In general F^-1(f(x))=f(f^-1(x)) wherein f^-1(x) is the inverse of f(x).
What is function?Function is a process or activity that fulfills a specific purpose or set of requirements. It is a building block of programming and can be used to create various types of applications. Functions allow coders to modularize their code and make it easier to debug and maintain. Functions can also be used to process data, perform calculations, and display outputs.
It is a mathematical law which states that if a function f(x) has an inverse function then the composition of the function with its inverse should be equal to the original function. This law is also known as the Involution Law or the Composition Law of Inverse Functions.
The Involution law or the Composition law of inverse functions is a fundamental law of mathematics. This law states that for any function f(x) which has an inverse function, f^-1(x), the composition of the function with its inverse should be equal to the original function. That is, F^-1(f(x))=f(f^-1(x)). This law is important as it helps to understand the relationship between the original function and its inverse. This law is useful in solving various mathematical problems and in understanding various mathematical concepts such as differentiation and integration.
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which of the following are solutions to the quadratic equation? check all that apply. x^2+8x+16=7
The solutions to the quadratic equation are -
{x} = - 6.646 and {x} = - 1.354.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the quadratic equation as -
x² + 8x + 16 = 7
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.The set X is called the domain of the function and the set Y is called the codomain of the function.A quadratic function is of the form → y = f(x) = ax² + bx + c.The given quadratic equation is -
x² + 8x + 16 = 7
x² + 8x + 9 = 0
Solving the equation graphically, we get -
x = - 6.646 and x = - 1.354
Therefore, the solutions to the quadratic equation are -
{x} = - 6.646 and {x} = - 1.354.
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10. Write a rational
expression that is
equal to the followi
rational expression
when x doesn’t = 1 or
(x+1)/
(x+1)(x-1)
The rational expression is
[tex]\frac{(x+1)}{(x-1)(x+1)} = \frac{1}{(x-1)}[/tex]
for x ∈ R - {1}
What is rational expression ?The ratio of two polynomials is a rational expression. If an expression is rational, it may be expressed in the form p/q, where p and q are polynomials.
When the numerator and denominator of an equation are both polynomials, the expression is said to be rational. The lowest form of the numerator and denominator is used to simplify rational formulas. An algebraic fraction is another name for a rational expression.
The value of a logical statement is diminished to its simplest form or lowest terms when it is simplified. Similar to how we simplify fractions, we can simplify a rational equation. In fractions, a rational number is said to be in its simplified form if its numerator and denominator share no factors other than 1. The only distinction is that when simplifying rational expressions, the same strategy also applies because the fraction contains polynomials.
The expression is
[tex]\frac{(x+1)}{(x-1)(x+1)} = \frac{1}{(x-1)}[/tex]
for x ∈ R - {1}
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4.) Harrison has $195 and wants to buy some
LOST
new clothes. He is buying a new pair of
shoes that cost $75 and the rest of his
money he wants to spend on t-shirts that
cost $20 each. Write an inequality that can
be used to determine how many shirts he
can buy, then solve the inequality.
AP.8A-
10.6
120-20-6
Answer: quizlet has all the answers
Step-by-step explanation:
Round to the nearest thousandth
The population was 6.98 million in 1900. The population of New York decreased with respect to time.
What is an exponential function?
An exponential function is a mathematical function with the formula f (x) = axe, where "x" is a variable and "a" is a constant that is called the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most commonly used exponential function base.
The population of New York state can be modeled by
[tex]P(t)=\frac{19.71}{1+61.22e^{-0.03513t}}[/tex]
P is the population and t is the number of years since 1800.
The difference between the year 1900 to 1800 is 100.
Putting t = 100 in the given model:
[tex]P(t)=\frac{19.71}{1+61.22e^{-0.03513\times 100}}[/tex]
[tex]P(t)=\frac{19.71}{1+61.22e^{-3.513}}[/tex]
P(t) = 19.71/2.8248
P(t) = 6.9774
P(t) = 6.977 (rounded to the nearest thousands)
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Tickets were cost $24.00 per person and there is one time $12 group registration fee.Write an expression for The cost of the whole group if there are p people going
At a certain high school the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 31 pounds. A random sample of backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. For samples of size 5, which of the following is the best interpretation of P(x > 22) = 0,067 The probabilty that each of the backpacks selected will have a wright above 22 pounds is approximately 0.05. The probability that each of the Shackpacks bected will have a weight above 19.7 pounds is approximately 0.05. c) The probability that the population mean in greater than 22 pounds is approximately 0.05 D) For al samples of size 5, approximately 5% of the sample will have a probability greater than 22 pounds E For all samples of size 5. the probability that the sample mean will be greater than 22 pounds is approximately 05,
Answer:
45 grapes
Step-by-step explanation:
23
How do you solve quadratic equations by factoring examples?
Quadratic equation ax² + bx + c = 0 can be solved by factoring the equation using two methods :
a. Splitting the middle term of the equation.
b. Quadratic formula x = ( -b ±√b² -4ac )/2a.
As given in the question,
Standard quadratic equation is given by :
ax² + bx + c = 0
This can be factoring by using two methods:
a. Splitting the middle term of the equation.
b. Quadratic formula x = ( -b ±√b² -4ac )/2a.
Example : x² + 8x - 9 =0
a. splitting middle term:
x² + 8x - 9 =0
⇒ x² + 9x - x - 9 =0
⇒ x( x + 9 ) - 1 ( x + 9 ) = 0
⇒ ( x - 1 ) ( x + 9 ) = 0
b. Quadratic formula:
here a = 1 , b = 8 , c = -9
x = ( -8 ± √8² - 4 (1 )(-9 ) )/ 2(1)
⇒ x = (-8 ± 10 ) / 2
⇒ x = 1 or x = -9
Therefore, the quadratic equation can be factoring by two methods :
a. Splitting the middle term of the equation.
b. Quadratic formula x = ( -b ±√b² -4ac )/2a.
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help me please! integral calculus!
Refer to the attached images.
a 6 ft man lifts a 100-lb weight from the floor to a height 1 ft above his head. how much work is done in lifting the weight?
700 ft-lbs of work is done in lifting the weight of the man.
Work, W= Fdcos∅
Where F is the force
d is displacement
and ∅ is the angle between them.
Since the direction of force is the same as the direction of displacement
so ∅ =0 thus cos∅ =cos0 =1
now, W=Fd
As we know force required to lift an object is equal to the weight of the object
F=100lb
Displacement = height of man+ height he needs to be lifted
Displacement = 6+1=7ft
Hence, W= 100x7
W=700 lbs-ft
Therefore, 700 ft-lbs of work is done in lifting the weight of the man 1ft above his head.
Work is the transferring of energy to or from an object via force along a fixed displacement.
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Write the function x3 - 6x^2 - x + 30 in factored form knowing that one of the roots is 5
Group of answer choices
(x - 5)(x -2)(x + 3)
(x + 5)(x - 2)(x + 3)
(x + 5)(x + 2)(x - 3)
(x - 5)(x + 2)(x - 3)
The required factors of the given expression x³ - 6x² - x + 30 is (x - 5)(x + 2)(x -3). Option D is correct.
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
Here,
Gien expression,
= x³ - 6x² - x + 30
= (x - 5)(x + 2)(x -3)
Thus, the required factors of the given expression x³ - 6x² - x + 30 is (x - 5)(x + 2)(x -3).
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How would the domain and range of the function be determined explain?
The domain of a function is the set of all input values (x-values) for which the function is defined. The range of a function is the set of all output values (y-values) that the function can produce.
To determine the domain of a function, look at the equation defining the function and identify any restrictions on the input values. For example, if the function is a square root, the input (x) value can not be negative.
To determine the range of a function, you can use the equation of the function and test several input values to find the corresponding output values. You can also use the graph of the function to identify the range. If the function is continuous, you can use the graph to see the range of the function.
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Geometry
What are the two main ways to classify triangles? List the categories or types involved in each method of classification.
There are two types of classifications for triangles, Classification according to internal angles and Classification according to the length of its sides.
What are triangles?A geometrical shape with three vertices, angles and sides, whose sum of internal angles is 180° is considered as a triangle.
Classification of triangles :-
There are two ways to classify triangles,
1) Based on the Angle :-
a) Acute Angled Triangle :- A triangle that has all three angles less than 90° is an acute angle triangle.
b) Right-Angled Triangle :- A triangle that has one angle that measures exactly 90° is a right-angle triangle.
c) Oblique Angled Triangle :- A triangle that has one angle that measures more than 90° is an obtuse angle triangle.
2) Based on the Sides :-
a) Scalene Angled Triangle :- A triangle that has all three sides of different lengths is a scalene triangle.
b) Isosceles Angled Triangle :- A triangle that has two sides of the same length and the third side of a different length is an isosceles triangle.
c) Equilateral Angled triangle :- A triangle that has all three sides of the same length is an equilateral triangle.
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Translate Detroit has eighty-five high schools. Which one do you attend?
into French in the box below:
Mike made 56 of his free throw attempts and Lisa made 79 of her free throw attempts. Choose two fractions that show 56 and 79 written with a common denominator. A. 1018 B. 1418 C. 1518 D. 2736 E. 3036
The two fractions that show 5/6 and 7/9 written with a common denominator are C. 15/18 and B. 14/18, respectively.
A fraction is a way of expressing a part of a whole. It is represented by two numbers written one above the other, with a horizontal line separating them.
The number on top is called the numerator and represents the number of parts being considered. The number on the bottom is called the denominator and represents the total number of parts in the whole.
To determine the fractions that shows 5/6 and 7/9 written with a common denominator, find the common multiples of their denominator.
multiples of 6 and 9 : 18, 36, 54, . . .
These multiples will now be the new denominator. Divide the multiple by the denominator, and multiply by the numerator to have the new numerator.
5/6 = 15/18 = 30/36
7/9 = 14/18 = 28/36
Hence, the answer is C. 15/18 and B. 14/18.
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What is the value of t in the following equation?
t + 14 = 2 7/12
A. t = 37
B. t = 123
C. t = 213
D. t = 323
these are fractions
By calculating the value of given expression is -137/ 12 .
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants .
Given ,
expression t + 14 = 2 7/12
t+14 = (2*12 + 7 ) / 12
So by sending 12 in LHS we get,
t+14 = 24+7 / 12
t+14 = 31/ 12
12 ( t+14) = 31
multiplying 12 on LHS
12 t + 12*14 = 31
12t = 31-168
12 t = -137
t = -137 / 12
Hence, the value of given expression is -137/ 12 .
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Jessica placed $1100 in a savings account which earns 3. 7% interest, compounded continuously. How much will she have in the account after 10 years? Round your answer to the nearest dollar
$1897 she has in the account after 10 years.
Use the formula for calculating compound interest
Compound interest can be regarded as the addition of interest on the loan to the principal sum of the deposit.
where A(t) is the account balance, P0 is the principal, r is the yearly interest rate (in decimal form), n is the frequency of compounding interest, and t is the time (in years).
P=$1,100, r=0.037, n=1, and t=15 are all given to us.
Using a calculator to calculate the result after entering the variables into the formula, we discover
A(t)=P(1+rn)n⋅t=$1,100(1+0.0371)(15)(1)≈$1,897.03
So the final answer is $1,897
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A term is a constant, a variable, or a ___ of numbers and variables.
A term is a constant, a variable, or a product of numbers and variables.
What is variable?A symbol (typically a letter) used in algebra to represent an unknowable numerical value in an equation or algebraic expression. A variable can be defined as a quantity that is changeable and not fixed. A variable in mathematics is an alphabet or term that stands in for an unknowable quantity, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are used. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.
Here,
A term can be a number, a constant, a variable, or the product of a number and a variable.
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To win a game, Roger needs to score 2,000
points. So far, he has scored 837 points.
How many more points does Roger need
to score?
Answer:
Step-by-step explanation:
the answer is 1163 :)
There's a moderate positive correlation between the length of a child's hair and the amount of time it takes for the child to run 100 meters.
Which statement is true?
Question 6 options:
The correlation is most likely due to a lurking variable.
The correlation is most likely a causation.
The correlation is most likely a coincidence.
Note that where there's a moderate positive correlation between the length of a child's hair and the amount of time it takes for the child to run 100 meters, then the statement that is TRUE is: "The correlation is most likely due to a lurking variable." (Option B).
What is a lurking variable?A correlation does not imply causation, and a moderate positive correlation is not enough to establish a causal relationship between two variables.
It is possible that the correlation is due to an underlying factor (lurking variable) that affects both the length of the child's hair and the time it takes for the child to run 100 meters. To establish causality, other methods such as experimental design and statistical analysis are necessary.
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Height=0.6 width=0.8 length=1.8 volume
Answer: 0.864
Step-by-step explanation:
0.6 x 0.8 x 1.8 = 0.864
Select the correct text. Jerome’s teacher gave him a homework assignment on solving equations. Since he’s been thinking about saving for a used car, he decided to use the assignment as an opportunity to model a savings plan. He already has $500, and he plans to save $375 every month. To model the situation, he created this equation, where y represents the total amount saved for the car and x represents the number of months since he started saving: 500 + 375x = y. He then solved the equation to determine how many months he would need to save to have enough to purchase the car. Review his work, and select the error. Justification 1: given 2: addition property of equality 3: simplification 4: division property of equality 5: simplification 6: substitution, y = 3,500 7: simplification Step 1:500 + 375x = y Step 2:500 + 375x − 500 = y − 500 Step 3: 375x = y − 500 Step 4: = Step 5: x = Step 6: x = Step 7: x = 8
The saving plan is an illustration of linear equations.
In his calculations, Jerome was faultless.
The equation is represented as;
Where:
x represents the number of months
The following procedures are used to identify Jerome's mistake (s)
Given
Addition property: Add -500 to both sides
Simplify
Division property: Divide both sides by 375
Simplify
Substitution: Substitute 3500 for y
Simplify
The steps above show that: He did not make any mistake
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This year, a teacher graded 84 more final exams than last year. If the teacher graded 600 final exams this year, how many final exams did the teacher grade last year?
Answer:516 exams
Step-by-step explanation:
600 this year
84 more
subtract
equals 516
516 exams this year
Arisia puts $500.00 into a savings account with an annual simple interest rate of 4.5%
How much interest does she earn per year?
Answer:
Simple interest is calculated by multiplying the principal amount (the initial deposit) by the interest rate and the number of years.
The formula for simple interest is:
I = P * r * t
Where:
I = Interest
P = Principal (initial deposit)
r = Interest rate (expressed as a decimal)
t = Time (in years)
In this case, the principal amount is $500.00, the interest rate is 4.5%, and the time is one year.
The interest rate is expressed as a percentage, so we need to convert it to a decimal by dividing it by 100:
r = 4.5/100 = 0.045
Now we can plug in the values into the formula:
I = $500.00 * 0.045 * 1 = $22.50
So, Arisia earns $22.50 in interest per year.
What is negative logarithm?
A negative logarithm represents the amount of times to divide it by. [tex]log \left(\frac{1}{a}\right) = -log a[/tex] denotes that the negative logarithm of a number is equal to the logarithm of 1 divided by that number.
The alternative to using exponents is to use logarithms. A number's logarithm with a base is equivalent to another number. Exponentiation's opposing function is a logarithm.
In mathematics, a logarithm is the power to which a number must be raised in order to obtain other numbers. It's the most useful methodology for representing huge numbers.
A logarithm contains a number of significant characteristics that demonstrate that addition and subtraction logarithms can also be used to represent the multiplication and division of logarithms.
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How do you solve a log table?
Without a calculator, larger computations such as squares, roots, multiplication, and division can be made using a log table also known as a logarithm table.
A log table for a given base is a table of logarithms that is used to determine the base-dependent logarithm of a given number. For different bases, such as 10, e (Euler's number), 2, etc., there are several log tables.
The logarithm table provides the quickest method for exactly determining a number's log value. The exponential function is thought of as the inverse of the logarithmic function.
Any number's logarithm has two components: the characteristic and the mantissa. A decimal point always separates these two components.
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solve the problem 17+50-100=
for a certain industry the mean annual salary rose from 68860 to 71350 calculate the percent of increase. round to the nearest 10th.
What is the volume of the rectangular prism? 1/2 cm
The volume of a rectangular prism is lwh unit cube.
What is a rectangular prism?A rectangular prism can be defined as a 3-dimensional solid shape that has 6 faces, with its base as rectangles.
The volume of a rectangular prism is given by, the product of its dimensions.
Let us consider length, width and height of the rectangular prism be l, w, h respectively,
Then, the volume will be = length x width x height
= l x w x h
= lwh
And its unit will be unit cube because there are 3 dimensions in the prism which are being multiplied.
Hence, the volume of a rectangular prism is lwh unit cube.
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What measurement is l used for?
The L angle is used for measuring the area of the rectangle.
A right angle is one that is 90 degrees in length. It is the most frequently encountered angle in our daily lives. It can be noticed in room corners, box edges, mobile phone screens, and so on.
A square's and a rectangle's sides always make a right angle with each other. It is represented in radians as /2.
The angle formed by two lines that are perpendicular to each other is called a right angle. A right angle is equal to 90° and is in the shape of the letter "L". In the following figure, ray AB and BC form a right angle ABC.
Thus, the L angle is used for measuring the area of the rectangle.
Complete question: What measurement is L angle used for?
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what intersects a circle at exactly one point and creates a right angle to the radius?
The line that intersects a circle at exactly one point and creates a right angle to the radius is called the Tangent .
What is Tangent ?
The tangent can be defined as a line that touches the circle at exactly one point .
The properties of tangent Lines are :
(i) The point where tangent line meets circle is called as the point of tangency.
(ii) The tangent line is perpendicular to the radius of circle, with which it intersects, that means , a right angle is created at the meeting point .
(iii) There is exactly one tangent that can touch the circle at any given point .
Therefore , by the property of tangent to circle , we can say that , Tangent intersects a circle at exactly one point creates right angle to radius .
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