(a) show that f is one-to-one. (b) use theorem 7 to find s (f ^-1) d9sad. (c) calculate f 21 sxd and state the domain and range of f 21 . (d) calculate s f 21 d9sad from the formula in part (c) and check that it agrees with the result of part (b). (e) sketch the graphs of f and f 21 on the same axes.
Answers
The function f(x) = 9 - x² is a one to one function and the value of f⁻¹(x) = √9 - x.
The graph of the function is attached below.
In math the term graph is defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Here we have the function f(x) = 9 - x² and here we also know that on the interval 0≤x≤3 and a=8.
Now, we have to check the given function is one to one or not, for that we have to plot the function on the graph then we get the graph like the following.
While we looking into the graph we have identified that each input value has exactly only one output, therefore it is said to be one to one function.
And the inverse of the function is calculated by rewritten the function as,
=> f⁻¹(x) = √9 - x.
And the graph of f⁻¹(x) is plotted as follows,
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Related Questions
Sauv drove 296 miles in 8 hours.If he continued at the same rate,how far would he travel in 10 hours?
Answers
370
EXPLANATION
DETAIL STEPS
...10 = 8
We know that.: {# = 10
v = 8
Substitute
into formula d = v × t:
It= 10
d = 8 × 10
Cross out the common factor: 10 × 37
Calculate the product or quotient: 370
1) Solve and graph the inequalitiy x + 8 < - 3
2) Write a statement that repersent the number line below
the pet shelter, for every 7 dogs there are 5 cats. What is the ratio of dogs to cats?
Answers
a) The inequality equation is x < -11
b) The inequality equation is x < 7
c) The ratio of dogs to cats is 7 : 5
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
a)
Substituting the values in the equation , we get
x + 8 < -3 be equation (1)
On simplifying the equation , we get
Subtracting 8 on both sides of the equation , we get
x < -11
Therefore , the inequality is x < -11
b)
The inequality representing the number line is x < 7
c)
Let the ratio be represented as A
The number of dogs = 7
The number of cats = 5
The ratio of dogs to cats = number of dogs / number of cats
Substituting the values in the equation , we get
The ratio of dogs to cats = 7 / 5
Therefore , the ratio is 7 : 5
Hence , the inequality relation is solved
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express a cosine and sine function in terms of an imaginary exponential. conversely, express the imaginary exponential in terms of cosine and sine
Answers
A cosine and sine function can be expressed in terms of an imaginary exponential using Euler's formula: e^(iθ) = cos(θ) + i*sin(θ).
This formula can be derived by using the Taylor series for e^x, and replacing x with iθ.
A cosine and sine function can be expressed in terms of an imaginary exponential using Euler's formula: e^(iθ) = cos(θ) + i*sin(θ).
Conversely, an imaginary exponential can be expressed in terms of cosine and sine by solving for θ in the above equation. This can be done by taking the inverse cosine and inverse sine of both sides to get θ = cos^(-1)(e^(iθ)) = sin^(-1)(i*sin(θ)). Combining these equations gives θ = sin^(-1)(i*(e^(iθ) - cos(θ))).
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9.) Multiple Choice: In triangle ABC, side AB has a length of 6cm and side BC has a length of 10cm. What is the length of AC?
Answers
The length of AC of the given right angle triangle is; AC = 8
How to use Pythagoras theorem?Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse, Opposite and the adjacent side.
Now, the given triangle is a right angle triangle and using Pythagoras theorem, we can say that;
AC = √(BC² - AB²)
Thus;
AC = √(10² - 6²)
AC = √64
AC = 8
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From a recent study, it was found that 10% of students travel outside of the country during spring break. Is this an example of descriptive statistics or inferential statistics?
Answers
This is an example of descriptive statistics. Descriptive statistics is used to summarize, organize, and present data in a meaningful way.
Is this an example of descriptive statistics or inferential statistics?It involves the collection, analysis, interpretation, and presentation of data. In this case, the study found that 10% of students travel outside of the country during spring break. This is a summary of the data collected and presents it in a way that is easy to understand. It gives a percentage of students who travel outside of the country during spring break, which can be used to describe the behavior or characteristics of students.On the other hand, inferential statistics is used to make predictions or draw conclusions about a population based on a sample of data. It involves using statistical methods to make inferences about a population from a sample. For example, if a study found that 10% of students at a particular university travel outside of the country during spring break, inferential statistics would be used to make predictions or conclusions about the behavior or characteristics of students at other universities.To learn more about inferential statistics refer to:
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NO LINKS!!
44. Between which two integers would the solution to 4^x = 50 lie? Second, find the exact solution by changing to logarithmic form and solving.
Answers
Answer: To find the two integers between which the solution to 4^x = 50 lies, we can take the logarithm base 4 of both sides of the equation: x = log4(50). The logarithm of 50 with base 4 is approximately 2.3219. Since the logarithm of a number is always positive, the solution to 4^x = 50 lies between 2 and 3.
To find the exact solution, we can change the equation to logarithmic form by taking the logarithm base 4 of both sides: log4(4^x) = log4(50)
Using the logarithmic identity: log(b^x) = x*log(b)
So we have: x*log(4) = log(50)
Dividing both sides by log(4), we have:
x = log(50) / log(4)
To find the exact solution we can approximate log(50) / log(4) using a calculator or logarithm tables. The exact solution is x ≈ 2.32192809488736218170856773213.
So, the exact solution is x = 2.32192809488736218170856773213, which is between 2 and 3, as stated before.
Step-by-step explanation:
a statistical study inbolves a data set of the different types of shoe designs by the designer calbvivn klein collected consistentyly over the years from 1987 to 2014 quizzlet
Answers
Answer:
c
Step-by-step explanation: got it right on test
De una botella que contenía 1litro de agua, Juan bebió 1/4 de litro.Expresa con forma de número decimal la cantidad de agua que queda en la botella
Answers
The fraction of water left from the bottle which was 1 liter is 3/4 liter.
How to calculate the fraction?Fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, from the bottle which was 1 liter, Juan drank 1/4. The amount that is left will be:
= 1 - 1/4
= 3/4
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Trapezoid ABCD and trapezoid EFGH are
congruent. What is the difference between
the area of triangle ABC and the area of
triangle EFJ?
Answers
The difference between the area of triangle ABC and the area of triangle EFJ is 0 square unis
How to determine the difference in the areasFrom the question, we have the following parameters that can be used in our computation:
Trapezoid ABCD and trapezoid EFGH are congruent.
From the complete question added as an attachment
We can see that the two triangles have the same base and the same height due to the congruence of the two trapezoids
This means that their areas are equal
The difference between equal values is 0
Hence, the area difference is 0
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5 A college student is paying for tuition through private loans. Two lenders have approved the student for a $25,000 loan. Offer 1: 5.99% annual simple interest, with a total account balance of $32,487.50 after a 60-month term Offer 2: 3.75% annual interest compounded monthly for a 66-month term Assuming no payments are made, what is the difference in the account balances at the end of the loan terms? Round your answer to the nearest penny. $1,245.00 $1,770.87 $2,964.36 $3,319.94
Answers
The difference in the account balances at the end of the loan terms is, $1770.87. So option B is correct
What is simple interest?Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).
Every time we calculate simple interest the principal values will be the same unlike compound interest.
Formula; Simple Interest(I) = P × R × T/100
Given that,
Offer 1- 5.99% annual simple interest, with a total account balance of $32,487.50 after a 60-month term Offer
Offer 2- 3.75% annual interest compounded monthly for a 66-month term
In offer 1,
Total amount A = $32487.50
In offer 2,
Total amount =
[tex]A = P[ 1 + r/n]^{nt}[/tex]
[tex]A = 25000[ 1 + 0.0375/12]^{12*5.5}[/tex]
A = $30,716.63
Difference = 32487.50 - 30716.63
= $1770.87
Hence, the difference in account balance is $1770.87
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Write the domain of the function using interval notation.
Photo added to help answer the question
Answers
The domain of a function refers to the set of all possible inputs for the function.
Write the domain of the function using interval notation?In interval notation, the domain of a function is written as a set of values that the function's input can take on. For example, the domain for the function f(x) = x2 + 3 can be written as the set of all real numbers, or (-∞,∞), or in interval notation, (-∞,∞). This means that any real number can be used as an input for this function, and the output will be a real number as well.Interval notation is a way of writing the domain of a function in a compact form. It describes the range of values that the input of a function can take on. To write the domain of a function in interval notation, one must first identify the set of all possible inputs for the function. Then, one must identify the range of values that the input can take on within this set. This range of values can then be written as an interval in the form (a,b), where a and b are the lower and upper bounds of the interval respectively.For example, the domain of the function y = x2 + 2x + 3 can be written as the set of all real numbers, or (-∞,∞), or in interval notation, (-∞,∞). This means that any real number can be used as an input for this function, and the output will be a real number as well.Interval notation is a useful tool for quickly and concisely writing the domain of a function. It allows for a compact representation of the set of all possible inputs for a function, and is a useful tool for quickly determining the domain of a function.To learn more about the domain of the function using interval notation refer to:
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Cual es el mínimo común múltiplo de 29 y 35?
Answers
Answer:
1015
Step-by-step explanation:
29 es un número primo.
Por tanto:
29*35 = 1015
El mínimo común múltiplo de 29 y 35 es:
1015
PLS HELPP
Which line is parallel to the liney=4x+5?
A)y=-4x+2
B) y=4x+3
C)4x+5
D)y=-1/4x+9
Answers
Answer:
c
Step-by-step explanation:
it is 4×+5 which is easy as u tines it by fixing the sum into parts and its eisier
One-half the sum of two numbers is 12. One of the numbers is three more than two times the other number. What are the two numbers?
Answers
Answer:
The two numbers are 17 and 7
Step-by-step explanation:
Translate this word problem into a math equation
If we let x and y be the two unknown numbers
One-half the sum of two numbers is 12 ==>
sum of two numbers : x + yone-half the sum of two numbers : (1/2)(x + y)one-half the sum of two numbers is 12: (1/2)(x + y) =12
So one equation is 1/2(x + y) =12
Multiplying throughout by 2 gets rid of the denominator:
2 x 1/2 x (x + y) = 2 x 12
x + y = 24 (1)
One of the numbers is three more than two times the other number:
x = 2y + 3
or
x - 2y = 3 (2)
Equation (2) - Equation (1) =>
x + y - (x -2y) = 24 - 1
x + y - x + 2y = 21
3y = 21
y = 21/3
y = 7
With y = 7, substituting in equation 1 gives
x + y = 24
x + 7 = 24
x = 24-7
x = 17
The two numbers are 17 and 7
which of the following sentences are conditional statements? [more than one of the statements may be conditional.] group of answer choices i will order a pizza tonight only if we eat dinner at home. rain delayed the game. are you the only one home? discrete mathematics is required for a computer science transfer degree from foothill college.
Answers
I will order a pizza tonight only if we eat dinner at home is a conditional statement.
Sentences are groups of words that convey complete and logical meaning. They have subjects and predicates. It can be in form of exclamation and questions consisting of main and subordinating clauses.
Conditional statements are sentences where the subordinating clause influences whether the action that will be performed or not in the main clause. In these statements, the subordinating clause is also called the antecedent, and the main clause is called the consequent.
There are two types of Conditional statements, they are Implicative and predictive statements. Implicative sentences are based on facts whereas predictive statements depend on a situation dependent on a hypothetical case.
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Sheila and Dora worked 3 1 2 hours and 5 1 2 hours, respectively, on a programming project. They were paid $198 for the project. How much (in dollars) did each earn?
Answers
Sheila get $77 and Dora get $121 paid.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Sheila and Dora worked 3 1/2 hours and 5 1/2 hours.
Total they get paid = $198.
In one hour the amount of work they done is 7/2 and 11/2.
So, the ratio of their work = (7/2)/ (11/2)= 7/11
So, the amount Sheila get
= 7/18 x 198
= $77
and, the amount Dora get
= 11/18 x 198
= $121
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Factor the expression 48+72 using the GCF
Answers
Using the greatest common factor the expression is factored to be
12 (4 + 6)What is greatest common factor?The largest number among all the common factors of the given numbers is known as the GCF (Greatest Common Factor) of two or more numbers.
The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
The greatest common factor of 48 and 72 is 12
hence we have
12 (4 + 6)
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Mrs. Gaither had 22 students in her
first class of the day. Today, only 18 of
them were present. What fraction of
her students were ABSENT? Write the
fraction in simplest terms.
I NEED IT ASAP PLEASE
Answers
Answer:
2/11
Step-by-step explanation:
Normally 22 kids. 22 kids on the attendance roster.
18 kids say, "Here!" when their name is called.
22 - 18 is 4. 4 kids don't say anything when their name is called because they are at home still. 4 kids absent.
4 out of 22 kids absent. 4/22 kids absent.
4/22 simplifies to 2/11.
2/11 of the kids are absent.
identify the sampling method that was used. fifteen instructors are chosen using random numbers to implement a new learning strategy.
Answers
Random sampling is the sampling method that was used.
Random sampling is a method in which all members of the population have an equal chance of being selected for the sample. In this case, fifteen instructors were chosen using random numbers to implement the new learning strategy.Random sampling is a useful tool when a researcher needs to select a representative sample from a population. By using random numbers to choose the sample, the researcher can ensure that the sample is truly representative of the population. Random sampling also helps to reduce bias, as the researcher has no control over who is chosen for the sample.
To calculate the probability of being chosen for the sample, the formula is (1/n) x 100, where n is the total number of population members. In this case, the population was the group of all instructors, and the sample was the group of fifteen instructors chosen. Therefore, the probability of being chosen is (1/n) x 100 = (1/15) x 100 = 6.67%.
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The bakery sales 9 sugar cookies for every 5 chocolate cookies sold. If the bakery sold 144 sugar cookies, what was the total number of cookies sold?
Answers
Answer:
224 total cookies sold
Step-by-step explanation:
if 9 sugar with every 5 cholates then, 144/9 = 16
so there were 16 times 5 cookies were sold with means
80 cholate cookies were sold
80+ 144= 224
:)
So, if 144 are sugar the total sold
= 144 * 14/9
= 16 * 14
= 224 Answer.
Ben scores 56 out of 79 on a maths test
what percent did he get?
Answers
If Ben scores 56 out of 79 on a maths test. The percentage he get is: 0.7089.
How to find the percentage he got?Using this formula to determine the percentage he got
Percentage gotten = Number of scores / Total score
Where:
Number of score = 56
Total score = 79
Let plug in the formula
Percentage gotten = 56 ÷ 79
Percentage gotten = 0.70886
Percentage gotten = 0.7089 (Approximately)
Therefore we can conclude that he got 0.7089 .
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Please help
The division 7+5i/2-5i, is performed by multiplying the numerator and denominator by
View image
Answers
there are 8 people who would like to share a box of granola bars that contains 8 bars haw many granola bars does each person get if they share equally
Answers
Answer:
One bar each
Step-by-step explanation:
8 people/8granola bars =1 bar each
5. The store is having a sale
on fruit. You can buy 6 kiwi for
$1.50. You can also get 5
mango for $3.00. What is the
total cost of buying 2 kiwis
and 3 mangoes?
Answers
Answer:
Step-by-step explanation:
1.50/6 = 0.25
3/5 = 0.6
0.25*2 = 0.5
0.6*3 = 1.8
1.80+0.50 = 2.30
$2.30
A bowl at a delicatessen contains a mix of 15 apples, 12
oranges, and 9 pears. What is the probability of a customer
who gets one piece of fruit from the bowl randomly choosing
an orange or a pear?
Answers
The probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear is 21/36
What is Probability ?
Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes
Given ,
A bowl at a delicatessen contains a mix of 15 apples, 12 oranges, and 9 pears
so , we have to find the probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear.
Choosing orange or a pear ,
= 12c1 + 9c1
= 12+9
= 21
Total = 36.
Probability = 12 + 9 / 36
= 21 / 36 .
Therefore , The probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear is 21/36
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Carl is preparing to clean out the gutters on his
house. The gutters are 24 feet from the ground.
The bottom of the ladder and the ground make a
60 degree angle. How far away from the house
should the ladder be placed in order to reach the
gutters?
Answers
Answer:
The gutters are 24 ft above the ground. For safety, the distance a ladder reaches up a wall should be four times the distance from the bottom of the ladder to the base of the side of the house. Therefore, the ladder must be 6 ft from the base of the house.
Please answer this question for me
Answers
The criterion that she should use to prove that triangles RST and XYZ are congruent are:
i. Hypotenuse Leg (HL)
ii. Side-Angle-Side (SAS)
What are congruent triangles?When the corresponding properties i.e. length of sides and measure of internal angles of two or more triangles are equal, then the triangles are said to be congruent. The relations can be shown using some theorems.
From the given triangles RST and XYX, it can be observed that;
TR ≅ XZ
RS ≅ XY
<R ≅ <X (given)
<T ≅ <Z (given)
Angles R and X are included angle of the triangles. Thus, the criterion that can be used to show that triangles RST and XYZ are congruent at;
i. Hypotenuse Leg (HL)
ii. Side-Angle-Side (SAS)
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Solve system of equations for unknown variables. X-4=11
Answers
The value of x which makes the equation true is 15.
What is the system of equations?
A system of equations is a set of two or more equations that contain multiple variables. These equations are typically used to describe a real-world situation and are solved simultaneously to find the values of the variables.
To solve a system of equations for unknown variables, you can use one of several methods, such as substitution, elimination, or graphing.
To solve a system of equations such as x-4=11, you have to find the value of x which will make the equation true.
x-4=11
x=15
Hence, the value of x which makes the equation true is 15.
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If m
and mzABD = (4x + 14)°. Find the
measurements of CBD and
Answers
The measure of the angles <ABC and <CBD are 48⁰ and 42⁰
How to calculate the measure of angles?The angle ABC and angle CBD are complementary angles, m <ABC=(3x+6)⁰ and m<CBD=(4x-14)⁰
The angles are complementary which means that they sum to 90⁰
Therefore, we get: <ABC + <CBD = 90⁰
3x + 6 + 4x - 14 = 90 ------ Substituting 3x + 6 and 4x - 14 for < ABC and <CBD
7x = 98
x= 98/7 = 14⁰
Therefore; Measure of <ABC:
Measure of<CBD:
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Correct question:
Find the measure of each angle angle ABC and angle CBD are complementary angles, m angle ABC=(3x+6)degrees, and m angle CBD=(4x-14)degrees stuck on this problem, Thank you fo
State if the three numbers can be the measures of
the sides of a triangle.
4,7,8
Select the correct response:
O True
O False
Answers
True. The three numbers can be the measures of the sides of a triangle.
What is the triangle inequality theorem?
The triangle inequality theorem is a fundamental principle in Euclidean geometry that states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This means that in any triangle, no side can be longer than the sum of the other two sides.
The three numbers 4, 7, and 8 can be the measures of the sides of a triangle. This is because of the triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for any triangle, the sum of two sides must always be greater than the third side.
For example, in this case,
4 + 7 = 11 > 8,
7 + 8 = 15 > 4,
4 + 8 = 12 > 7
Hence, 4, 7, and 8 can be the measures of the sides of a triangle, so the correct response would be "True".
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