Answers
The inverse of the function f(x) = (4x - 1)/(-2x +2) is equal to f⁻¹(x) = (2x + 1)/(4 + 2x).
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of this function f(x) = (4x - 1)/(-2x +2), we would interchange both the input value (x) and output value (y) as follows:
y = (4x - 1)/(-2x +2)
x = (4y - 1)/(-2y +2)
Cross-multiplying, we have:
x(-2y +2) = 4y - 1
2x - 2xy = 4y - 1
Next, we would rearrange the function by collecting like terms as follows:
4y + 2xy = 2x + 1
y(4 + 2x) = 2x + 1
Dividing both sides of the function by (4 + 2x), we have:
y = (2x + 1)/(4 + 2x)
y = f⁻¹(x) = (2x + 1)/(4 + 2x)
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Related Questions
. You lean a 16 foot ladder against the wall. If the base is 4 feet from the wall, what angle does
the ladder make with the ground? Round your answer to the nearest tenth.
Answers
Check the picture below.
[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{16}}\implies cos(\theta )=\cfrac{1}{4}\implies \theta =cos^{-1}\left( \cfrac{1}{4} \right)\implies \theta \approx 75.5^o[/tex]
Make sure your calculator is in Degree mode.
I need help with this please help me
Answers
Answer:
Step-by-step explanation:
Hi, Danna, these are tough to figure out...
so, first check to see if the 3 known angles add up to 180°, they don't I checked, so, it tells us that the one angle 96° up at the top, does not include ∠2 , which is good, b/c we now know 2 of the angles in that inner triangle.. and we know that a triangle adds up to 180° , so just find that last angle... the one opposite to ∠1 .... nice, if we get the ∠1' angle we can then also figure out ∠1
180-96-30=54
∠1' =54°
so ∠1= 180-54 =126°
we now know ∠1
use that , and that the next smaller triangle also adds up to 180
to find ∠2
∠2= 180-28-126=26°
∠1=126°
∠2 = 26°
:) it's tough to think all of that through. don't worry. just keep working these , they will get easier.
A toaster oven usually sells for $60. If the toaster oven is 20% off, and sales tax is 7%, what is the total price of the toaster oven, including tax?
Answers
Work:
what expression is equivalent to 3x+3(x+y)
Answers
Answer:
6x + 3y
Step-by-step explanation:
Distribute:
=3x + (3)(x) + (3)(y)
=3x + 3x + 3y
Combine Like Terms:=3x + 3x +3y
=(3x + 3x) + (3y)
=6x + 3y
Answer:
I do not see the choices. There could be more than one right answer
6x + 3y
Step-by-step explanation:
3x + 3(x+y)
3x + 3x + 3y
6x + 3y
Find the area of the given figure
Answers
Answer:
you multiply the numbers to find the area so W*H with times hight so the answer would be 6,250
Select the correct answer. The equations y = 1 2 x + 1 and y = 2 x + 4 are graphed on the coordinate grid. A nonlinear function starting from the line (minus 2, 0), and (0, 2) another line intercepts the x and y-axis (minus 2, 0), and (0, 1) How many real solutions does the equation 2 x + 4 = 1 2 x + 1 have? A. 0 B. 1 C. 2 D. cannot be determined from the graph
Answers
These lines y = 12x + 1 and y = 2x + 4 intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.
What are the types of solutions in a system of equations?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Given are two equations y = 12x + 1 and y = 2x + 4.
Now by graphing we conclude that these lines intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.
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find 5 consecutive odd integers if the sum of the first 3 integers more than the sum of the last 2
Answers
The five consecutive odd integers are 11, 13, 15, 17 and 19.
What are odd integers?An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Odd numbers are whole numbers that cannot be divided exactly into pairs.
Therefore, odd integers are integers that cannot be divided exactly into pairs.
Hence, let's find five consecutive odd integers if the sum of the first three integer is 3 more than the sum of the last 2.
let
the first odd integer = x
x + x + 2 + x + 4 = x + 6 + x + 8 + 3
3x + 6 = 2x + 17
3x - 2x = 17 - 6
x = 11
Therefore, the consecutive odd integers are 11, 13, 15, 17 and 19.
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An applicant receives a job offer from two different companies. Offer A is a starting salary of $55,000 and 5% increase for 5 years. Offer B is a starting salary of
$56,000 and an increase of $2,000 per year.
Part A: Determine whether offer A can be represented by an arithmetic or geometric series and write the equation lor A, that represents the total salary received after
n years. Justity your reasoning mathematically. (3 points)
Part B: Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for B, that represents the total: salary received
after n years. Justity your reasoning mathematically. (3 points)
Part C: Which offer will provide a greater total income after years? Show all necessary math work. (4 points)
Answers
After 5 years, Offer A will offer a higher total salary.
What is arithmetic mean?The result of adding together and dividing by the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value.
What is geometric mean?The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.
Given
a) that a candidate receives job offers from two different companies, with Offer A offering a starting salary of $ 55,000 and a 5% increase for 5 years and Offer B offering a starting salary of $ 56,000 and an increase of $ 2,000 per year, it is necessary to perform the following calculation to determine which offer will result in a higher total income after 5 years:
b) Offer A -> Arithmetic
=>55000 x 1.05 ^ 5 = X
=>55000 x 1.2762 = X
70,195.48 = X
Offer B -> Geometric
=>56000 + (5 x 2000) = X
=>56000 + 10000 = X
66,000 = X
c) Hence comparing the above 2, Offer A will provide a greater total income after 5 years.
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A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days: f(d) = 11(1.01)°
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm.
What is a reasonable domain tc plot the growth function?
(4 points)
Part B: What does the y-intercept of the graph of the function f(c) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)
Answers
Answer:
Step-by-step explanation:
a.
f(d)=11(1.01^d
d=6.97 days
b.
t
f(c) represents the size of algae after c days
c.
f(2)=11(1.01)^2
f(7)=11(1.01)^7
[tex]rate=\frac{f(7)-f(2)}{7-2} \\=\frac{11(1.01)^7-11(1.01)^2}{5} \\=\frac{11[(1.01)^7-(1.01)^2]}{5} \\\approx 0.0104 ~mm[/tex]
About 65% of American teenagers wear orthodontal corrective devices..
In Heritage High School, there are about 1,800 teenagers. How many of them would you expect to have corrective devices?
Answers
Answer:
1170 teenagers would have corrective devices
Step-by-step explanation:
hope this helps :)
A package contains 12 electrical locks, each with a unique key. A package is delivered to 16 job site superintendents. How many unique keys will result from the distribution
Answers
Using the multiplication, 192 unique keys will result from the distribution.
In the given question we have to find the number of unique keys will result from the distribution.
As given that a package contains 12 electrical locks, each with a unique key. A package is delivered to 16 job site superintendents.
So 1 package have 12 electrical locks with a unique key.
Package delivered to 16 job site.
We can find the total number of unique keys y multiplying the total number of electrical locks with a unique key in a pckage to the total number of site of package delivery.
So total keys=12×16
Total keys=192
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1.Glenda wants to glue glitter over a piece of felt shaped like a parallelogram with a height of 52 in. and a base of 58 in.
If the glitter costs $1.10 per ft², how much will it cost to cover the felt?
2.The shape of a patio is trapezoidal with a height of 10 ft. and bases of 19 ft. and 13 ft.
What is the cost of outdoor carpeting to cover the patio if the carpeting costs $1.50 per ft².?
Answers
The cost of covering the felt with glitter is $3,317.60.
The cost of the outdoor carpeting to cover the patio is $240.
What are the costs?The first step is to determine the area of the parallelogram. A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length
Area = base x height
52 x 58 = 3,016 in²
Cost of covering the felt = cost of the glitter per feet are of the felt
$1.10 x 3,016 = $3,317.60
A trapezoid is a shape that has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Area of a trapezoid = 1/2 x (sum of the lengths of the parallel sides) x height
Area of a trapezoid = 1/2 x (19 + 13) x 10
Area of a trapezoid = 1/2 x 32 x 10 = 160 ft²
Cost of the outdoor carpeting =cost per square feet x area of the patio
$1.50 x 160 = $240
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A 40-foot rope is cut into 2 pieces. Seven less than four times the length of the longer rope piece x is five times the length of the shorter piece, which is (40 − x) ft. Find the length of the longer rope piece x (in ft). (Enter an exact number.)
Answers
If a 40-foot rope is cut into 2 pieces. the length of the longer rope piece x is 23ft.
How to find the length?Seven less than 4 times = 4x-7
4x-7=5(40-x)
4x-7=200-5x
Collect like terms
9x=207
Divide both side by 9x
x = 207 /9
x=23 ft (longer part of the rope)
Shorter part of the rope
40-x where x is 23
40 -23
= 17ft
Therefore the longer part is 23ft.
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Write an equation for a parabola with x-intercepts (-4,0) and (3,0) which passes through the point (2, -12).
Answers
Answer:
y = 2(x + 4)(x - 3)
Step-by-step explanation:
Knowing the x-intercepts, we can set up the equation:
y = (x + 4)(x - 3)
However, we are unaware of whether there is a dilation applied to it, so we input a point on the parabola. "a = dilation"
-12 = a(2 + 4)(2 - 3)
-12 = a(6)(-1)
-12 = -6a
2 = a
Now, we can write the equation for the parabola:
y = 2(x + 4)(x - 3)
Work out M and C for the line:
Y=2x+5
M= C=
Answers
In the given equation we get the following values:
M = 2
C = 5
Given, we have the equation:
Y = 2x + 5
we are asked to determine the following values of m and c.
The given equation is in the form of slope intercept form.
slope intercept form is given as:
y = mx+c
hence :
M = 2 and
C = 5
One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).
The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. This relationship will be the equation of a straight line:
the line must satisfy the coordinates of every point along it.Any location that is not on the line will not satisfyhence we get the required values.
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WHAT IS THE NAME OF THIS FORMULA????
Answers
Answer:
Estimation and Confidence Intervals
Step-by-step explanation:
Just found it on a math website basically.
Ed and Flo share money in
the ratio 3:5. Flo gets £40
more than Ed. How much
money was shared in total?
Answers
5x - 3x = 2x
2x = 40
x = 20
x * 8 = 160
Solve the equation by using the square root property. Express all radicals in simplest form.
k²=17
Answers
The simplest form of radicals is [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]
What is a radical expression?
An nth root of a number x is a number r that, when multiplied by n, equals x, where n is a positive integer, also known as the degree of the root. Degree 3 roots are referred to as cube roots, while degree 2 roots are known as square roots.
We have,
k² = 17
The variable in this non-linear equation needs to be separated. This is achieved by exponentiating both sides by the reciprocal of the exponent of the variable, which in our example is equal to 1/2.
[tex](k^{2} )^{\frac{1}{2} } = 17^{\frac{1}{2} }[/tex]
[tex](k^{2} )^{\frac{1}{2} } = -17^{\frac{1}{2} }[/tex]
[tex]k= 17^{\frac{1}{2} }[/tex]
[tex]k = -17^{\frac{1}{2} }[/tex]
Hence, the simplest form of radicals is [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]
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Which of the following expressions contains only 1 constant? Select TWO that apply.
A 18+5r³
B
C.
90(h - 4)
766
D. 41y-8y + 7y
Answers
The expressions which have only one constant are:
A. 18+5r³
B. 90(h-4)
Given: we have a set of equations.
an equation is a combination of variables and constants.
In the given set of equations we have a single variable with a single constant.
those are:
→ 18+5r³
→ 90(h-4)
In the other equations we don't have constants.
A constant is defined as an object whose value is fixed regardless of changes in its usage.
Even after the expression is changed, these values stay the same.
Natural numbers, whole numbers, real numbers, integers, and decimal numbers are examples of constants in mathematics.
A variable is a thing whose value changes depending on how it's used and isn't fixed.
Hence we get the required answer.
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HW1.
The vertices of a triangle ABC are A(2, 1), B(-2, 3) and C(4, 5). Find the equation of the median through the
vertex A
A
Assume D be the midpoint of BC
Answers
Answer:
y = -3x +7
Step-by-step explanation:
You want the equation of the median line through point A, given that the vertices of the triangle are A(2, 1), B(-2, 3) and C(4, 5).
Midpoint of BCThe median will go through the midpoint of the segment opposite vertex A. That midpoint is ...
D = (B +C)/2
D = ((-2, 3) +(4, 5))/2 = (-2+4, 3+5)/2 = (2, 8)/2 = (1, 4)
SlopeThe slope of the line is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
Then the slope of AD is ...
m = (4 -1)/(1 -2) = 3/-1 = -3
Point-slope equationThe point-slope equation of the line with slope m through point (h, k) is ...
y -k = m(x -h)
The equation of the line with slope -3 through point A(2, 1) is ...
y -1 = -3(x -2) . . . . . equation of the median line
This can be simplified to slope-intercept form:
y = -3x +6 +1 . . . . . eliminate parentheses, add 1
y = -3x +7 . . . . . slope-intercept equation of the median line
Logic
Consider the following statements:
Alex's bag is heavier than Hisham's bag
Hisham's bag is lighter than both Aya's bag
and Irene's bag
Aya's bag is heavier than Alex's bag and
Irene's bag
Whose bag is the heaviest?
Aya
Answers
In given order puzzle Aya's bag is the heaviest bag .
What is order puzzle?
A puzzle is a thing that is difficult to understand or explain. The term also refers to a game, toy, or problem designed to test ingenuity or knowledge. Math puzzles are problems that require mathematical logic and calculation. These types of puzzles carry recreational as well as educational value for the pupils.
Here the given statements ,
=> Alex bag > Hisham bag
And Hisham bag < Aya bag and Irene bag
Now ,
=> Aya bag > Alex bag and Irene bag
Then combine the given ,
=> Aya bag> Alex bag>Irene bag>Hisham bag.
Therefore Aya's bag is the heaviest bag.
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Two students share 8 markers equally enter the numerical expressions in he box that models the situation
Answers
Answer: 8÷2 or 8/2 and also just in case, the answer is 4
Step-by-step explanation: Ok, 8 markers split equally between 2 students, this means that for each marker that student one takes, student two also takes one. they repeat this until there are no more markers left. This ends up with the two students each having four markers. Now, what is 8 divided by 2? Why yes, the answer is 4, just like the word problems answer. So the word problem "Two students share 8 markers equally" translates to 8÷2.
Hope this helps!
Which statement about the ordered pairs (-9, 3) and (2, 4) is true for the equation 6x = 14?
(-9, 3) is a solution to the equation. O Both ordered pairs are solutions.
O Neither ordered pair is a solution.
(2, 4) is a solution to the equation.
Answers
The correct statement will be "Neither ordered pair is a solution".
What are ordered pairs?
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.In order to understand a point visually, it can be helpful to position it on the Cartesian plane.An ordered pair's numerical values may be fractions or integers.Ordered Pair is equal to (x,y), where x is the distance between a point and the principal axis (x).Additionally, y = ordinate measures how far a point is from the secondary axis "y."Given equation is: 6x = 14
For ordered pair (-9, 3) , the values of x=-9 and y=3
Plugging these values into the given equation
6(-9) = 14
-54 = 14 (False)
Now for ordered pair (2, -4) , the values of x=2 and y=-4
Plugging these values into the given equation
6(2) = 14
12 = 14 (False)
The correct statement will be "Neither ordered pair is a solution".
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Can someone please look in the photo and explain? Thanks so much I appreciate the help.
Answers
Answer:
25.12
Step-by-step explanation:
C = [tex]\pi[/tex]d The d is the diameter. This is the distance across the ha that goes through the middle of the circle.
C 3.14(8) The c stands for the circumference or the distance around the circle. We generally use 3.14 for [tex]\pi[/tex]
C= 25.12
25.12
Explanation:
To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). In this case, 8 multiplied by pi would give you around 25.12. Hope this helps!
Select the true statement about the following linear equation.
y= -2x + 4
The graph is a curve
The y-intercept is -2
The slope is -2
The slope is 2
Answers
The general form of a linear equation is slope m and y-intercept c is given as y = mx + c thus the slope of the line y = -2x + 4 is -2 so option (C) is correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given line,
y = -2x + 4
The general form of a linear equation is the slope(m) and y-intercept (c) is given as
y = mx + c
Compare,
m = -2 and c = 4
Slope = -2 and y-intercept = 4
Hence "The slope of the line y = -2x + 4 is -2 and y-intercept is 4".
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solve 5x+y=24x+y=4 use the linear combination method
Answers
Answer:
(x,y)=(0,4)
Step-by-step explanation:
write as systems as equations, multiply both sides of the equation by -1, sum the equations vertically to eliminate at least one variable, divide both sides of the equation by -19, substitute the given value of x into the equation 5x+y=4, The possible solution of the system is the ordered pairs (x,y) =(0,4), then you're done. whew. ;)
Tom rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a facto
r of 21.
Answers
The probability of getting a total that is a factor of 21 is 2/9
Tom rolls 2 fair dice and adds the results from each
Total number of outcomes = 6 × 6
= 36
The probability = Number of favorable outcomes / Total number of outcomes
The factors of 21 = 1, 3, 7, 21
The possible outcomes = {(1,2), (2,1), (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
Number of possible outcomes = 8
The probability = Number of favorable outcomes / Total number of outcomes
Substitute the values in the equation
= 8 / 36
= 2/9
Hence, the probability of getting a total that is a factor of 21 is 2/9
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Simplify: (A + C)(AD + AD) + AC + C
Answers
Answer:
It looks just fine! Well done!
It looks just fine! Well done!A bit more simply,
It looks just fine! Well done!A bit more simply,(A+C)(AD+AD)+AC+C=(A+C)AD+AC+C=AAD+CAD+AC+C=AD+(AD+A+1)C=AD+C
Step-by-step explanation:
Hope this helped
Write an slope equation form of the equation of the line through the given points
through: (0, -3) and (-5, 4)
Answers
The slope equation form is :
m = - 7/5
Slope Solution
To calculate the slope use the slope formula.
m = (y2- y1)/(x2- x1)
Where (x1,y1) and (x2,y2) are 2 coordinate points.
Here the 2 points are (0,-3) and (-5,4)
let (x1,y1) = (0,-3) and (x2,y2) = (-5,4)
m = (4 - (-3))/((-5) - 0)
m = 7/((-5) )
m = - 7/5
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Find the distance between the point (6,7) and the line y = 6x + 7 (rounded to the nearest hundreth).
A) 2.42
B) 5.92
C) 5.84
D) 1.38
Answers
Answer:
5.92
Step-by-step explanation:
Line in standard form
-6x + y - 7 = 0
distance = |-6 * 6 + 1 * 7 - 7|/([tex]\sqrt{(-6^2)+ 1^2)}[/tex]
|-36 +7 - 7| = √37
|-36|/√37
36/√37
5.918363 = 5.92
B is the answer.