The inverse function is written as [tex]f^{-1}(x)[/tex] =x³+15x²+75x+125 and the inverse is a function.
The inverse of a function is defined as the opposite function . Ideally we use a function to map the dependent variable y based on the independent variable x. Inverse function is the relation which defines the value of x depending on a particular value of y.
For an inverse function the domain of the function changes to the range and vice-versa.
Mathematically for a function defined as y=g(x) where g(x) is a polynomial of x . We solve the equation for x in terms of y.
Given function is g(x)=∛x-5
Therefore it can be written as
y= ∛x-5
or, y+5=∛x
Cubing both sides we get:
(y+5)³=(∛x)³
or, y³+15y²+75y+125=x
or, x=y³+15y²+75y+125
So the inverse function can be written as:
[tex]f^{-1}(x)[/tex]=x³+15x²+75x+125 and the inverse function exists.
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Classify each number as rational or irrational:
Help asap
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\textsf{\textbf{Rational} and \textbf{Irrational} numbers}[/tex]
[tex].\qquad\bullet\textsf{\textbf{Rational} numbers can be written in fraction form, p/q.}\\.\qquad\bullet\textsf{\textbf{Rationals} can be \textbf{terminating} fractions.}[/tex]
[tex]\therefore[/tex]
[tex].\qquad\bullet\textsf{\textbf{Irrational} numbers \textbf{cannot} be written \textbf{as fractions.}}[/tex]
[tex]\textsf{These are the \textbf{rationals:}}[/tex]
[tex]\boldsymbol{\dfrac{11}{3}}[/tex]
[tex]\boldsymbol{0.01045}[/tex]
[tex]\boldsymbol{\sqrt{\dfrac{16}{81}} }[/tex]
[tex]\boldsymbol{6.25}[/tex]
[tex]\boldsymbol{0.\overline{42}\Leftarrow it's\:a\:terminating\:fraction}[/tex]
[tex]\textsf{These are the \textbf{irrationals:}}[/tex]
[tex]\boldsymbol{\sqrt{48}}[/tex]
[tex]\boldsymbol{16\pi}[/tex]
[tex]\boldsymbol{\sqrt{\dfrac{3}{16}} }[/tex]
[tex]\textsf{We come to the conclusion that there are more rationals than irrationals. \ddot\smile}[/tex] [tex]\ddot\smile[/tex]
[tex]\Large\overbrace{\underbrace{\boldsymbol{\rm{Reflection\:-RoSe}}}}^\star_\star[/tex]
Germaine is saving money to buy a $367 mountain bike. He plans to save $45 every week from his paycheck until he has enough money. So far, he has saved $62. How many weeks will it take Germaine to get the mountain bike?
It will take Germaine to get the mountain bike 6.77 weeks (approximately)
let X represent the number of weeks it will take to save enough money
Money to buy a mountain bike = $367
He planned to save money every week from his paycheck = $45
So far, He had saved money already to buy bike = $62
now the required amount to buy a mountain bike is
$367-$62 = $305
Number of weeks Germaine will take to get the mountain bike is
X = 305/45
X = 6.77 weeks (approx)
It will take Germaine to get the mountain bike 6.77 weeks (approximately).
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All of the students at Mountain Ridge Middle School take a foreign language. of the students take Spanish. of the students take French. The remaining students take Chinese. What fraction of the students take Chinese?
Based on the fraction of students who take Spanish, and French and Mountain Ridge Middle School, the fraction of students who take Chinese are 3/40
How to find out the fraction?To find the fraction of students who take Chinese, subtract the fraction of students who take Spanish and French from 1.
The number of students who take Chinese is therefore:
= 1 - 5/8 - 3/10
= 1 - 25/40 - 12 /40
= 3/40
The full question is:
All of the students at Mountain Ridge Middle School take a foreign language. 5/8 of the students take Spanish. 3/10 of the students take French. The remaining students take Chinese. What fraction of the students take Chinese?
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URGENT!!Given the function f(x) = 4x − 1 and the linear function g(x), which function has a greater slope? linear function increasing through 2 comma 3 and 3 comma 7 f(x) has a greater slope. g(x) has a greater slope. The slopes of f(x) and g(x) are the same. The slope of g(x) is undefined. WILL MARK BRAINLIEST!
The slopes of the linear function f(x) = 4x-1 is 4 and of the given linear function g(x) has also slope 4 . The option that the slopes of f(x) and g(x) are same is correct.
What is slope of a linear function?The slope of a linear function is the measure of steepness of the line traced by given linear function.
If a linear function is given by line y = mx +c then the slope is m
If a linear function passes through two given points (x₁, y₁) and (x₂, y₂), then its slope is (y₂ - y₁)/(x₂ - x₁)
Given the function f(x) = 4x -1 then comparing it to the form f(x) = mx + c
Slope of f(x) = m = 4
If it is given that g(x) is increasing through (2,3) and (3,7)
Then the slope of g(x) = (7- 3)/(3-2) = 4/1 = 4
Therefore, Slopes of both f(x) ang g(x) is 4.
Thus, the slopes of f(x) and g(x) are the same.
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Answer:
The answer is they are the same. Just took the test Your welcome!
Step-by-step explanation:
Solve the equation
9x²29x28 = 0
Give your answers to 2 decimal places when appropriate.
Answer:
9x²29x28 = 0
The answer is 211932=0
9x2 - 29x - 28 = 0
The answer is 29x=−10
Step-by-step explanation:
3ax + 2b/c = 4d
Solve for x
The point J(4, – 4) is reflected over the y-axis. What are the coordinates of the resulting point, J'?
The coordinate of the resulting point J' is (-4, -4).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the Coordinates.
The point is given as;
⇒ J (4, -4)
Now, The rule of the reflection of a point across the y-axis is equal to
(x, y) ⇒ (-x, y)
Hence, The coordinate of the resulting point J' after reflection over the y - axis of point J (4, -4) is,
(4, -4) ⇒ (-4, -4)
Hence, The coordinate of the resulting point J' is (-4, -4).
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Greta wrote a total of 8 pages over 2 hours. After spending 3 hours writing this week, how many pages
will Greta have written in total?
The number of 12 pages written by Great in 3 hours.
What exactly is the unitary method?The unitary method is used to determine the value from one unit provided a multiple.Furthermore, once the value of a single unit has been determined, we can multiply a certain number by the number of units required. This methodology is normally used to demonstrate ratio and proportion concepts.For the given question;
Time take by Greta to write total of 8 pages is 2 hours.
Use unitary method for solving;
2 hours --------> 8 pages.
Divide both side by 2.
1 hour -------> 4 pages.
Now, fore finding the number of pages written in 3 hours.
Multiply each side by 3.
3 hours ---------> 12 pages.
Thus, the number of pages written by Great in 3 hours are 12 pages.
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Simplify each expression.
ln e⁴/8
We will get Ine⁴/8 after simplifying the given expression ln · e⁴/8.
What exactly is an expression?An expression in mathematics is a sentence that contains at least two numbers or variables and at least one mathematical operation.Math operations include addition, subtraction, multiplication, and division.The structure of an expression is as follows: An expression is (Number/variable, Math Operator, Number/variable).So,
Given: ln · e⁴/8
Then,
ln · e⁴/8Ine⁴/8Therefore, we will get Ine⁴/8 after simplifying the given expression ln · e⁴/8.
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The difference of two numbers is 29. The largest number is 3 more than twice the smallest number. What are the two numbers?
Group of answer choices
26 and 55
25 and 54
27 and 56
28 and 57
Answer:
x-x=29 answer is equal to 28and
What happens to the value of the expression 5/x+5 as x decreases
What happens to the value of this expression 5/x + 5 as x decreases from a large positive number to a small positive number is that: A. It increases.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
What is quotient?Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number. As a general rule, the smaller the divisor (denominator) of an expression, the larger would be the quotient.
Evaluating the given expression, we have:
When x = 3;
5/3 + 5 = 6.7
When x = 2;
5/2 + 5 = 7.5.
When x = 3;
5/1 + 5 = 10.
In conclusion, as x decreases from a large positive number to a small positive number in this expression 5/x + 5, its value would increase.
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Complete Question:
What happens to the value of the expression 5/x + 5 as x decreases from a large positive number to a small positive number? Choose 1 answer:
A. It increases.
B. It decreases.
C. It stays the same.
Simplify. 4√162 +3 4√32
The question focuses on indices. Start by factorization of 162 and 32. Simplifying 32 yields 2^5 and 162 gives 3^4×2. Simplify the two expressions using the factors. Use the indices rule implying: b√a^c =a^(c⁄b)
∜162+3∜32
162= 81×2=3^4 ×2
32 = 2^5 = 2^4 ×2
∜(2×3^4 )+3∜(2^4×2)=∜(3^4 ) ∜2+3∜2^4 ∜2
3^(4⁄4)× ∜2+3×2^(4⁄4)×∜2 = 3×∜2+3×2∜2
3∜2+6∜2 = ∜2×(3+6) = 9∜2
= 9∜2
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i need help
simplify: 4^8/4^-4
Answer:
[tex]4^{12}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]\frac{4^{8} }{4^{-4} }[/tex] = [tex]4^{(8-(-4))}[/tex] = [tex]4^{(8+4)}[/tex] = [tex]4^{12}[/tex]
What is the slope of the line through (-1,8)(−1,8)left parenthesis, minus, 1, comma, 8, right parenthesis and (3,-4)(3,−4)left parenthesis, 3, comma, minus, 4, right parenthesis?
Choose 1 answer:
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{-12}{3 +1}\implies \cfrac{-12}{4}\implies -3[/tex]
1. I look like this _ _ _ _ . _
2. all of my digits are odd.
3. my thousands digit is equal to the sum of my tens, ones, and tenths digit.
4. my tenths and ones digits are equal
5. the product of my tenths and ones is more than my tens digit
6. my hundreds digit is larger than my thousands digit
Answer:
I think the answer could be 7913.3
Step-by-step explanation:
Using clue number 2 we know that all the numbers in this are odd so that mean the only numbers that can be there are 1,3,5,7 and 9 Using clues 3 and 4 there are a few combinations some of which can be 1 + 1 + 3 = 5 , 1 + 1 + 7 = 9, 1 + 1 + 5 = 7, and 3 + 3 + 1 = 7 With clue 5 in being mentioned the dights in the ones place can't be 1 and 1 because it would equal one and any other dight besides it would be greater then that so I went with 3 and 3 as the tenths and ones dights since 3 × 3 = 9 and 1 being in the tenths place is less then 1The only other clue is clue 6 which means that the hundreds dights has to be a odd number greater than 7 and 9 is the only option that's greater than 7. The number is 7,913.3What is Point slope Form of
(2, 9); m= -2
Point-slope: y - 9= -2(x - 2)
Slope-intercept form (Just in case you need it): y = -2x + 13
Use the Venn diagram shown to list the set An C in roster form.
U
5
A 3
1
6
9
13
2
11
8
7
4
10
14
12
B
O A. (2, 3, 4, 6, 8, 9, 10, 11, 12, 13}
OB. {11}
O C. {4, 11, 12}
O D. (11, 13)
Answer:
Not Available
Step-by-step explanation:
Use the Venn diagram shown to list the set An C in roster form.
U
5
A 3
1
6
9
13
2
11
8
7
4
10
14
12
B
O A. (2, 3, 4, 6, 8, 9, 10, 11, 12, 13}
(8 + 3²) x 3 quick asking 4 a friend
Stefan and Kendrick both walk to work each day. It takes them the same amount of time, even though Stefan lives farther away. One morning, they decide to meet at a coffee shop. The coffee shop is the same distance from each of their apartments. Who will likely get to the coffee shop in less time?
Answer:
Stefan
Step-by-step explanation:
Stefan
is the expression (17)/(2)g-(9)/(2)h the same as (9)/(2)h-(17)/(2)g ? Explain.
The fraction expression (17)/(2)g - (9)/(2)h is not the same as (9)/(2)h-(17)/(2)g.
How to subtract fractions?
We are given the fraction expression;
(17/2)g - (9/2)h
Now, the fraction (17/2) is greater than (9/2) and as such the result of the subtraction of the fractions will be positive.
Now, if we change the order of the subtraction to be;
(9/2)h - (17/2)g
This means that the result will now be negative since (9/2) is less than (17/2).
Thus, we can conclude that the expression (17)/(2)g - (9)/(2)h is not the same as (9)/(2)h-(17)/(2)g.
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mai bought some party supplies from an online store.the shop charges a 7.95 shipping fee or 6.25%of the total purchase.whichever is greater.suppose Mai's total purchase is 128.how much shipping will she pay?
The required amount of shipping paid by Mai is 8.
What is percent?In mathematics, a percent is a number or ratio expressed as a fraction of 100. It is often denoted using percentage sign "%".
Now it is given that,
Amount of shipping fee = 7.95
percentage of shipping fee = 6.25% of the total purchase
Total amount purchased = 128
Thus, amount of shipping for this purchase is given as,
Amount of shipping = 6.25% of 128
Solving,
Amount of shipping = 0.0625*128 = 8
Since the shop charges shipping fees of whichever is greater
and 7.95 < 8
Thus, amount of shipping paid by Mai = 8
Thus, the required amount of shipping paid by Mai is 8.
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DF
bisects LEDG. Find the value of x. The diagram is not to scale.
Answer:
x = 6
Step-by-step explanation:
Since ray DF bisects angle EDG, angles EDF and GDF are congruent. By reflexive property of congruence, ray DF is congruent to ray DF. Since all right angles are congruent, angles FED and FGD are congruent. By AAS, triangles FED and FGD are congruent. Since corresponding parts of congruent triangles are congruent, segments EF and GF are congruent, so 8x + 42 = 15x
7x = 42
x = 6
Solve each equation. log₇(2 x-3)²=2
The solution of the given logarithmic equation is 16.189.
What are the various properties of the logarithm?
Out of several properties of logarithms, some of the main properties are given below:
Product Rule
log (ab) = log a + log b
Change of base
log ₇ x = log x / log 7
Power Rule
log a² = 2 log a
Quotient Rule
log (a / b) = log a - log b
Solving the given equation log₇(2x - 3)² = 2
We are given a logarithmic expression: log₇(2x - 3)² = 2
Using properties of the logarithm, we have
log (2x - 3)² / log 7 = 2
log (2x - 3)² = 2 × log 7
2 log (2x - 3) = 1.6901
log (2x - 3) = 3.3802
Using exponential on both sides,
e^[log (2x - 3)] = e^(3.3802)
2x - 3 = 29.3766
2x = 32.3766
x = 16.189
Hence, the solution of the given equation is 16.189.
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The question is in the picture attached below. Pls answer, will give 50 points.
The required factorized expression is given as 3x²y + 12xy² + 3xy = 3xy(x + 4y + 3).
An incomplete equation is given we have to determine the missing terms.
The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.
Here,
The given equation,
_x²y +_y² + 9_ = 3x_(_+ 4y + _).
So, factorized expression is given as 3x²y + 12xy² + 3xy = 3xy(x + 4y + 3).
Thus, yhe required factorized expression is given as 3x²y + 12xy² + 3xy = 3xy(x + 4y + 3).
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/A and /B are vertical angles. If mA = (4x − 4)° and m/B = (5x – 29)°,
-
then find the measure of /A.
the measure of angle A is 96° when A and B are vertical angles.
We are given the two vertical angles as:
A = (4x − 4)° and B = (5x – 29)°
We know that, vertical angles are equal to each other.
So, we get that:
4 x - 4 = 5 x - 29
5 x - 4 x = 29 - 4
x = 25
A = 4 x - 4
A = 4 ( 25 ) - 4
A = 100 - 4
A = 96°
Therefore, the measure of angle A is 96° when A and B are vertical angles.
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Etsuko practices origami. The square papers she used have a side length of either 7.5 cm or 25.4 cm. Etsuko says the length of the larger paper is 32.9 cm greater than the length of the smaller paper
To find how many centimeters greater the length of the larger paper is than the length of the smaller paper, the lesser number of centimeters needs to be subtracted from the greater number of centimeters which gives the result that is 17.9cm. Etsuko is incorrect because 25.4 is greater than 7.5cm.
How much greater is the side length of the paper?The mathematical operation that would be used to determine how much greater the larger paper is compared to the smaller paper is subtraction. Subtraction is the process used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.
To subtract the numbers, the length of the longer paper would be subtracted from the shorter paper.
Difference in the length of the papers = 25.4 - 7.5 = 17.9cm
Etsuko is wrong because instead of subtracting the lengths, she added the lengths. Addition is used to determine the sum of two or more numbers.
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Answer:
It's easy,
To find how many centimeters greater the length of the larger paper is than the length of the smaller paper, the lesser number of centimeters needs to be subtracted from the greater number of centimeters, which gives a result that is between 7.5 and 25.4. Etsuko is not correct because 25.4 cm is 17.9 cm more than 7.5 cm.
Step-by-step explanation:
*Wish you luck on the test*
A chemist is heating water so it can dissolve a larger amount of sodium chloride. The water's temperature increases 7°C each minute from an initial temperature of 21°C. How long will it take for the water to reach 49°C?
If water's temperature increases 7°C each minute from an initial temperature of 21°C. Then the time taken by the water to reach 49 degree Celsius is 4 minutes.
What is temperature?Temperature defines the atmosphere hotness. And it is expressed in different scales as well as in different parameters like Celsius etc. It is measured through the device known as thermometer.
According to the question, larger amount of sodium chloride is dissolved in the heating water. And the given data states that the water temperature increases 7 degree Celsius every minute.
Initial temperature of water is 21 degree Celsius.
Let us assume, water reaches at 49° C after 'x' minutes.
As per question, every minute temperature increases as 7°C. So, the expression can be written as: (21 + 7x)°C
⇒ 21 + 7x = 49
⇒x = 4 minutes
Hence, the time taken to reach 49° C is 4 minutes.
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The depth of a local river averages 16 ft, which is represented as |−16|. In January, it measured 4 ft deep, or |−4|, and in July, it was 18 ft, or |−18|. What is the difference between depths in January and July?
22 feet
14 feet
10 feet
2 feet
Answer:14 ft
Step-by-step explanation:hope it helps, brainliest? i could really use it
At the gym, Hillary swims every 5 days and runs every 7 days. If she did both activities today, in how many days will she do both activities again on the same day?
Answer:
She will actually do it on the 35th day of gym
choose all the values that are equivalent to -(5/3)
1. -5/3 2. 5/-3 3. 5/3 4. -5/-3 5. - (-5/3)
Fractions represent the parts of a whole or collection of objects. the equivalent fractions to -(5/3) are -5/3, 5/-3.
What is Fraction?Fractions represent the parts of a whole or collection of objects.
-(5/3) is a fraction, Actually it a improper fraction with negative sign.
The equivalent fractions are obtained by multiplying same sign or same number in numerator and denominator.
-(5/3) is equivalent to -5/3
-(5/3) is equivalent to 5/-3
-(5/3) is not equivalent to 5/-3
-(5/3) is not equivalent to -5/-3 because when negative and negative are multiplied the result will be positive but to be equivalent fraction it should be negative.
-(5/3) is not equivalent to -(-5/3) because when negative and negative are multiplied the result will be positive but to be equivalent fraction it should be negative.
Therefore the equivalent fractions to -(5/3) are -5/3, 5/-3.
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