The equation of the inverse function is f'1(x) = x^2 + 6 and the domain is all set of real numbers
How to determine the inverse functions?The function f(x) is given as
f(x) = √x -6
Rewrite as
y = √x -6
Switch/swap the positions of x and y in the above equation
The equation becomes
x = √y -6
Make y the subject of the formula in the above equation
The equation becomes
y - 6 = x^2
Add 6 to both sides
y = x^2 + 6
Rewrite as an inverse function
f'1(x) = x^2 + 6
Hence, the inverse function is f'1(x) = x^2 + 6
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Answer:
f(×)=(×+6)^2;×>-6 there we go..
Write an equation of the line that passes through each pair of points
[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-10)}}} \implies \cfrac{-9}{2 +10} \implies \cfrac{ -9 }{ 12 }\implies -\cfrac{3}{4}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{3}{4}}(x-\stackrel{x_1}{(-10)}) \implies y -4= -\cfrac{3}{4} (x +10) \\\\\\ y-4=-\cfrac{3}{4}x-\cfrac{15}{2}\implies y=-\cfrac{3}{4}x-\cfrac{15}{2}+4\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-\cfrac{7}{2} \end{array}}[/tex]
The school that Brenda goes to is selling tickets to a choral performance. On the first day of
ticket sales the school sold 14 adult tickets and 5 student tickets for a total of $140. The school
took in $190 on the second day by selling 10 adult tickets and 10 student tickets. What is the
price each of one adult ticket and one student ticket?
The price of one adult ticket is $5 and one student ticket is $14
What is algebra ?Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.
Given that : first day of ticket sales the school sold 14 adult tickets and 5 student tickets for a total of $140. The school took in $190 on the second day by selling 10 adult tickets and 10 student tickets.
Let the price for adult ticket x and for student ticket y
we have ,
14x + 5y =140.....(i)
10x + 10y = 190....(ii)
10 x + 10y = 190
x + y = 19
y = 19-x .....(iii)
put the value of y in equation i
14x + 5(19-x) = 140
14x + 95 - 5x = 140
9x = 45
x = 5
Now put value of x in equation iii
y = 19 - 5
y = 14
The price of one adult ticket is $5 and one student ticket is $14
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Do the ordered pairs represent a function?
Answer: A.
Step-by-step explanation:
Something is a function if the x value is not repeated. The y value can be repeated however.
The stemplot shows how much money a sample of high school students makes per month.
Use the stemplot to answer the questions.
The mean paycheck is $.
The mean is a .
This mean paycheck indicates that
The sum of the values is
[tex]67+85+92+123+147+181+181+196+198+213+252+277+287+325+459=3083[/tex]
Dividing this by the number of values, which is 15, the mean is 3083/15.
The mean is a measure of central tendency, and indicates that people make an average of about $205.53 per month.
Answer:
Use the stemplot to answer the questions.
The mean paycheck is $
✔ 205.53
.
The mean is a
✔ statistic
.
This mean paycheck indicates that
✔ on average, students earned $205.53 per paycheck
.
Step-by-step explanation:
edge 2023
What is the amplitude of the function y = sin 5лx?
The amplitude of the function y = sin 5лx is found as 1.
What is defined as the amplitude of function? The maximum deviation of a variable out of its mean value is referred to as its amplitude. The amplitude formula aids in the calculation of the cosine and sine functions. A is the symbol for amplitude. The amplitude formula can also be conveyed as the average of the sine or cosine function's maximum and minimum values.The sine (or cosine) function can be written as,
x = A sin (ωt + ϕ) or x = A cos (ωt + ϕ)
x = displacement of wave (meter)A = amplitudeω = angular frequency (rad/s)t = time periodϕ = phase angleTo find the variables used to calculate the amplitude, use the formula;
y = asin(bx - c) + d.
Where a is the amplitude.
The given equation of function is y = sin 5лx.
Comparing the function with the standard form
a = 1
Thus, the amplitude of the function y = sin 5лx is found as 1.
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I have tried multiplying it by 0.5 or 50% and dividing it by 0.5 ( by it i was meaning the 10*10*2)
It is to be noted that the height of the bread is 5 centimeters. The hint given is in the information about the surface area. See the explanation below.
What is the surface area?In this case, the surface area of bread is the total sum of the area of the base and perimeter. The surface area of the bread is given below.
That is:
A = 2 x b + p x H,
Where b is the area of the base, p is the perimeter of the base and h is the height.
Recall that it is stated that 50% of the surface area of the bread is the crust.
The implication is that the surface area of both sides of the base is equivalent to the surface area of its perimeter.
That is:
2 x b = p x h
We can compute the perimeter of the bread as:
P = 4 x length
p = 4 x 10
p = 40cm
The area of the base is:
b = 10 x 10
b = 100cm²
Substituting the values in the above formula,
2 x 100 = 40 x h
200 = 40h
h = 200/40
h= 5cm.
Hence the height of the bread is 5cm.
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The equation y=0.52x+186 gives the cost y of renting a car if the care is driven x miles. Based on this equation, for every mile the car is driven the cost of increases by how much?
For every mile the car is driven, the cost increases by 0.52 units.
Consider a line that passes through the origin at a distance 'a' from the Y-axis and has a slope of m. In this situation, the distance an is the definition of the line's y-intercept. At this moment, the line will cross the y-axis (0, a). The equation for the line will then be y = mx + a. The same goes for a line that crosses the X-axis at a position b from the origin and has a slope of m. (b,0). The distance b is the line's x-intercept. The equation for the line will be y = m* (x-b)
Given, the equation that relates cost of renting and miles driven is
y = 0.52 x + 186
Therefore, for a car travelling one mile, cost is y₁ = 0.52*1 + 186 = 186.52
For a car travelling two miles, cost is y₂ = (0.52*2) + 186 = 187.04
Thus, for every next mile the cost increases by = y₂ - y₁ = 187.04 - 186.52 = 0.52 units
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helppppppppppppppppp
Answer:
C
Step-by-step explanation:
Ram, a self-employed salesperson, purchased two to a september 2021 concert for himself and a prospective client. he also took the client out to dinner prior to the show. the tickets cost $200 each and the meal cost $110. how much may ram deduct as a business expense?
Answer:
$620 Ram deduct as a business expense.
Step-by-step explanation:
GIVEN-
Ram, a self-employed salesperson, purchased two for a September 2021 concert for himself and a prospective client. he also took the client out to dinner before the show;
The tickets cost $200.
The meal cost $110.
to answer-how, much may ram deduct as a business expense?
total expense for two persons =$200*2+$110*2
=$620
$620 ram deduct as a business expense
Answer:
no 110 tax cuts and job act took away tickets and entertainments
Step-by-step explanation:
Find the value of the exterior or interior angle!!
Answer:
137°
Step-by-step explanation:
By the exterior angle theorem, [tex]m\angle JKX=93^{\circ}+44^{\circ}=137^{\circ}[/tex].
In the rectangle below
What is the value of (−15)3 when evaluated? 3,375 45 −225 −3,375
The value of the exponential form (-15)³ is -3375.
The f(x)= exp (x) or eˣ are used to represent the exponential function in mathematics (where the argument x is written as an exponent).
The term typically refers to the positive-valued function of a real variable, unless otherwise specified, though it can also be extended to the complex numbers or modified to refer to other mathematical objects like matrices or Lie algebras. The exponential function originated from the concept of exponentiation, or repeated multiplication; but, more recent definitions—of which there are many that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.We know that any exponential form such as (-15)³ can be written as
-15×-15×-15 = -3375
Therefore the solution of the exponential form is -3375 .
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Elijah buys 112worth of stereo equipment from stereo store there is a 2.5 processing fee for using a credit card what is the totalcost of the stereo equipment
By using percentage, we conclude that the total cost of the stereo equipment is $114.8.
The worth of stereo equipment is $112 and there is a 2.5% processing fee for using a credit card.
Whenever we purchase anything with a credit card we have to pay a processing fee that a Bank charges.
To find the total cost of the stereo equipment, we have to add the worth of the stereo equipment and processing fee for using a credit card.
And to find the processing fee for using a credit card, we have to calculate 2.5% of the worth of the stereo equipment.
So, 2.5/100 x 112 = 2.8
Therefore, the required processing fee for using a credit card is $2.8.
The total cost of the stereo equipment = $112 + $2.8 = $114.8
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The population of a town is increasing by 300 inhabitants each year. If its population at the beginning of 1990 was 27,541, what was its population at the beginning of 1995?
Answer:
29041
Step-by-step explanation:
1995-1990
300×5=1500
27541+1500=29041
The population of a city decreases by 1.7% per year. If this year's population is 366,000, what will next year's population be, to the nearest individual?
The population of the city next year, after decreasing, will be 359,778
Here, we are given that the population of a city decreases by 1.7 percent per year.
This, means that the city's population will decrease by 1.7% in 1 year, (1.7 × 1.7)% in 2 years and so on.
The population of the city this year is given to be 366,000.
Thus, next year, the population will decrease by-
1.7% of 366,000
= 1.7/100 × 366,000
= 17/10 × 3,660
= 17 × 366
= 6,222
Thus, the city's total population next year will be-
366,000 - 6,222
= 3,59,778
Hence, the city's population to the nearest individual comes out to be 359,778.
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please helpp i have a test tmr
The answer is X= 3, -2
is 2y-3>11 a expression equation or inequality
Answer:
Inequality
Step-by-step explanation:
An expression is a mathematical phrase that contains numbers, variables, or both. Expressions never have an equal sign. An equation is a mathematical sentence that says two expressions are equal.
SHOW YOUR WORK FOR BRAINLIEST
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
The answer is 33.6
Answer:
Explanation below:
Step-by-step explanation:
So basically x is the diameter - so is the radius times by 2
The radius is the length from the center of the circle to the edge which in this case is 7.9 + 8.9 = 16.8
So from this we have worked out the radius which is 16.8
But x is the diameter so we have to times 16.8 by 2 which gives 33.6
As a football team kept winning, the attendance of their games increased. Use Demos (or calculator) to write a linear equation to model this data.
The data:
Game # ||| Attendance
1. 722
2. 763
3 772
4 826
5 815
6 857
7 897
A line of best fit (linear equation) to model this data is y = 27x + 699.43
What is a line of best fit?A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.
In this scenario, the game would be plotted on the x-axis of the scatter plot while the attendance would be plotted on the y-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that a linear equation for the line of best fit is given by:
y = 27x + 699.43
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4(13+5) what is the value of the expression
Answer: 22
If the question is to add them all together then the answer will be 22.
Hope this helps
Step-by-step explanation:
The graph shows a polynomial function. The domain of the function is -4.2 ≤x≤4.7. What is the range of the function?
Answer: :( I don’t know how to solve the problem
Step-by-step explanation:
brainlyist Write a paragraph proof. Given: ∠1≅∠4; Prove: 2≅∠3
From the figure given the required prove is achieved using transitive property of equality to show that 2 ≅ ∠3
What is transitive property of equality
The term transitive property of equality is used in situation where say three values: x, y, and z are related as follows
if x = y and y = z then x = zHow to Prove that 2 ≅ ∠3
given data
Given: ∠1 ≅ ∠4
Information deduced from the figure
∠1 ≅ ∠2 vertical opposite angle∠4 ≅ ∠3 vertical opposite angleHence we can say that ∠2 ≅ ∠3 using the transitive property of equality
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Find three consecutive odd integers such that the sum of three times the smaller and twice the largest is equal to one less than four times the middle. find the integers.
Answer:
-1, 1, 3
Step-by-step explanation:
Let x equal the first odd integer.
The three consecutive odd integers would be represented by x, then x+2, then x+4.
So 3x + 2(x + 4) = 4(x + 2) - 1
Solve for x
3x + 2x + 8 = 4x + 8 -1
5x + 8 = 4x + 7
x = -1
Solve the problem
A = (50+50)
B=(85*85+A)
C = (15*0.9+B)
D = (10*15+4+C)
Answer:
7,492.5
Step-by-step explanation:
Solve the problem
A = (50+50)
B=(85*85+A)
C = (15*0.9+B)
D = (10*15+4+C)
10*15+4+15*0.9+85*85+50+50=
150+4+13.5+7,225+100=
7,492.5
Answer:
A= 100
B= 7,325
C= 7,338.5
D= 7,492.5
Factor a² + 3a- 18
I’m having Trouble with math , 2.3 part 2&3, trinomials of the form
Answer:
Step-by-step explanation:
(a+6)(a-3)
2a + 3b and 6x +10y =40
what is the value of 6a+9b what is the value of 3x +5y
2a + 3b = 7
-> 3(2a + 3b) = 21
6x + 10y = 40
-> (6x+10y)/2 = 20
Therefore, 6a + 9b = 21 ; 3x + 5y = 20.
The value of 6a + 9b is 21 and the value of 3x + 5y is 20
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equations are,
2a + 3b = 7 (1)
and 6x + 10y = 40 (2)
To find the value of 6a + 9b,
Multiply equation (1) with 3,
3(2a + 3b) = 7 x 3
6a + 9b = 21
To find the vale of 3x + 5y,
Divide equation (2) by 2,
1/2(6x + 10y) = 40/2
3x + 5y = 20
The required values are 21 and 20.
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Jeweler has 36 inches of silver chain. she needs 4 times that much to make some necklaces and 3 times that amount to make some bracelets. how much silver chain does the jeweler need to make her necklaces and bracelets? the jeweler needs necklaces and bracelets. inches of silver chain to make her
Jeweler needs 144 inches of silver chain to make the necklaces and 108 inches of silver chain to make the bracelets.
What is defined as multiplication?Multiplication, along with addition, subtraction, and division, is one of the four fundamental arithmetic operations. Multiplication in mathematics refers to the repeated addition of gatherings of equal size.The signs cross (x), asterisk (*), and dot (.) represent multiplication.The commutative property states so when we multiply 2 numbers, the order has no effect on the product.The Associative Property states because if we multiply three or more numbers one after the other, this same order does not matter.For the given question;
The total length of silver chain jeweler had = 36 inches.
Length of silver chain required to make necklaces = 4 times.
So, multiply 36 with 4 to get the result;
36 x 4 = 144.
Thus, the silver chain required to prepare the necklaces is 144 inches.
For the making of bracelets = 3 times the length of silver chain.
So, multiply 36 with 3 to get the result.
36 x 3 = 104
Thus, the length of silver chain required to prepare bracelets is 104 inches.
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Avani and her children went into a grocery store and will buy peaches and mangos.
Each peach costs $0.75 and each mango costs $1.75. Avani has a total of $15 to spend
on peaches and mangos. Write an inequality that would represent the possible values
for the number of peaches purchased, p, and the number of mangos purchased, m.
The inequality which represents the possible values for the number of peaches and mangos purchased will be;
⇒ $0.75p + $1.75m = $15
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Avni and her children went into a grocery store and will buy peaches and mangos.
Each peach costs $0.75 and each mango costs $1.75.
And, Avni has a total of $15 to spend on peaches and mangos.
Now,
Let number of peaches purchased = p
And, Number of Mangos purchased = m
Since, Each peach costs $0.75.
Hence, Total cost of peaches purchased = $0.75p
And, Each mango costs $1.75.
Hence, Total cost of mangos purchased = $1.75m
Since, Avani has a total of $15 to spend on peaches and mangos.
So, An inequality that would represent the possible values of peaches and mangos will be;
⇒ $0.75p + $1.75m = $15
Thus, The inequality which represents the possible values for the number of peaches and mangos purchased will be;
⇒ $0.75p + $1.75m = $15
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The area of a rectangle is 280 and one dimension is 14. What is the other dimension?
Answer:
20
Step-by-step explanation:
280 divided by 14 is 20
Area= (length)(width)
280= (14)(x)
280=14x
divide by 14
20=x
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Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.
2
3
4
5
Answer:
k = 4
Step-by-step explanation:
g(x) higher than by 4 units
Answer:
k = 4
Step-by-step explanation:
'k' represents the vertical translation