quantify the size of an angle in mathematics. The degree measure of an angle is typically represented by the symbol "degrees" (°) or simply "deg" and it is a unit of measurement.
In a triangle, the degree measure of all angles add up to 180 degrees. Therefore, we can use this property to find the degree measure of each angle in the triangle.
m angle l = (x + 5) deg
m angle J = (4x + 7) deg
m angle K = (7x) deg
So we can use the following equation:
m angle l + m angle J + m angle K = 180
(x + 5) + (4x + 7) + (7x) = 180
12x + 19 = 180
12x = 161
x = 13.4
Hence, the degree measure of each angle in the triangle are:
m angle l = (x + 5) deg = (13.4 + 5) = 18.4
m angle J = (4x + 7) deg = (413.4 + 7) = 57.6
m angle K = (7x) deg = (713.4) = 93
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What are the solutions of the equation x4 5x2 36 0?.
The solutions of the equation x⁴ - 5x² - 36 = 0 are: x = -3, x = 3, x = 2i and x = -2i
Consider given equation x⁴ - 5x² - 36 = 0
Let us assume that x² = p
so, we get an equation,
p² - 5p - 36 = 0
Now we solve above quadratic equation.
p² - 5p - 36 = 0
using the Quadratic Formula where
a = 1, b = -5, and c = -36
[tex]\Rightarrow p=\frac{-b\pm \sqrt{b^2 -4ac} }{2a}\\\\\\ \Rightarrow p = \frac{5\pm \sqrt{25+144} }{2}\\\\\\\Rightarrow p = \frac{5\pm \sqrt{169} }{2}\\\\\\ \Rightarrow p=\frac{5\pm 13 }{2}[/tex]
So, p = 9 and p = -4
But p = x²
So, x² = 9 OR x² = -4
For x² = 9, by taking square-root we get x = 3, x = -3
an equation x² = -4 has complex roots, x = 2i and -2i
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Each gift bag include a bouncy ball,ticker,and cookie. There are red,yellow,or green bouncy ball;iri,lily,or daiy ticker;and chocolate chip or oatmeal cookie. How many different gift bag could be made?
There are a probability of 6 different possible combinations of the gift bag with a bouncy ball, ticker, and cookie. These combinations include a red bouncy ball, an iri, lily, or daiy ticker, and either a chocolate chip or oatmeal cookie.
There are a total of 6 different possible combinations of the gift bag with a bouncy ball, ticker, and cookie. These combinations include a red bouncy ball, an iri, lily, or daiy ticker, and either a chocolate chip or oatmeal cookie. The red bouncy ball offers a vibrant and exciting option, while the iri, lily, and daiy ticker add a fun element of surprise. The two cookie options offer something delicious and comforting to enjoy. With all of the different combinations, there is something for everyone to enjoy! Each combination offers a unique and special gift bag that will be sure to bring a smile to anyone's face.
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How do you express your answer as a polynomial in standard form?.
The standard form of polynomial is to write the polynomial so that the term with the highest power of the variable comes first, followed by the other terms in order of descending powers of the variable.
A polynomial in standard form requires that the polynomial be written in descending order of exponents. Polynomials are written in standard form for ease of computation. A polynomial is in its canonical form when it is expressed with the highest order term first, followed by the higher order terms, and so on. For example: 14x⁴ - 5x³ - 11x² - 11x + 8. You can see that in this standard form polynomial, the exponents are ordered in descending powers. These algebraic equations are called polynomials. Procedure for writing polynomials in standard form:
Write the terms Make the groups of all similar terms.The highest exponent write the as first term.Write the rest of the terms with small exponents in descending order.Write the constant term.The normal form polynomial of degree 'n' is : aₙxⁿ + aₙ₋₁ x⁽ⁿ⁻¹⁾ + ... + a₁ x + a₀
Let us assume a polynomial, p(x) = x² + 8x - 9 + 7x³ - 6x + x⁴ , using the above steps we can write the standard form of p(x).
x² + 8x - 9 + 7x³ - 6x + x⁴ x² - 9 + 7x³ - 6x + 8x+ x⁴ = x² - 9 + 7x³+ 2x + x⁴x⁴ + 7x³ + x² + 2x - 9 ( standard form)To learn more about Standard form polynomial, refer:
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[tex] \frac{?}{?} [/tex]
5 to the power 0
To the power of 5, 0 is 1 . Any power with a value of 0 yields a response of 1. [tex]5^0[/tex] = 1 can be used to represent 5 to the power of 0.
Why any number to the power of 0 is 1?Because 1*x = x for any other number x, the number 1 is the multiplicative identity. Due to the fact that every integer raised to the power of zero is just the sum of zeroes, or the multiplicative identity, 1, any number raised to this power is one.
The value 0 to the power 0 cannot have any values since they would conflict. In this way, 0 to the power 0 is undefinable. Reverse values are indicated by negative exponents. A negative power of a number is one more than the positive opposite power of the same number. Negative zero is a mathematical nonsense. the sign bit of a binary integer is set to 1, and all other bits are set to zero.
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According to the hitogram of travel time to work from the US 2000 cenu (Page 6 of "Journey to Work: 2000"), approximately what i the median travel time, in minute (i. E. 50% of commuter have at mot that travel time, 50% have at leat that travel time)?
The percentage of commuters that travel more than 45 minutes is 90%.
What is percentage ?
A percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%" and is used to express a proportion or rate as a part of a whole. Percentages can be used to compare different quantities or to express how much one quantity has changed relative to another.
The percentage of commuters that travel more than 45 minutes is the quotient of the commuters that travel more than 45 minutes and the total number of surveyed commuters.
So, we have ,
Percentage = [tex]\frac{450}{500}%Percentage[/tex] =500450
Divide 450 by 500
Percentage = 0.9 Percentage=0.9
Express as percentage
Percentage = 90 Percentage=90%
Hence, the percentage of commuters that travel more than 45 minutes is 90%.
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For the following equation, a. Write the value or values of the variable that make a denominator zero. These are the
restrictions on the variable. b. Keeping the restrictions in mind, solve the equation.
For the given equation, the value of x = -21.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
For the given equation,
x ≠ ±3
On taking LHS,
⇒ [tex]\frac{5}{x+3} - \frac{2}{x-3}[/tex]
Taking LCM,
⇒ [tex]\frac{5(x-3) - 2(x+3)}{(x+3)(x-3)}[/tex]
⇒ [tex]\frac{5x - 15 - 2x - 6}{x^2 - 9}[/tex]
⇒ [tex]\frac{3x - 21}{x^2 - 9}[/tex]
On Comparing both sides,
⇒ [tex]\frac{3x - 21}{x^2 - 9} = \frac{4x}{x^2 - 9}[/tex]
⇒ 3x - 21 = 4x
⇒ x = -21
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How do you solve complex fractions and unit rates?.
A unit rate is a ratio that has a denominator of 1, such as miles per hour or dollars per item. To solve a complex fraction that involves a unit rate, you can follow the same steps as solving a regular complex fraction, but with an additional step to convert the final expression to a unit rate.
Factor the numerator and denominator of the complex fraction if possible.
Multiply both the numerator and denominator by the reciprocal of the fraction(s) in the denominator.
Simplify the resulting expression by combining like terms, if possible.
Check your work by multiplying the numerator and denominator of the original complex fraction by the reciprocal of the fraction(s) in the denominator, and verifying that the simplified expression you obtained is equivalent.
Divide the numerator by the denominator to get the unit rate.
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The sixth term of an arithmetic
Sequence is 17 and the tenth Term
IS 33, Determine the first term and
Common difference.
Answer: 1st term: -3. Common difference: +4
Step-by-step explanation:
-3, 1, 5, 9, 13, 17, 21, 25, 29, 33
add 4 each time
A river guide conducts kayak and canoe tours along a scenic river. He charges a booking fee plus a variable rate depending on the number of passengers. The total cost for different numbers of passengers, including the initial fee, is shown on the graph.
Find and interpret the rate of change.
For the specified Data, the rate of change will be 8.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given this, Kayak and canoe experiences are led by a river guide along a beautiful river. In addition to a booking fee and a variable tariff based on the number of passengers, he charges. The graph displays the total cost for various passenger counts, including the booking fee.
From general formula of rate of change = (y₂ - y₁)/ (x₂ - x₁)
in our case
y₂ = 72
y₁ = 56
x₂ = 4
x₁ = 2
thus rate of change = 16/2 = 8
Since A rate of change is the proportion of one quantity's change to another's change. There is a constant rate of change in linear relationships.
Therefore, The rate of change for the given equation will be 8.
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Who i El Cero and how did he change? What doe the narrator think contributed to thi change?
Answer:
He contributed because he was a life-changing character
Step-by-step explanation:
The passage states that u should read into the character
sum of two numbers is 95.theother by 15 find the numbers?
Answer:
The two numbers are 40 and 55.
Step-by-step explanation:
Let one of the numbers be x.
Then the other number is 95 - x.
If we assume x to be larger among two of them,
⇒ x - (95 - x) = 15 (as one exceeds the other by 15)
⇒ 2x = 15 + 95
⇒ x = 110 / 2 = 55
The other number is (95 - x) which is 95 - 55 = 40
Thus, the two numbers are 40 and 55
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What is true about the completely simplified difference of the polynomials?.
The sum is a binomial with a degree of 6 is correct about the completely simplified difference of the polynomials.
The polynomial's difference is a binomial of degree six. An expression known as a polynomial only uses the operations of addition, subtraction, and multiplication of variables. Degree-based classifications for polynomials include linear, quadratic, cubic, and more. The polynomial's difference is a binomial of degree six.Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates.In polynomial expressions, division by variable is not possible, but addition, subtraction, multiplication, and positive integer exponents are all possible. The single-variable polynomial x2+x-12 serves as an example. In this example, x2, x, and -12 are three different terms.To learn more about polynomials here
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What is true about the completely simplified sum of the polynomials 3x2y2 − 2xy5 and −3x2y2 + 3x4y?
A. The sum is a trinomial with a degree of 5.
B. The sum is a trinomial with a degree of 6.
C. The sum is a binomial with a degree of 5.
D. The sum is a binomial with a degree of 6.
Find the bearing of b from a in each diagram
Answer:
well where is your diagram
To train for an upcoming race, Ranell runs the same route every morning from his house. He runs east for 3 miles and north for 4 miles. Then, he runs a straight-line home. What is the total distance Ranell will run after 5 days of training?
Answer: 35 miles.
Step-by-step explanation: 3+4 = 7
If f(x)= 2x2 + x - 7 and g(x)= x + 5, then evaluate g(f(3)).
Answer:
g(f(3)) = 19
Step-by-step explanation:
This would be your functions: [tex]\displaystyle{f(x)=2x^2+x-7}[/tex] and [tex]\displaystyle{g(x)=x+5}[/tex]. In order to evaluate g(f(3)), we must find the value of f(3) first which we can find by substituting x = 3 in the f(x).
[tex]\displaystyle{f(3)=2(3)^2+3-7}\\\\\displaystyle{f(3)=2\cdot 9 - 4}\\\\\displaystyle{f(3)=18-4}\\\\\displaystyle{f(3)=14}[/tex]
Therefore, g(f(3)) is basically equal to g(14), we substitute x = 14 in the g(x).
[tex]\displaystyle{g(f(3))=g(14)=14+5 = 19}[/tex]
Hence, g(f(3)) is 19.
Been stuck on this for a while Please Help!
Answer:
x = 23°
Step-by-step explanation:
Sum of interior angle
(n - 2)180. note: the sides are 3
(3 - 2)180
(1)180
180°.
the value of x
31° + 3x° + 34° + 2x° = 180°
31° + 34° + 3x + 2x = 180°.
65° + 5x = 180°
5x = 180° - 65°
5x = 115°
5x/5 = 115/5
x = 23°
What is the length of the square's side? (Show Work)
Answer:
[tex]\dfrac{6}{\sqrt{2}}[/tex]
Step-by-step explanation:
For a square of side a, the diagonal is a√2
This is because the diagonal and the two sides of the square form a right triangle
By the Pythagorean theorem, diagonal d = √(a² + a²) = √2a
Since we are given the diagonal as 6 we have
6 = √2 · a
[tex]\sf{Or\; a =\dfrac{6}{\sqrt{2}}[/tex]
The answer you have selected is right
3/4 • 200. Helpppppppp
Cross - division step
Answer:
150
Step-by-step explanation:
Given problem,
→ (3/4) × 200
Let's solve the problem,
→ (3/4) × 200
→ (3 × 200)/4
→ 600/4
→ 150
Hence, solution is 150.
introduction paragraph about Peter G. L. Dirichlet
Answer:
Johann Peter Gustav Lejeune Dirichlet (German: [ləˈʒœn diʀiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician who made contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis
Please help for 10 points… I need this asap!!!
Answer: Is there an answer for 1/2? I'm not sure.
Step-by-step explanation: If you look at the line it's going up by one and over by 2.
To solve for slope (Rate of Change) you need to find the change and y over the change in x. (y2-y1) divided by (x2-x1) take two points on the graph that is touching a line.
Two points on your graph is (2,2), and (6,4). You would take the second y which is 4 and subtract it from the first y which is 2. (4-2 = 2). Then you take the second x (6) and subtract it from the second y (2). (6-2 = 4). Now that you have the change and x over the change in y. you divide the top number by the bottom number. If it's a fraction just simplify it. (2/4 = 1/2). I'm not that good at explaining but I hope this helps a lot!
Who find the number, zero?.
The number zero was invented by Aryabhatta, an astronomer and mathematician from India.
As we know the origin of zero in India came from a well-known astronomer and mathematician Aryabhatta.
A number zero had been used as a placeholder number since before Aryabhatta and Brahmagupta. In the 5th century, Aryabhatta is credited with using zero in the decimal system.
Whereas in the 7th century, Brahmagupta used zero in mathematical operations like addition and subtraction.
In India, a number zero was called ‘Sunya’, when the number reached Italy, it was named ‘Zefero’ and later it was called ‘Zero’ in English.
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Aadan and Chinyelu viit the market in Gao to buy an Azawakh, a breed of dog that i popular for guarding ancient Mali village. When Aadan' dog wa a puppy, it weighed `8` kg, which i `30\%` of it current adult weight. What i the current weight of Aadan’ dog?
Write an equation in which `x` repreent the current weight of Aadan' dog
The current weight of Aadan's dog is approximately 26.67 kg.
What is weight ?
Weight is a measure of the force of gravity on an object. The weight of an object is equal to the force exerted on the object by gravity. The weight of an object is typically measured in units of force such as newtons (N) or pounds (lb). On Earth, the weight of an object is equal to its mass multiplied by the acceleration due to gravity, which is approximately 9.8 m/s².
Let's call the current weight of Aadan's dog as "W".
As per the information given,
Aadan's dog was a puppy and it weighed 8 kg which is 30% of it's current adult weight.
So, 8kg = 30/100*W
We can find the current weight of Aadan's dog by solving the equation above:
8 = 30/100W
8 = 3/10W
8 = 0.3W
W = 8/0.3
W = 8/(3/10)
W = 8(10/3)
W = 8*3.333
W = 26.666 kg ( approx 26.67 kg)
So the current weight of Aadan's dog is approximately 26.67 kg.
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8kg = 30/100*W
8 = 30/100W
8 = 3/10W
8 = 0.3W
W = 8/0.3
W = 8/(3/10)
W = 8(10/3)
W = 8*3.333
W = 26.666 kg ( approx 26.67 kg)
find the product of 7/2 and 22
Answer:
98765
Step-by-step explanation:
Pleaseeee help
Consider the function f(x)=x^3-1. Which of the following functions is f^-1(x)?
The inverse function of f(x) = x^3 - 1 is f^-1(x) = (x + 1)^(1/3).
What is the inverse of a function?
An inverse function is a function that returns the original value for which a function has given the output. If f(x) is a function that gives output y, then the inverse function of y, i.e. f-1(y) will return the value x.
The inverse of a function f(x) is denoted as f^-1(x), and it is defined as the function that "undoes" f(x).
To find the inverse of a function, we need to swap the roles of x and y, and then solve for y in terms of x.
Given f(x) = x^3 - 1, the inverse function f^-1(x) is the function such that:
f(f^-1(x)) = x
f^-1(f(x)) = x
So we need to solve for x in terms of y.
x^3 - 1 = y
x = (y + 1)^(1/3)
Therefore, the inverse function of f(x) = x^3 - 1 is f^-1(x) = (x + 1)^(1/3).
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What are the values of the three basic trigonometric ratios?.
The values of the three basic trigonometric ratios are Sine, Cosine, tangent.
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. The sin, cos, and tan functions can be used to obtain the other significant trig ratios, cosec, sec, and cot.
Sine: The ratio of the perpendicular to the hypotenuse is known as the sine ratio for every given angle. Sine of angle in the given triangle can be expressed as sin = AB/AC.Cosine: The proportion of an angle's base to its hypotenuse is known as the cosine ratio. The cosine of angle in the given triangle can be expressed as cos = BC/AC.Tangent: The ratio of the perpendicular to the base is known as the tangent ratio for every given angle. The tangent of angle in the given triangle can be expressed as tan = AB/BC.Learn more about trigonometric ratios;
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Ms. Wilson is buying packages of pencils. Each package cost $11.52 and contains 96 pencils. What is the unit price of a pencil?
Answer:
$0.12
Step-by-step explanation:
Unit price=$11.52/96(per pencil)
11.52/96=$0.12
Hope this helps
Answer:
$0.12
Step-by-step explanation:
First, you have to divide 11.52
to 96 which will be equal to 0.12.
We know how to divide because
in the question the keyword is
EACH. That's how you know when
to divide!
Hope This Helps :)
11.52÷96≈ 0.12
