The inverse of f(x) is restricted to the domain x ≥ 1, since this is when[tex]x^2 − 2x + 1[/tex] is always greater than 0.
To find the inverse function of f(x), we must first determine the domain of f(x). We can do this by finding the values of x where f(x) is greater than or equal to 0.
We can start by setting f(x) to 0 and solving for x:
[tex]x^2 − 2x + 1 = 0[/tex]
[tex]x^2 − 2x + 1 − 1 = 0 − 1[/tex]
[tex]x^2 − 2x = -1[/tex]
(x − 1)(x − 1) = -1
x = 1
Therefore, the inverse of f(x) is restricted to the domain x ≥ 1, since this is when [tex]x^2[/tex] − 2x + 1 is always greater than 0.
The inverse of a function f(x) is a function that "undoes" f(x). In order to find the inverse of a function, the domain of the function must first be identified. This is done by solving f(x) = 0 and determining which values of x make the equation equal to 0.In the case of f(x) =[tex]x^2[/tex] − 2x + 1, the equation is equal to 0 when x = 1. This means that the inverse of f(x) is restricted to the domain x ≥ 1, since this is when [tex]x^2[/tex] − 2x + 1 is always greater than 0.Once the domain of the function is restricted, the inverse function can be found by switching the x and y values, and solving for the new equation. This process can be used to find the inverse of any function, as long as the domain is appropriately restricted.
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Trigonometry question
The value of sin (θ/2) in the trigonometry is π/9
How to find sin (theta / 2)Information given in the problem
tan θ = 7/8,
where
0 < θ < π/2
solving for θ, from tan θ = 7/8
tan θ = 7/8
θ = arc tan (7/8)
θ = 0.7188 radians
soling for sin (θ/2)
= sin (θ/2)
= sin (0.7188/2)
= 0.3517 approximately π / 9
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Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $725 per week. What were her sales last week if her total earnings for the week were $1,058.25?
Danielle's sales last week were $
Danielle's sales last week were $. At her job at an electronics store, Danielle receives a $4,295.16 commission on every sale.
What is an electronics store?
Courses in calculus (single and multivariable), complex analysis, differential equations (both ordinary and partial), linear algebra, and probability are typically required for jobs in electronics engineering. Additionally, topics like Z-transforms and Fourier analysis are frequently covered in electrical engineering curricula.More mathematics is required for electronics and telecommunications technicians, such as complex numbers, trigonometry, basic geometry, fundamental statistics, and differential and integral calculus.Every subject wants their students to be able to examine mathematics using technology, such as spreadsheets.Let's start by first finding out how much commission Danielle earned last week. We know that her total earnings were $1,058.25 and her base salary was $725 per week. Therefore, her commission must have been:
$1,058.25 - $725 = $333.25
We also know that Danielle earns a 7.75% commission on everything she sells. Let's use "x" to represent her total sales last week. Then we can set up an equation to solve for x:
0.0775x = $333.25
Solving for x, we get:
x = $333.25 / 0.0775
x = $4,295.16
Therefore, Danielle's sales last week were $4,295.16.
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Which ordered pair is a solution of the equation? y=4x-7
A only (2,1)
B only (4, 9)
C both ( 2,10) and (4,9)
D neither
Answer: To find the ordered pair that is a solution of the equation y = 4x - 7, we need to substitute the values of x and y into the equation and see if it is true.
If (x, y) is a solution, then y = 4x - 7 must be true for that particular x and y.
Option A: (2, 1)
Substituting x = 2 and y = 1 into the equation, we get:
1 = 4 * 2 - 7
1 = 8 - 7
1 = 1
Since the equation is true for x = 2 and y = 1, (2, 1) is not a solution of the equation.
Option B: (4, 9)
Substituting x = 4 and y = 9 into the equation, we get:
9 = 4 * 4 - 7
9 = 16 - 7
9 = 9
Since the equation is true for x = 4 and y = 9, (4, 9) is a solution of the equation.
Option C: Both (2, 10) and (4, 9)
Substituting x = 2 and y = 10 into the equation, we get:
10 = 4 * 2 - 7
10 = 8 - 7
10 = 3
Since the equation is not true for x = 2 and y = 10, (2, 10) is not a solution of the equation.
So, the only ordered pair that is a solution of the equation y = 4x - 7 is (4, 9). The answer is B) only (4, 9).
Step-by-step explanation:
how many such strings are if 2 of the ones are to be next to each other and the third is not next to the other two?
The number of strings where exactly two of the ones are next to each other, while the third one is not next to the other two, is (n-1) x (n-2).
In combinatorics, one of the fundamental concepts is counting the number of strings or sequences of symbols that satisfy certain conditions.
Let us first consider the case where the two ones that are next to each other are at the beginning of the string. In this case, we can place the third one in any of the remaining positions, which are n-2, where n is the total length of the string. Therefore, the number of such strings is (n-2).
Similarly, if the two ones are at the end of the string, we can place the third one in any of the n-2 remaining positions, and the number of such strings is again (n-2).
Now let us consider the case where the two ones are in the middle of the string. In this case, we can place the two adjacent ones in (n-2) ways, and the third one can be placed in any of the remaining n-3 positions, since it cannot be adjacent to the other two ones. Therefore, the number of such strings is (n-2) x (n-3).
To get the total number of strings that satisfy the given condition, we need to add up the number of strings in each of the three cases:
Total number of strings = (n-2) + (n-2) + (n-2) x (n-3)
Simplifying this expression, we get:
Total number of strings = (n-1) x (n-2)
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B = { x: 1≤ x ≤ 11 where x is a prime number} What is x?
Answer: x is anything from the set {2, 3, 5, 7, 11}
This is the list of primes between 1 and 11. The value 1 is not prime.
AHHHHHHHHHHHHHHHHHHH
Answer: look at the image for the answer and solution
Step-by-step explanation:
Answer: x = 365
Step-by-step explanation:
find the angle bisector and divide and multiply it
Please help me by determine the value of the missing angle using the inverse trig function
By applying the Pythagorean theorem to the provided question, we can say that in this triangle =>
AC =[tex]\sqrt{115}[/tex]
What exactly is a triangle?Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.
Pythagorean theorem applies here, in this triangle
AC = [tex]A^2 + B^2[/tex]
AC = [tex]\sqrt{14^2 -9^2}[/tex]
AC = [tex]\sqrt{115}[/tex]
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Two more than 3 times a number is 20. Find the number.
Answer: the number is 6
Step-by-step explanation: First, set up an equation. Two more means +2, 3 times a number means 3x. So your equation would be 3x+2=20. Then solve the equation for x.
Answer:
x = 6
Step-by-step explanation:
Let the number be 'x'
Then, the equation becomes,
2 + 3x = 20
3x = 20 - 2
3x = 18
x = 18/3
x = 6
Hope it helped :)
[tex]64x {}^{3} + y {}^{3} [/tex]
factorise fully
Ata school
number of boys : number of girls = 11: 9
There are 124 more boys than girls.
Work out the total number of students at the school.
Answer:
Step-by-step explanation:
Let's call the number of boys "b" and the number of girls "g". From the ratio, we know that b/g = 11/9.
Also, we know that b = g + 124, so we can substitute the second equation into the first:
b/g = 11/9
b = g + 124
g + 124 / g = 11/9
Cross multiply:
9g + 1112 = 11g
Solve for g:
-2g = -1112
g = 556
So there are 556 girls and 556 + 124 = 680 boys at the school.
The total number of students at the school is 556 + 680 = 1236.
On 1 June Sipho opened a savings account at the Postbank that paid 4.5% interest. He deposited R600. Ten days later on 10 June he deposited R1 000.F days later on 15 June he deposited R500. No other deposits or withdrawals w made. Fifteen days later, at the end of the month, the bank calculated the nterest. a. How much simple interest (calculated to the nearest cent) did he earn? . What was the balance of the account at the end of the first 30 days?
Sipho earned R33.15 in simple interest.
The balance of the account at the end of the first 30 days was R2 133.15.
How to calculate thisa. To calculate the simple interest earned by Sipho, we need to calculate the total amount deposited and the interest earned on that amount.
Total amount deposited = R600 + R1 000 + R500 = R2 100
Interest earned = R2 100 x 4.5% x 30/365 = R33.15 (rounded to the nearest cent)
Therefore, Sipho earned R33.15 in simple interest.
b. The balance of the account at the end of the first 30 days can be calculated by adding the total amount deposited and the interest earned to the initial deposit:
Balance = R600 + R1 000 + R500 + R33.15 = R2 133.15
Therefore, the balance of the account at the end of the first 30 days was R2 133.15.
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Simplify the following using the properties of exponents.
Answer:
Step-by-step explanation:
7/x^-8 = 7x^8
please help !!!! i will mark brainliest if correct
Answer:
Step-by-step explanation:
is this a bot or girl
pls hurry! Write the equation for the line in slope-intercept form: y=mx+b.
can someone help please
Answer: x=3, y=-1
Step-by-step explanation:
2x+y=5
2y=2x-8
In equation 1, y=5-2x.
Substitute this value in equation 2.
2(5-2x)=2x-8
10-4x=2x-8
Thus,
4x+2x=10+8 (collecting terms)
6x=18
x=3
Now, we said earlier that y=5-2x.
Therefore, y=5-2(3) [because x=3]
y=5-6
y=-1
Hope this helps :]
What are some fast animals you can think of? What are some slow wins? How can fast can you run? Think about how you can predict who would win this race. Research the speed of at least four different animals. Then time how long it takes you to run 1/4 mile. If you and these four types of animals ran a marathon at those speed to win? How far into the race with the four other racers be when the winner cross the finish line? Would a sport article or research or record a sports new cast to predict the outcome of this race. Use the information you learned in this topic to justify your predictions. PLEASE HURRY!!!!
The answers include the following:
Some fast animals are cheetah, falcon.Some slow animals are snail, slug etc.Speed of cheetah is 114 km/hr, speed of lion is 81 km/hr. speed of snail is 0.048km/hr and speed of deer is 48.2km/hr.The time it will take me to run 1/4 mile is 2 minutes.Yes, a sport article or research or record a sports new cast to predict the outcome of this race.What is Speed?This is referred to as the ratio of distance to the time in which the distance was covered and it is a scalar quantity.
Sport article or research or record a sports new cast will be able to predict the outcome of this race due to the data being gathered which will provide more information about the race.
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7. Mark starts out the week with $8. Every day he gives sister $2. Write an equation and
graph the situation. What is the meaning of the values when x is greater than 4?
Answer:
y = -2x + 8
When x = 4, Mark has no more money , so when x is greater than 4, Mark is in debt or is not able to give his sister any more money.
Step-by-step explanation:
how many pattern block triangles would create 2 hexagons
To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Six triangles are needed for each hexagon.
To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Each hexagon requires six triangles to make it, so two hexagons would need double that amount. Since the pattern blocks come in the shapes of triangles, you can easily construct the hexagons by placing the triangles together. Each triangle has two sides that fit together and two sides that overlap, so the six triangles will create a complete hexagon when they are all put together. Once you have two hexagons constructed, they will fit together to make a larger shape, depending on how you place them. With this method, you can easily make two hexagons out of pattern blocks.
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While racking a circuit breaker in energized gear, what means could be used to reduce the arc flash hazard to 0 incident energy exposure to a worker?
The only way to completely eliminate the risk of arc flash is to de-energize the equipment before performing any maintenance or testing.
Racking a circuit breaker in energized gear poses a significant arc flash hazard to workers due to the potential for electrical energy to be released and cause an arc flash.
If it is not possible to de-energize the equipment, the following means could be used to reduce the arc flash hazard to 0 incident energy exposure to a worker:
Use remote racking: Remote racking systems allow workers to rack circuit breakers from a safe distance, reducing the risk of exposure to the arc flash hazard.Wear personal protective equipment (PPE): Workers should wear appropriate PPE.Implement an energy control program: An energy control program should be in place to ensure that workers are properly trained.Use a remote video camera: A remote video camera can be used to monitor the racking process from a safe distance, allowing workers to rack circuit breakers without being in the line of fire.Learn more about circuit breaker here:
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yall know what the blanks are supposed to be??????
Answer: Region Z
Step-by-step explanation: Region X is smaller than Region Y, while Region Y is smaller than Region Z.
Harvey has some 1 bills and some 5 in all he has 6 bills worth 22 let x be the number of 1 bills and let y be the number of 5 bills write a system of equations to represent the information and use substitution
which of the following is an example of a statistic? a.) average number of all high school graduates who will attend college b.) standard deviation of tuition costs for all private universities c.) 25 random students are asked how much they spent on books d.) summary value of a population
25 random students are asked how much they spent on books is an example of a statistic.
The primary areas of study in statistics include data collection, organization, organization, analysis, interpretation, and presentation. It is customary to begin with a statistical population or a statistical model that will be examined when applying statistics to a scientific, industrial, or social problem. There are many different groups of people or things that can be referred to as populations, such as "each person living in a country" or "each atom making up a crystal." Every aspect of data is covered by statistics, including the planning of data collection in terms of survey and experiment design. Statisticians gather data using custom experiment designs and survey samples in the absence of census data.
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Multiply and simplify. Show work to earn full credit. (2 − 3)(7 2 − + 8
We can make advantage of the distributive property of multiplication over addition, which says that a(b + c) = ab + ac. As a result, -55 is the simplified expression.
What is distributive property, and what are some examples?When you multiply a value by a sum, the distributive property of multiplication over addition is put to use. For instance, you wish to multiply 5 by the product of 10 plus 3. Since the numbers are similar terms, we typically add the numbers first and then multiply by 5=> 5(10 + 3) = 65.
What is distributive property class 7?An algebraic principle known as the distributive property indicates that it is necessary to multiply each of the two integers by the factor being multiplied by the sum or difference of two terms.
Using this property, we can expand the expression as follows:
(2 − 3)(7 2 − + 8) = 2(7 2 − + 8) − 3(7 2 − + 8)
Now we can simplify each term separately:
2(7 2 − + 8) = 2(49 − 2 + 8) = 2(55) = 110
and
−3(7 2 − + 8) = −3(49 − 2 + 8) = −3(55) = −165
Therefore, putting the results together, we have:
(2 − 3)(7 2 − + 8) = 110 − 165 = -55
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Pls solve 3,4,5!!! Tyyy (I will mark brainliest!)
Answer:
Step-by-step explanation:
4 = d
5=1/5
3 the first one is 4x1/12 and 2x3/12
Pls help me fast fast fast
The value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "."
The two triangles are similar thus the measure of its angle are also equal.
Using the similar triangle we have:
Angle D = Angle A = 82 degrees.
Angle F = 67 degrees
Using the sum of interior angles of triangle we have:
∠D + ∠F + ∠E = 180
82 + 67 + ∠E = 180
∠E = 31
From the figure we observe that,
∠E + ∠G = 180 (straight line)
31 + ∠G = 180
∠G = 149
Hence, the value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.
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Kirk prepared 24 kilograms of dough after working 4 hours. How much dough did Kirk prepare if he worked for 7 hours? Solve using unit rates.
If Kirk had worked for 7 hours he would have made 42 kg of dough.
What is unit rate?A unit rate means a rate for one of something.
Given that, Kirk prepared 24 kilograms of dough after working 4 hours, we need to find the amount of dough if he worked for 7 hours.
Calculating the unit rates,
Since, he worked for 4 and made 24 kg,
So, in 1 hour = 24/4 = 6 kg
Therefore, in 1 hour he will make 6 kg
Therefore, in 7 hours he will make = 7x6 = 42 kg
Hence, If Kirk had worked for 7 hours he would have made 42 kg of dough.
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What is the perimeter of a square if the area is 49cm^2
Answer:
Step-by-step explanation:
take length as x,
perimeter= 28cm
Answer:
28cm
Step-by-step explanation:
7+7+7+7
The distance between Dallas and Houston is about 364 kilometers. There are approximately 8 kilometers in 5 miles. Which measurement is closest to the number of miles between these two towns?
Answer: Approximately 226 miles
Step-by-step explanation:
Km. to Mi.
364 = 226
Question 2: Express each of the following numbers using exponential rotation
a. 343 b. 3145
Use the net to find the surface area of the prism.
5 in.
12 in.
13 in.
8 in.
Step-by-step explanation:
Rather than give you the full answer, let me point out the things that you need to know to work this out for yourself.
The surface area of the solid is the sum of all of the areas of its faces.
The area of a right triangle is a well-known formula. You should already know this.
