as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]2(x-2)^2=8(7+y)\hspace{5em}\stackrel{\textit{quick switcheroo}}{2(y-2)^2=8(7+x)} \\\\\\ (y-2)^2=\cfrac{8(7+x)}{2}\implies (y-2)^2=4(7+x)\implies (y-2)^2=28+4x \\\\\\ y-2=\pm\sqrt{28+4x}\implies \boxed{y=2\pm\sqrt{28+4x}}\qquad \impliedby f^{-1}(x)[/tex]
Why is it called revolution?
The term "revolution" is often used to refer to a dramatic and sudden change in a situation, especially number of a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another.
Revolution is a term used to refer to a dramatic and sudden change in a situation, especially a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another, thus making it a revolution.
The term "revolution" is often used to refer to a dramatic and sudden change in a situation, especially number of a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another.
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NEED HELP ASAP
PLEASE REFER TO PICTURE
what is k if 1 1/3k=1/3
Answer: k = 11
Step-by-step explanation:
[tex]\frac{11}{3k} = \frac{1}{3} \\\\[/tex]
Cross multiply:
[tex]11 * 3 = 1*3k[/tex]
[tex]33 = 3k[/tex]
[tex]k = 11[/tex]
Tamika is ordering a taxi from an online taxi service. The taxi charges $3. 50 just for the pickup and then an additional $0. 75 per mile driven. How much would a taxi ride cost if Tamika is riding for 5 miles? How much would a taxi ride cost that is m miles long?
Cost for 5 miles:
Cost for m miles:
If the pickup charge for taxi is $3.50 and additional charge of $0.75 per mile , then the cost for riding 5 miles is $7.25 and cost for riding m miles is $[tex]3.50+0.75m[/tex] .
The pickup charge that taxi service charges is = $3.50 ;
the additional charge for per miles driven is = $0.75 ;
we have to find the cost for riding 5 miles ;
So , the total cost for riding 5 miles is = [tex]Pickup Charge + (Additional Charge)\times(Number Of Miles Driven)[/tex] ;
substituting the values , the total cost equation becomes ;
[tex]Total Cost = 3.50 + 0.75\times5[/tex]
= [tex]3.50+3.75[/tex]
= 7.25
So , the cost for 5 miles is = $7.25 ;
to find cost for driving "m" miles ,we substitute the number of miles = m;
[tex]Total Cost = 3.50+0.75\times m[/tex]
= [tex]3.50+0.75m[/tex]
Therefore , the cost for riding m miles is $ [tex]3.50+0.75m[/tex] .
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What is the value of a if 2 is a zero of the polynomial 4x² 2x 5a?
The value of a is [tex]-\frac{12}{5}[/tex] if 2 is a zero of the polynomial [tex]$4 x^2-2 x+5 a$[/tex].
As per the given data, the polynomial is p(x) = [tex]$4 x^2-2 x+5 a$[/tex]
The polynomial is zero polynomial if x is 2
The places where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (0).
Replace x with 2 we get
Therefore [tex]4(2)^2-2(2)+5 \mathrm{a}=0[/tex]
[tex]\Rightarrow[/tex] 4 (4) - 2 (2)+5 (a) = 0
[tex]& \Rightarrow[/tex] 16 - 4 + 5 (a) = 0
[tex]& \Rightarrow[/tex] 12 + 5 (a) = 0
Add -12 on both sides we get
12 + 5 (a) - 12 = 0 - 12
5 (a) = -12
Divided by 5 into both sides we get
a = [tex]-\frac{12}{5}[/tex]
Therefore the value of a is [tex]-\frac{12}{5}[/tex]
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a company spent 762500 to make a movie that will be shown in theaters for 8 weeks. If the movie makes 1250000 in its first week how much money does the movie need to earn in the next 7 weeks to make profit of atleast 2,000,000
The movie need to earn $ 1,512,500 in the next 7 weeks.
What is Unitary Method?The unitary technique involves first determining the value of a single unit,
followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A company spent 762500 to make a movie.
The total movie will be earned
= 762500 + 2000000
= 2,762,500
First week the movie earned 1, 250,000.
So, in 7 weeks the movie needs to earned
= 2,762,500 - 1, 250,000
= 1,512,500
Hence, the movie earn 1,512,500 more.
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Shay and Nadine solve this problem in two different ways.
Mark has $25 in his bank account.
He makes $7 per hour babysitting.
How many hours must he babysit to have a total of $165 in his account?.
Use the drop-down menus to complete the sentences below.
Shay's
Assignment
25+7h-165
25-25 7h-165-25
7h-140
7h-140
7h 7h
A-20
Nadine's
Assignment
166-25-140
You need to make
$140 babysitting
140
-20
You need to babysit
for 20 hours
Please Help!
On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.
What is proportionality?When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
Here,
U/5 = 17/11
U = 17/11 X 5
U = 7.72
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Find the radius of convergence R of the series. [infinity] n bn (x − a)n, b > 0 n = 1
R= ____
Find the interval of convergence of the series.
The radius of convergence R = 1/b
The radius of convergence for a power series is given by the formula:
1/R = lim sup |bn|^(1/n)
In this case, the radius of convergence is given by:
1/R = lim sup |bn|^(1/n) = lim sup b^(1/n) = b^(1/n) as b > 0.
So R = 1/b
As for the interval of convergence, it is the set of values of x for which the series converges. The series converges when |x-a| < R, and diverges when |x-a| > R. So the interval of convergence is (a-R, a+R) which is (a-1/b, a+1/b)
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Write an equation for the parabola that passes through (-2,7), (1, 10), and (2,27)
An equation for the parabola is y=.
Answer: To find an equation for a parabola that passes through three specific points, we can use the method of algebraic manipulation.
Since the parabola is symmetric about the y-axis, the equation of the parabola will have the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Given three points (-2,7), (1, 10), and (2,27), we can use the vertex form of the equation and substitute the x, y values of the three points to find the values of a, h and k
y = a(x-h)^2 + k
Since it is passing through (-2,7), we can substitute the values of x and y in the equation and get
7 = a(-2 - h)^2 + k
It passing through (1, 10), we can substitute the values of x and y in the equation and get
10 = a(1 - h)^2 + k
It passing through (2,27), we can substitute the values of x and y in the equation and get
27 = a(2 - h)^2 + k
Now we have three equations with three variables, we can solve it using any of the techniques such as substitution, elimination or matrix. But the final equation will be in the form of y= a(x-h)^2 + k
Here, x= (-2, 1, 2) and y = (7, 10, 27) . Therefore it has a unique parabola passing through these points.
Step-by-step explanation:
What is the product of - 2 1/2 and - 3 1/3
What type of triangle is 70 70 40?
70-70-40 is an isosceles triangle.
The isosceles triangle has three acute angles, which means that the angles are less than 90°.The summation of three angles of an isosceles triangle is always 180°. In an isosceles triangle, if two sides are equal, then the angles opposite to the two sides correspond to each other and are also always equal.The two equal sides are defined as the legs and the third side is defined as the base of the triangle.The two angles opposite the legs are equal and are always acute, so the categorization of the triangle as acute, right, or obtuse depends only on the angles between its two legs.Read more about the isosceles triangle:
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The tables show the prices for ordering team jerseys from two different companies. You can use the information to write ratios showing the relationship between the cost and the corresponding number of jerseys. 1/5=5 25/5=5 50/10=5 75/15=5. 5/1=5 20/5=4 40/10=4 69/15=4. These ratios are all equivalent. These ratios are not all equivalent. This relationship is proportional. This relationship is not proportional. Explain how you can tell whether a group of ratios represents a proportional relationship.
Even though this relationship is proportional, not all of these ratios are equal.
What is the solution to the 3 to 5 ratio?Verify that the ratios provided are equal. The ratios of 3:5 and 15:25 are both equal. Because the first ratio 3: 5 can be derived by multiplying the ratio 15: 25 by 5 on both the numerator and denominator. The initial ratio of 3: 5 can be multiplied by 5 to get the ratio 15: 25, and vice versa.
What is an illustration of a 4:1 ratio?This indicates that you would require an 8 fl oz can (a quarter of a quart) of Part B if you were ordering a quart of Part A. You will have 1.25 after combining Parts A and B.
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On a coordinate plane, a line is drawn from point L to point M. Point L is at (negative 4, 8) and point M is at (4, 8).
The rule DO,0.25 (x, y) → (0.25x, 0.25y) is applied to the segment LM to make an image of segment L'M', not shown.
The coordinates of L' in the image are
.
The coordinates of M' in the image are
.
The length, L'M', is
.
The slope of the original segment and dilated segment are
.
Answer:
L' = (-1,2)
M' = (1,2)
L'M' = 2
The slope of the original segment and dilated segment are both zero
Step-by-step explanation: just did it on edge!
what is the total cost with sales tax? price 120.00 tax 5%
Answer:
5% of 120 is 6, so you would add that 6 to 120.
120 + 6 = 126.
The total cost will sales tax would be $126.00.
Step-by-step explanation:
Hope it helps! =D
F(x) = 3x -4 find each value of F(0)
Answer:
Step-by-step explanation:
Rewrite the function as an equation.
y
=
3
x
−
4
Use the slope-intercept form to find the slope and y-intercept.
Tap for fewer steps...
The slope-intercept form is
y
=
m
x
+
b
, where
m
is the slope and
b
is the y-intercept.
y
=
m
x
+
b
Find the values of
m
and
b
using the form
y
=
m
x
+
b
.
m
=
3
b
=
−
4
The slope of the line is the value of
m
, and the y-intercept is the value of
b
.
Slope:
3
y-intercept:
(
0
,
−
4
)
What is the difference between an undecidable problem and an intractable problem?
Therefore , the solution of the given problem of tractable problem comes out to be Undecidable troubles are those for which there will never be a computer solution.
What does a tractable problem actually mean?a technique that completes a manageable task in a polynomial period of time. Utilizing the polynomial upper bound is advantageous. A problem is said to be intractable if it cannot be solved in a polynomial amount of time. The bound has a minimum that is exponential.
Here,
Intractable problems would be those in which there is significant proof that, while they can be solved by a desktop, they cannot be solved quickly enough to be actually useful in practice.
Undecidable troubles are those for which there will never be a computer solution, whereas undecidable difficulties are those for which there will never be a computer solution.
Therefore , the solution of the given problem of tractable problem comes out to be Undecidable troubles are those for which there will never be a computer solution.
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f(n) = 2n-1 find the arithmetic sequence ?
An arithmetic sequence is a sequence of numbers in which the difference between any two successive members of the sequence is a constant value. The general form of an arithmetic sequence is:
a, a + d, a + 2d, a + 3d, ...
where "a" is the first term of the sequence, and "d" is the common difference between successive terms.
Given the function f(n) = 2n - 1, we can see that the function outputs a sequence of integers, with a common difference of 2. So f(n) is not an arithmetic sequence.
Arithmetic sequence is a list of numbers in which each number is the sum of the previous number and a constant number.
Example: 1,3,5,7,9 is an arithmetic sequence because the constant difference is 2.
If you have any other question feel free to ask.
The mean and median of the five Numbers are the same 4 6 x y 10
The value of x is 7 and value of y is 8
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given data set is {4, 6, x, y, 10}
The mean and the median are the same value.
The median is the middle value, which is x, and the mean is:
M = (4 + 6 + x + y + 10)/5
Then we have that:
(4 + 6 + x + y + 10)/5 = x
Now let's solve this:
(4 + 6 + x + y + 10) = 5x
20 + x + y = 5x
20 + y = 4x
And x and y are whole numbers. Then we can take x = 7 to get:
20 + y = 4*7
y = 28 - 20 = 8
Then we have x = 7 and y = 8.
Hence, the value of x is 7 and value of y is 8 in the data set 4 6 x y 10
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Which is greater, 1 2cup or 1 3cup? How much greater *fractions*
Answer:
Step-by-step explanation:
A half of a cup is greater than 1/3 of a cup. This is because if you convert the fractions to the nearest common denominator (6) you can see that 1/2 = 3/6 and 1/3 = 2/6, so 1/2 of a cup is greater.
I hoped this helped!!
(I NEED THIS RIGHT AWAY!) (PLS HELP) Lynette earns $5 by delivering newspapers. She saves $3 and she spends the rest. If she saved $27 one month, how much did she spend?
Answer:
$18
Step-by-step explanation:
To find how many times she has saved money, you would do 27/3=9. This means that she worked 9 times. Since she worked 9 times, she earned $45 in total. To find how much she saved you would do 45-27=$18
What is the slope of the line that passes through the points (-5, 8)(−5,8) and (-5, 4)(−5,4)?
The slope of the line that passes through the points (-5, 8)and (−5,4) is undefined.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
A line that passes through the points (-5, 8)and (−5,4).
If a line passes through two points (x₁ ,y₁) and (x₂, y₂),
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
m = (4-8) / (-5 + 5)
m = -4/0
The slope is undefined.
Therefore, the slope is undefined.
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Claire keeps track of the miles per gallon her car gets per week. She has accumulated the following data: (1, 22.42), (2, 22.84), (3, 23.26), (4, 23.68) What is the common difference or ratio
The common difference is 0.42. The comparison of each ratio's successive values over time for a single firm.
Now, According to the question:
What is meant by ratio?
When expressed in numbers or amounts, a ratio is a relationship between two things. For example, if a room contains ten boys and thirty girls, the boy-to-girl ratio is 1:3, or one to three.A ratio, or getting rationed, on the occurs when replies to a tweet vastly outnumber likes or retweets. This means that people are reacting negatively to the tweet's content.It usually means that your comment has received more replies than likes. This implies that there are more people who disagree with your comment than agree with it.Therefore, simplifying the equation then we get,
if you take the ranges (y) and subtract one from the other you get 0.42.
(22.84 - 22.42)/(2 - 1) = 0.42/1 = 0.42
(23.26 - 22.84)/(3 - 2) = 0.42
(23.68 - 23.26)/(4 - 3) = 0.42
Hence, The common difference is 0.42
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How do you graph the transformation of an absolute value function?
By translating, stretching and contracting, or reflecting, two functions from the same function family can become one another. Any function from a function family can be obtained by applying one or more transformations to a parent function.
By altering the graph of the parent absolute value function, many other absolute value functions can be created. The resulting absolute value functions take the following form:
[tex]y = |x-h| + k[/tex], where h and k are real numbers.
Absolute value functions can be created using the same kinds of operations that produce new linear functions. They also have a similar impact on absolute value functions. The transformations may, however, appear differently graphically due to some important discrepancies between linear functions and absolute value functions.
Here are some of the transformations:
Vertical Transformations
Translation up k units, k > 0; [tex]y = |x|+k[/tex]Translation down k units, k < 0; [tex]y = |x| + k[/tex]Horizontal Transformations
Translation to the right h units, h > 0; [tex]y = |x - h|[/tex]Translation to the left h units, h < 0; [tex]y = |x - h|[/tex]This is how we graph the transformation of an absolute value function.
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What number should be added to the polynomial 2x³ − 3x² − 8x so that the resulting polynomial leaves the remainder 12 when divided by 2x 1?
The number that should be added to the polynomial 2x³ - 3x² - 8x is 12x
When a polynomial is divided by a linear factor, the remainder is equal to the constant term of the polynomial multiplied by the reciprocal of the linear factor.
In this case, the polynomial is 2x³ - 3x² - 8x, and the linear factor is 2x-1.
To find the remainder when this polynomial is divided by 2x-1, we need to multiply the constant term of the polynomial, which is -8, by the reciprocal of 2x-1, which is 1/(2x-1).
So the remainder should be -8*(1/(2x-1)) = -8/(2x-1) = -4/(x-0.5)
To make the remainder 12, we will add 12x to the polynomial so that the new constant term is 12.
The polynomial 2x³ - 3x² - 8x + 12x will have a remainder of 12 when divided by 2x-1.
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Suppose that ƒ(−1)=10 and ƒ'(x)≥−3 for all values of x. What is the least possible value of ƒ(3)?
Using the mean value theorem, the least possible value of f(3) is - 2
What is the mean value theorem?The mean value theorem states that for a function f(x) on the interval (a, b), there exists a value c such that
f'(c) = f(b) - f(a)/(b - a)
How to find the least possible value for f(3)?Since ƒ(−1) = 10 and ƒ'(x) ≥−3 for all values of x, we require the least possible value of f(3).
Using the mean value theorem where
b = 3, a = -1 and f'(c) ≥ 3.We choose f'(c) = 3 since f'(x) = 3 is the minimum value of f'(x).
So, substituting the values of the variables into the equation, we have that
f'(c) = f(b) - f(a)/(b - a)
f'(x) = f(3) - f(-1)/(3 - (-1))
f'(x) = f(3) - f(-1)/(3 + 1)
f'(x) = f(3) - f(-1)/4
So, making f(3) subject of the formula, we have that
f(3) = f(-1) + 4f'(x)
Since
f'(x) = 3 and f(-1) = 10,Substituting the values of the variables into the equation, we have that
f(3) = f(-1) + 4f'(x)
f(3) = 10 + 4(-3)
f(3) = 10 - 12
f(3) = - 2
So, the least possible value is - 2
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In the figure, JKLM-EFGH. Complete the following table,
type your answer
Value of x
Value of y
Scale factor of JKLM to EFGH
type your answer.
type your answer
Value of z
type your answer.
The values of x , y and z are 80,2,110 respectively from the given figure where JKLM ~ EFGH
What is Quadrilateral ?
Quadrilateral can be defined as the type of the polygon in which it contains four sides.
Given ,
JKLM ~ EFGH
Since , JKLM ~ EFGH
3/30 = 11/z
z = 30*11/3
z =110
3 / 30 = 8/ x
3 * x = 8 * 30
x = 80
3 / 30 = y/ 20
y = 20 * 3 / 30
y = 2
Hence the values of x , y and z are 80,2,110 respectively.
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The null and alternative hypotheses divide all possibilities in to:
a. two sets that may or may not overlap .
b. as many sets as necessary to cover all possibilities c. two non-overlapping sets d. two sets that overlap reset selection
Answer:
Step-by-step explanation:
b
A line pae through the origin and through point A(−2, b í 14) and B(14 í b, 72). What i the greatet poible value of b?
The greatest poible value of b is (72-14)/(14-(-2))×(x+2)+14.
What is possible value?Possible value is the potential for something to have a particular outcome, result, or consequence. It is the amount of beneficial or desirable result that can be achieved, given the available resources. Possible value is often determined by assessing various factors such as cost, risk, and time. It is an important concept in economics, finance, and business, as it helps to identify the most beneficial course of action.
The greatest possible value of b is found by solving the equation of the line through A and B, which is y = (72-14)/(14-(-2))×(x+2)+14.
Setting the y-value to 0 and solving for x gives x = -14, which means b = 14. Therefore, the greatest possible value of b is 14.
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PLS HELP
using factorisation solve
E=(a+1)(a-1)-3(a+1)²
Answer:
Step-by-step explanation:
factoring
e =
(a+1)(a-1-3(a+1))
= (a+1)(a-1-3a-3)
= (a+1)(-2a-4)
= -2(a+1)(a+2)
Zasha spent $6 on packages of gum. How many more packages of gum that cost $1.20 each can she buy if she has a $20 bill?
Answer: Zasha spent $6 on packages of gum, which means that she bought 6 / $1.20 = 5 packages of gum.
If she has a $20 bill, she has $20 - $6 = $14 left to spend on gum.
Zasha can buy an additional 14 / $1.20 = 11.6666666666666666666666667 packages of gum with this money.
Rounded down, Zasha can buy an additional 11 packages of gum.
Therefore, Zasha can buy a total of 5 + 11 = 16 packages of gum.
Step-by-step explanation: