By using the concept of function, it can be calculated that
[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here, the function is
[tex]f(x) = 2x + \frac{4}{3}\\[/tex]
Let f(x) = y
[tex]2x + \frac{4}{3} = y\\\frac{6x + 4}{3} = y\\[/tex]
6x + 4 = 3y
6x = 3y - 4
[tex]x = \frac{3y - 4}{6}[/tex]
[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]
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Which choice is equivalent to the fraction below 2/√x - √x+2
The fraction is equivalent to the [tex]\sqrt{x+2}-\sqrt{x}[/tex].
The correct option is (C).
Given,
The fraction is given as:
[tex]\frac{2}{\sqrt{x} -\sqrt{x+2} }[/tex]
To find the above fraction which choice is equivalent to the fraction?
Now, According to the question:
Simplify or expand
[tex]\frac{2}{\sqrt{x} -\sqrt{x+2} }[/tex]
Rationalize the denominator:
[tex]\frac{2(\sqrt{x} -\sqrt{x+2} )}{(\sqrt{x} -\sqrt{x+2})(\sqrt{x} -\sqrt{x+2} ) }[/tex]
Expand the expression:
[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{(\sqrt{x})^2-(\sqrt{x+2} )^2 }[/tex]
[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{x-(x+2)}[/tex]
[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{-2}[/tex]
Determine the sign and cross out the common factor:
[tex]\sqrt{x+2}-\sqrt{x}[/tex]
Hence, The fraction is equivalent to the [tex]\sqrt{x+2}-\sqrt{x}[/tex].
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Calculate capital if assets are £451,100, liabilities are £20,500, income is £351,200 and expenses are £270,600.
The capital is £430,600.
Define capital.
The money that a company has on hand to support both its current operations and potential expansion is known as capital. One source of funding for it is the earnings from its operations. When calculating a company's capital worth, all of the company's physical assets and financial assets would be included (minus its liabilities).
The capital account—also referred to as the capital and financial account—records the net flow of investment transactions into an economy and is used in macroeconomics and international finance.
Solution Explained:
Given, Assets = £451,100 and liabilities = £20,500
Capital = Assets - Liabilities
= 451100 - 20500
= £430,600
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Start Fraction w superscript 12 baseline over w superscript 18 baseline End Fraction
A. w30
B. w–30
C. w6
D. w–6
Answer:
answer should be d
Step-by-step explanation:
it's d because if u fraction 6 u will get d
A rectangular playground is enclosed by 440 feet of fencing. If the length of the playground is 20 feet less than 3 times the width, find the dimensions of the playground.
The dimensions of the playground are;
Width = 60 feet
Length = 160 feet
How to determine the dimensionsThe formula for calculating perimeter of a rectangle is expressed as;
Perimeter = 2( l + w)
Where;
l is the length of the rectanglew is the width of the rectangleWe have the values as;
Perimeter = 440 feet
Length = 3w - 20
Width = w
Now, substitute the values into the formula, we have;
440 = 2( 3w - 20 + w)
expand the bracket
440 = 2( 4w - 20)
440 = 8w - 40
collect like terms
8w = 480
Make 'w' the subject of formula
w = 60 feet
Length = 3(60) - 20
Length = 180 - 20
Length = 160 feet
Hence, the values are 60feet and 160 feet
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I am running out of points please help I have 13
Answer:
(A∩B)={1,15}
Step-by-step explanation:
A ship sails at a speed of 36 nautical miles per hour due east. An hour later it changes its direction to N 32° E and continues at the same speed and direction for a half hour. At this point, what are the ship's distance and direction of bearing from the starting point? Round your answers to the nearest hundredth:
The ship is____________ nautical miles from the starting point at a directional bearing of N _______ ° E.
The distance and direction of the ship from the starting point is found using vectors as follows;
The ship is 48.03 nautical miles from the starting point at a directional bearing of N 18.53° E
What are vectors?A vector is a quantity that has a property of magnitude or size and direction.
The ship's speed = 36 nautical miles per hour
Direction of the ship = Due east
The duration the ship continues in the direction = 1 hour
The new direction of the ship = N32°E
The duration in which the ship continues in the new direction = Half an hour
The vector of the distances traveled by the ship are;
[tex]\overrightarrow{d_1}[/tex] = 36·i
[tex]\overrightarrow{d_2}[/tex] = 0.5 × 36×sin(32°)·i + 0.5 × 36×cos(32°)·j = 18×sin(32°)·i + 18×cos(32°)·j
The sum of the distances traveled by the ship is therefore;
36·i + 18×sin(32°)·i + 18×cos(32°)·j = (36 + 18×sin(32°))·i + 18×cos(32°)·j
(36 + 18×sin(32°))·i + 18×cos(32°)·j = 45.54·i + 15.26·j
The distance of the ship from the starting point, d, is therefore;
d ≈ √(45.54² + 15.26²) ≈ 48.03
The distance of the ship from the starting point is approximately 48.03 miles.
The direction from the North of the ship from its starting point, θ, is therefore;
[tex]\theta = arctan\left(\dfrac{15.26}{45.54} \right) \approx 18.53^{\circ}[/tex]
Then direction of the ship is N 18.53° E
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Given: AB=BC AC < bisector of
Considering the given figure we have that
< BAC = < CAD definition of angle bisection
< BAC = < BCA base angles of isosceles triangle
What is angle bisection?This refers to when angles are being shared or divided into two equal parts.
In the given problem, line AC is the bisector of < BAC. creating wo equal angles in the process. hence
< BAC = < CAD definition of angle bisection
Triangle BAC is an isosceles triangle, since the sides BA and BC are equal. the angles are also equal therefore
< BAC = < BCA base angles of isosceles triangle
Line AC is also a transversal line, connecting the two parallel lines BC and AD. This creates opportunity for alternate angle theorem
< BCA = < CAD alternate internal angle theorem
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Graph the polygon with the given vertices and its image after a reflection in the line y=x.
A(2, -1), B(-1, 2), C(2, 3), D(4,2)
In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).
Graphing the polygon and reflection in a graph:
A polygon is a 2 - dimensional shape, that is formed by three or more straight edges. To graph, a polygon, plot the given points on the plane and connect the vertices using straight lines, without crossing any lines.
Reflecting image in the line y = xTo reflect the image in the line y = x, switch the values of x to y and y to x. After switching the points, join the formed points and draw the reflected image.
Here we have
A(2, -1), B(-1, 2), C(2, 3), D(4,2)
After switching the values of x to y and y to x the resultant points are
A'(-1, 2), B'(2, -1), C'(3, 2), D'(2,4)
In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).
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Select all of the numbers that are correctly written in scientific notation.
A. 42 times 10 superscript 5 baseline
B. 1.1 times 10 superscript 4 baseline
C. 7.0 times 20 superscript 4 baseline
D. 6.01 times 10 superscript negative 4 baseline
E. 18 point 0 time 10 cubed
The numbers that are correctly written in scientific notation are:
B) 1.1 x 10⁴D) 6.01 x 10⁻⁴.What is scientific notation?Scientific notation is a shorthand (approximate) manner of writing long or short numbers using decimal forms raised to 10 power a baseline.
The rules for correctly writing a scientific notation include the following:
The base should always be 10. The exponent must be a non-zero integer (either positive, like option B, or negative, like option D). The absolute value of the coefficient is greater than or equal to 1 but should be less than 10.Coefficients can be positive or negative numbers including whole and decimal numbers.Thus, the scientific notation rules are correctly satisfied by Options B and D, unlike Options A, C, and E.
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Answer Options:A) 42 x 10⁵
B) 1.1 x 10⁴
C) 7.0 x 20⁴
D) 6.01 x 10⁻⁴
E) 18.0 x 10³
Use Structure A shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The store decides to discount the packs of socks by 40%. Is the discounted price $5?
Multiple choice question.
cross out
A)
yes; The packs of socks are marked up to $7 and then discounted to $5.
cross out
B)
yes; The packs of socks are marked up to $9 and then discounted to $5.
cross out
C)
no; The packs of socks are marked up to $7 and then discounted to $4.20.
cross out
D)
no; The packs of socks are marked up to $5.20 and then discounted to $4.99.
The correct option regarding the price is C. no; The packs of socks are marked up to $7 and then discounted to $4.20.
How to calculate the price?In this situation, a shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The price will be:
= Original price + Markup
= 5 + (40% × 5)
= 5 + 2
= $7
Then, the store decides to discount the packs of socks by 40%. This will give a price of:
= 7 - (40% × 7)
= 7 - 2.8
= $4.2
The price isn't discounted to $5.
In conclusion, the correct option is C.
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A sample of 39 customers was taken at a local computer store. The customers were asked the prices of the computers they had bought. The data are
summarized in the following table.
Number of computers Price (in dollars)
13 - 2300
11 - 1800
15 - 2150
Find the mean price for this sample. Round your answer to the nearest dollar.
The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47
What is mean?A group of two or more numbers is simply averaged mathematically to get the term "mean." There are several ways to calculate the mean for a given collection of numbers, including as the arithmetic mean approach, which utilizes the sum of the series' values, and the geometric mean method, which uses the average of a group of products. However, the majority of the time, the results from all of the main approaches to calculating a simple average are roughly the same.acc to our question-
Mean price = total amount spent on computers / number of computers= (6*900 +18*800+14*2600+5*1750)/(6+18+14+5) =64,950/43 = 1510.47x f fx900 6 5400800 18 144002600 14 364001750 5 875043 64950xbar = Σxf/Σf = 64,950/43 = 1510.47hence,The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47
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Productive Investments Limited provided the
returns for Laska stocks for 2017 to 2021. Use the
information supplied to answer the questions below.
Year
2017
2018
2019
2020
2021
Laska return
-2.2%
-3.4%
12.5%
-0.8%
8.6%
a) Calculate the range of the market returns. (2
Marks)
b) Calculate the mean market return for 2022 (2
Marks).
c) Calculate the variance of the market returns (6
Marks).
d) Calculate the standard deviation of the market
returns (2 Marks).
e) Comment on your results (4 Marks).
The range of market return is 15.9% and the mean of market return is 2.94%
Productive Investments Limited provided the returns for Laska stocks for 2017 to 2021.
Year Laska return
2017 -2.2%
2018 -3.4%
2019 12.5%
2020 -0.8%
2021 8.6%
The range of market return = Highest return - lowest return
= 12.5 - (-3.4)
= 15.9%
mean market return = (-2.2 +(-3.4) + 12.5 +(-0.8) + 8.6)/5
mean market return = 2.94%
Therefore, the range of market return is 15.9% and the mean of market return is 2.94%
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Marissa has a savings account with $48 in it that earns 2% simple
interest per year.
How much money, to the nearest penny, will Marissa have in 7 years?
Give your answer in dollars.
Marissa will have $720 in 7 years when she has $48 in her saving account that earns 2% simple interest per year.
What is simple interest?Simple interest is a quick and simple approach to figuring out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of many forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest.S.I. = P R T,where
P = Principal, R = Rate of Interest in% per annum, and T = Time periodThe interest rate is expressed as r/100 and is expressed as a percentage or r%.Principal: The principal is the sum that was first invested or borrowed from the bank. P stands for the principal.Rate: Rate is the interest rate at which the principal sum is granted to someone for a specific period of time; examples of rate interest are 5%, 10%, and 13%. R stands for the interest rate.Time: The amount of time that the principal is given to someone. T represents time.Amount: When a borrower repays a bank loan, the term "Amount" refers to the sum of the principal borrowed plus the interest paid.Amount = Principal + Simple Interest or A = P(1 + RT)Calculation
From, A = P(1 + RT)
where, p = $48
R = 2%
T= 7 years
A = 48(1 + 2*7)
A = $720
Hence, Marissa will have $720 in her bank account after 7 years.
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right answers only please
Given graph represent the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
Given,
In the question;
The equation is:
g(x) = - [tex]x^{2} (x -2)[/tex] or h(x) = [tex]x^{2} (x -2)[/tex]
To find the is this the graph of g(x) or h(x).
Graph is given in the figure.
Now, According to the question;
g(x) = [tex]-x^{2} (x -2)[/tex] and h(x) = [tex]x^{2} (x -2)[/tex]
g(x) = 0 h(x) = 0
[tex]-x^{2} (x -2) = 0[/tex] [tex]x^{2} (x -2)[/tex] = 0
x = 0, 2 x = 0, 2
If we put x = 1 then,
g(1) = [tex]-(-1)^2(1-2)[/tex] and h(1) = [tex](1)^2(1-2)[/tex]
g(1) = -1 (-1) h(1) = 1(-1)
g(1) = 1 h(1) = -1
But as shown in graph, graph take positive value at x = 1
∴Given graph is the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
Hence, Given graph represent the graph of g(x) = [tex]-x^{2} (x -2)[/tex]
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A rectangle has an area of 14y³ - 63y.
a. What are expressions for the length and width where one dimension is
the GCF?
pls help.
The length and breadth expressions where one dimension is the GCF are; 7y and (2y²-5).
Area of a Rectangle
Given that a rectangle is a two-dimensional shape with one of the dimensions being the GCF, as specified in the question;
Consequently, the length and breadth expressions are 7y and (2y²-5) respectively.
Additionally, the rectangle's area when y=2 is; 14(2³) - 35(2) = 52.
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simplify this expression-12÷3×(-8+(-4)²-6)+2
Answer: -6
Step-by-step explanation:
1. Draw a picture, write and solve an equation to find Mary's weight, w, when she was 10 years old.
The Weight of Mary is 80. Students who are having trouble solving a problem can use the "draw a picture" method to create a visual representation of the issue.
"Draw a picture" method ?Students who are having trouble solving a problem can use the "draw a picture" method to create a visual representation of the issue.
the justifications.
Inquiry 1.
Formula: w = 10 8 pound
Answer: x = 80 lb
Inquiry 2:
Formula: d = 108 lb - 8 pound
d = 72 lb
Explanation:
First of all
When Mary was born, she weighed 8 pounds.
Statement 2: Mary weight 10 times as much when she was 10 years old.
w = 10 8 pounds, or 80 pounds.
Description of the illustration:
She was born weighing 8 pounds, which is represented by each cell. The 10 cells indicate that the number 8 lbs. has been repeated 10 times.
Next, the sum of the multiplication is shortened:
8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 10 × 8 = 80.
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Help please willing to give brainliest badge an points
The slope intercept form equation of the straight line is y = -1/2x + 6
Slope intercept form
Slope intercept form of the equation used to calculate the equation of a straight line by using the slope and intercept value.
And the general form of slope intercept equation is
y = mx + c
where
m refers the slope
c refers the y - intercept
Given,
Here we have the graph of straight line.
Through the given graph we have to identify the equation of slope intercept form.
In order to find the slope intercept form equation we need two values they are slope and the y intercept.
So, to find these two values, we need two points,
So we have selected the points from the given graph. They are (2,5) and (4,4).
Now we have to use the slope formula to find the value of the slope,
m = (4 - 5) / (4 - 2)
m = -1/2
Now, we have to use the slope and one of the point (4,4), to find the value of y intercept,
4 = -1/2 (4) + c
4 = -2 + c
c = 6
Now, we have identified the values of slope and the intercept.
Then the slope intercept form equation of these straight line is written as,
y = -1/2x + 6
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On a map of Texas, the cities of Midland, Lubbock, and Odessa form a triangle.
Midland is
20 miles from Odessa, and Lubbock is 113 miles from Midland. What is the farthest,
in miles,
Odessa could possibly be from Lubbock?
If Midland is 20 miles from Odessa, and Lubbock is 113 miles from Midland. Then 111.22 miles is Odessa from Lubbock.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
The cities of Midland, Lubbock, and Odessa form a triangle.
The distance between Midland and Odessa is 20 miles.
The distance between Lubock and Odessa is unknown, we need to find this.
This can be find by using Pythagorean theorem
Odessa from Lubbock=20²+x²
113²=20²+x²
12769=400+x²
12369=x²
x=111.22
Hence, 111.22 miles, Odessa could possibly be from Lubbock.
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Lightest weight
750g
0.7kg
7.5kg
705g
7.05kg
Answer:
.7 kg
Step-by-step explanation:
1. Convert answers in grams into kilograms
1000g = 1 kg
750g = .75kg
705g = .705 kg
2. Find smallest number of kg
= .7 kg
Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip to Country A and Country B. Country A's currency is trading at $1.30 per currency A, and Country B's currency is trading at $1.60 per currency B. She plans to spend more time in Country A, so she wants to have four times as much of currency A as currency B. Set up and solve a system of equations to model this problem, and explain what the answer means in practical terms.
If Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip .The currency needed is 200 euro and 500 pounds.
How to find the currency needed?Formulate an equation
1.30x + 1.60y = 3400
Hence,
x =4y Equation 1
1.30x + 1.60y = 3400 Equation 2
Substitute eq1 into eq2
1.30(4y) + 1.60y = 3400
5.2y +1.60y =3400
6.8y =3400
Divide both side by 6.8y
y =3400/6.8
y = 500
Number of euro
4y where y = 500
4(500)
=2000
Therefore the answer in practical terms is : 2000 euro of European currency and 500 pounds of Britain currency are needed.
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Complete a trend analysis for sales (round to nearest whole percent and use 2010 as the base year). 2013 2012 2011 2010 Sales $ 620,000 $ 580,000 $ 450,000 $ 600,000 (D) (C) (B) (A)
The completion of the trend analysis for sales with 2010 as the base year is as follows:
Trend Analysis of Sales:2013 2012 2011 2010
Sales $ 620,000 $ 580,000 $ 450,000 $ 600,000
Trend Analysis 103% 97% 75% 100%
What is trend analysis?Trend analysis is a technical analysis that uses historical data over some periods to predict and monitor future developments in a particular topic.
To undertake a trend analysis for sales, a base year is chosen and the sales account for the base year is set at 100% and used to check how sales have changed during the review periods.
The other years' results are compared to the base year's by dividing each year's result by the base year's.
Percentages are used to depict trend analysis so that the resulting increases and decreases can be easily compared to the base year.
Sales Trend Analysis:2013 (D) = 103% ($620,000/$600,000 x 100)
2012 (C) 97% ($580,000/$600,000 x 100)
2011 (B) 75% ($450,000/$600,000 x 100)
2010 (A) = 100% ($600,000/$600,000 x 100)
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What Is a factor?
Hi
A factor is a number that divides another number, leaving no remainder
Two photos are similar the ratio of the corresponding side length is 3:4 what is the ratio of their areas
The ratio of the areas of these two photos is equal to 9:16.
What is a ratio?In Mathematics, a ratio simply refers to a mathematical expression that is typically used for denoting the proportion of two (2) or more quantities with respect to one another and the total quantities.
This ultimately implies that, a ratio is generally expressed as a quotient of two numerical quantities or variables.
Generally speaking, the corresponding ratio of the areas of two geometric figures (shapes) is equal to the square of the ratio of their corresponding side length:
Area of photos = (a:b)²
Substituting the given parameters into the formula, we have;
Area of photos = (3:4)²
Area of photos = 9:16
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Find the solution set of 12x-31 + 1 = 6.
x = 1 or x=-1
x = 4 or x = -1
x = 5 orx = -2
x=4 or x = -4
1/3[6y+3]-24=3[1/3y-6]
y-3=y-7
x+2x=1/3x-8
y-9=y-2
x-5=6x-5
step by step explanation please
Answer:
Step 1: Simplify both sides of the equation.
1/3(6y+3)−24 = 3(1/3y−6)
1/3(6y) + 1/3(3) -24 = 3(1/3y) + 3(-6)
2y +1 −24 = y−18
2y −23 = y −18
Subtract y from both sides.
2y−23−y=y−18−y
y−23=−18
Step 3: Add 23 to both sides.
y−23+23 = −18+23
y = 5
Step-by-step explanation:
What is 1 5/9+2 7/9 in simplest form
Answer:
13/3
Step-by-step explanation:
3 [tex]\frac{12}{9}[/tex]
[tex]\frac{12}{9}[/tex]= 1 [tex]\frac{1}{3}[/tex]
3+1 1/3
4 [tex]\frac{1}{3}[/tex]
13/3
Answer:
Step-by-step explanation:
step one just add 5/9 +7/9 since they have the same denominator then that will equal 4/3
2nd step add the 1 and 2 together since they are both whole numbers. which equals 3
3rd step 4/3 + 3/1 which equals 13/3 maybe or if the answers wants a mixed number than the answer might be 4 1/3!
I'm not quite sure but try and see if its correct! :)
125 square foot to the nearest integer
SOMEONE HELP ME.
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. What are the dimensions of this rectangular room in the actual building.
The dimension of the rectangular room in the actual building are 55 feet by 30 feet.
How to find the dimension of the rectangular room in the actual building?Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building.
The dimensions of this rectangular room in the actual building can be found as follows:
let's find the length of the actual room
1 inches = 10 feet
3 inches = ?
cross multiply
length = 30 ft
Let's find the width of the room
1 inches = 10 feet
5.5 inches = ?
cross multiply
width = 55 ft
Therefore, the width and length of the room are 55 feet and 30 ft respectively.
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Evaluate the expression when m = -3.
2
m² -7m+6
Answer:
36
Step-by-step explanation:
substitute m = - 3 into the expression
m² - 7m + 6
= (- 3)² - 7(- 3) + 6
= 9 + 21 + 6
= 36